TECHNICAL INTELLIGENCE TRANSLATION - AEROFOTOTOPOGRAFIYA
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Document Creation Date:
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Document Release Date:
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Sequence Number:
7
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Publication Date:
April 8, 1957
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MISC
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(` 3
(Title Unelassiticd)
:~^PH0PO POG&:PHY
(orotototopogratiya)
by
M. D. Konshin
C.
Source: Izdatcltstvo
Goodczichcskoy i
Kartograticheskoy
Litoratury
MOSCOW 1952
Chapters V .. VIII
Pages 109-.260
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CHAPTER V
DEVELOPING THE MAP CONTOURS
36. Use of Aerial Photographs for Plan Plotting
-: In aerophotosurveying, all features of the ground relief are recorded on the
i
(photograph. In order to make a map from this photograph, it is first necessary to
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2' interpret the print and identify the contours and then to transpose these contours
F
nto a asp. This chapter will deal with the various methods of transposing the re-
'. (lief features from a photographic print to a map.
i If the photograph was taken at a strictly horizontal position and had no tilt,
the image, in case of flat terrain, will resemble the actual map plan but at a cer-
i
Rain scale and at arbitrary orientation. The aerial photograph is of much greater
I
Evalue than prints made by geodetic surveys since it captures much more relief detail
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which, in turn, makes it easier to correctly orient the contours and furnishes val-
Liable data for many branches of the national economy (land management, hydrotechnol-
!, ogy, planning of communication lines, geology, etc.). The relative position of con-
!tours is also much more accurately recorded on an aerial photograph.
p J If the aerial photograph was taken at a tilt, its image cannot be used directly
to make a map. The distortion of the photograph (i.e., deviation from its plan), as
shown by eq.(10), increases from the center toward the edges. In cases of small an-
. ~gles of tilt, the central section of the print may be considered as undistorted.
? 1For example, if a < 0.5?, fk = ?0 ma, and r = 65 mm, the maximum distortion at the
hedges of the central section will not exceed ba = 0. 5 ai^.
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However, if the angle of tilt during exposure is t3? or even 5?, the resultant
distortion will not interfere too ouch with using these photographs for ?ap oaking.
The distortion can be easily corrected by the transformation process which is a means
of projecting the print onto a tilted surface, coapensating for the original tilt
from the horizontal. During the transformation process the image is also adjusted to
the desired scale, which is either enlarged or diminished compared to the original.
A more serious drawback is the displacement of points on a print, caused by the
nature of the relief. If the magnitude of these displacements does not exceed the
;specified accuracy limits of the map, which is coon in areas of flat contours,
ithen these prints are used directly for map making. If, however, relief distortion
exceeds specified limits, then a special process of transforoation is employed
i(transformation by sections) or the map is prepared by stereophotogrammetric mapping
;'
haethods.
2- I
I This means that aerial photographs, irrespective of their position in space
;. i
(angle of tilt) can be used to determine the contours of a map without field survey-
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).ng of the relief. Field surveys are uses only to obtain supplementary information
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;o establish details not captured by the aerial photographs.
I however, the photograph gives the contours of the terrain but does not orient
*hew with respect to the coordinate system of the area (map), and appears at a
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Slightly different scale. It is therefore mandatory, even in the case of strictly
(vertical photographs, to have two control points (whose locations on the map are
~Cnown). These are required for establishing the proper scale ratio between map and
photograph and to orient the photograph with the coordinates of the map. However,
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photographs with tilt are used in the processing, which must be transformed. To
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transform the photograph, at least four control points of the photo must be avail-
, ~
fable on the map. Some of these control points are determined by geodetic means and
art by photogrammetric measurement of the prints.
Aerial photographs are not used exclusively for photogrammetric purposes. They
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are often of great help to the topographer in plane-table field surveying. There
are cases, especially under wartime conditions, when only a few sectional photo-
graphs or a partial strip of prints are available for the terrain to be mapped, which
do not cover the entire area. In such cases, for the sake of speed, the topographer
i '.
Imust make full use of the available prints by interpreting them and transposing these
idata to a map. To do this, the topographer must be able to measure distortion and
)f
. Ito compensate for it.
I
Another valuable use for aerial photographs is in the revision and restoration
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of obsolete maps. Most of the corrective work in this case can be performed in the
1. !
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drafting roo? or laboratory by using the unchanged or basic relief of the map as
control points. Field surveying is necessary in this case only to establish the
. (detail which did not appear on the aerial photographs. In revising and restoring
obsolete maps measurement of the relief distortion of the aerial photographs is re-
quired.
y.:
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? 7. Photomap and Mosaic
., ; The easiest and fastest way of making a map from aerial photographs is by the
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preparation of a photomap. This fact has led to extensive use of photomaps in map-
ping flat terrain.
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The photomap is an area plan, assembled from aerial photographs which had been
Corrected for scale and for angle of tilt (transformed).
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instruments, such as transforming printers. In cases in which high map accuracy is
Preparation of a photomap comprises the following steps:
1) Photogramnetric densification of the control network;
2) Transformation of aerial photographs;
I 3) Assembly of aerial photographs by control points.
{
1 To make a photomap,a grid of geodetic control points is needed, while photogram-
metric work requires the processing of the photographs at a station using complicated
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often used.
not required, e.g. for general study of an area, preliminary exploration, small-area
;topographic work (relief surrey, field interpretation) an uncontrolled mosaic is
An uncontroll eel mosai
c
represents an assembly (composite) of aerial photographs,
{joined by their coemon contours, without the use of special control points. Contact
Iprints are commonly used in such mosaics. These prints are not corrected for tilt
I'
~a; storti nn and are not brought to a
'~`?"~? --?? common scale.
I
]; f38. Making an Uncontrolled Mosaic
1;
The simplest method of assembling a mosaic from adjacent photo^aps is through
, ntour points located in the overlap section of the prints (Fig.'53). However, due
9? Ito scale variations and tilt distortion, it is iossible to ^
ake all contour lines
q,
poincide, so that it usually is attempted to watch points having the least distor-
ion, e.g., point a and b of prints 1 and 2 (.Fig. 54), or points c and d of prints 2
2; ~nd 3, or points k and b of prints 1 and 23 in the adjacent flight strips located
Tong the line ab, cd, kb of the overlapping prints. After placing the photographs
~.n their overlap position, the accuracy of overlap is checked by making Pin pricks
~hrough the top print onto the bottom print for selected contour points. For exam-
'
le, if the points c and d do not coincide, because of scale differential of the
prints, then analogous points c2, c3 and d2, d3 are determined on line cd in such a
!,
rray that points c3 and d3 would be located at equal distances from points c2 and d2,
. but in opposite directions.
the contour points a and b, c and d are selected relative to the terrain, usu-
rlly having the same elevation, so that their relief distortion variance would be
rt a minimum.
t i
After matching the prints in overlap, they are held flat with weights and cut
M-ith a scalpel along line ab. The line of cut is usually not straight, in order to
intersect a given contour line as few timed as possible and at less sharp angles.
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The cutting line is made in zones of best coincidence of contour lines and in zones
of similar hatchures depicting the terrain.
Next the prints are cemented to a sheet of cardboard or heavy paper, leaving the
edges unglued since they may be cut off in mounting the next photograph.
After cementing from 2 to 4 prints of one flight strip to the board, the adj a-
scent prints of another flight strip are mounted, and the a+ork is continued simulta-
~neously on two to three flight strips. For example, print 23 (Fig. 54) is mounted by
Fig. 53 - Overlapping the Prints Fig. 54 - Selecting the Direction
of Cut
;the above method, while print 24 and the following prints are mounted simultaneously
. along both sides of the overlap, side lap and end lap, along the points b, n and
r
- Ib, d. If the contour points do not coincide, the print is mounted in such a way
/r
that the discrepancy is at a minimum. The prints are cut at this time along the
r
lines of the end lap. A strip of thin celluloid (0.2 a9m) is placed under the prints
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;to be cut, in order to protect the print below it as well as the base mount. The
!t I
i side lap is trieamed off after all or a major portion of a flight strip has been
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amounted.
During mounting of the prints, there is a cumulation of errors due to inaccu-
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gate mounting as well as to print distortion. In order to minimize the errors of
iassembly, the mosaic is laid from the center of the area to be assembled, i.e., from
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the center of the Biddle flight strip.
To nini^i ze the errors, due to rotation of the photographs and the bend of the
flight strip, the mounting is often done along the initial radial (direction between
the centers of the prints). The center points are pin pricked on the prints (con-.
4tour points with a circle outline of r a fk : 50 around the principal point, which
12_._j
Can be easily located on adjacent photographs). These points are also pricked on the
Ijacent prints. The radials are then Marked on all the prints front the center point
pf a given photograph to the images of the center points of adjacent photographs
(Fig. 55).
2E
1
o1 A, g!
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_ ._I
The prints of a strip in such a case are no
longer mounted according to the points a and b,
but by superimposing the initial radials 0102 of
the first photograph and o2o 1 of the second print.
Having aligned these directions, the prints are
Fig. 55 - Initial Radial
shifted along them until their coon contour
(.. point k1 is aligned. This point lies half way along the initial radial or, other-
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- wise, at the center of side lap. The rest of the flight strip is mounted, pasted,
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land trimmed by the above-described method.
s'
In transforming of prints, they are corrected for distortion due to angle of
I tilt during photography and are made to conform to a common scale. The solution of
X39. Transforming Aerial Photographs
!!
Ethe photograph into such a position, with respect to the horizontal plane, as it
~' this problea* lies in the process of conversion (transformation) during which the im-
e of the tilted print is projected onto a horizontal surface compensating .jagfor the
{
,jinitiai tilt.
I The principle of transformation can be explained as follows:
f
'' i Taking into account the external and internal elements of orientation we place
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occupied at the instant of exposure. Or, having illuminated the print fro. above,
we can establish the relationship of its projected rays aS, nS, bS, cS, oS, dS
(.Fig. 56) which will pass through the points A, N, B, C, 0, D, on the horizontal
plane of the screen E, the image on which will be corrected to resemble the image of
a true vertical photograph. r
By altering the height of screen E with respect to
area T, i.e., the distance of the screen from the center of projection S, the scale
Fig. 56 - Principle of Transformation
jof the image on the screen is changed, making it conform to the desired scale of the
rint. By placing a sheet of photographic paper on the screen and exposing it, a
print corrected for tilt distortion and at the desired scale is obtained.
There are several ways to accomplish transformation of prints. These can be
40. Graphic
divided into four categories: optico-mechanical (transforming printers), optico-
graphic (projectors and tracing instruments), mechanical-graphic (perspectograph)
~
hand graphic. The first two methods are conventionally used for production.
The graphic transformation of prints is performed with the aid of perspective
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grids whose construction was described in Chapter IV. After constructing the per-
spective grids on the plan, the perspective contours of the photograph are trans-
posed onto the plan square by square.
then making a plan where ac < 3? it beeowes difficult to construct a grid of the
type described in Chapter IV, since the line of the true horizon hihi in this case
lies at a great distance. In such cases, the grid is plotted on the plan with the
._ i following arrangeaent of the perspective image (print).
Let us asauree that the following contour points are available on the plan: ao
bo, co, do, no, ko, which represent the points a, b, c, d, n, k on the photograph
'Re
/' 0
Fig. 57 - Constructing the Family of Radials
a
0
(Fig.57), Let us draw a family of radials to all points on the map, denoting the
!apex by a0. Next intersect this family by an arbitrary line rr and mark on it the
points of intersection for b', n', c', k', d', Then, draw a family of correspond-
ing radials to the points b, n, c, k, d from point a. E y transferring the line rr,
with its points of intersection, from the map to the print and aligning its points
; b', c' and d' with the radials ab, ac, and ad, then all other points on rr (e.g.,
n', k') will coincide with their corresponding radials (an, ak).
The above-described principle of perspective representation can be used for
;transferring radials to definite points from the photograph to the ^ap. In this
case, the number of points on the map, corresponding to points of the photograph,
must be not less than four.
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'P ?##?''?
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._J Let as assuse that we have the point a,b,c,d on the photograph and the corre-
2.~ 'D.._siontro1_pQiat5 . b0 , c0, d0 on the aR ~(Fig. 58).._ Joining _theaa-Ro1n
._ to
-~o
it is simpler tt have them divide the lines into equal por-
-tiona, which, however, is not necessary. Next draw radials from point A to points 1,
,_In selecting these points
10-
12
32
14.-
16.
18
P,Jn
Ps-in t
Fig. 58 - Constructing the Perspective Grid
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Jits points b', c', d' are
of paper across these radials in an arbitrary posi-
the points b', c', d', 1', 2, 3', 10', 11', 12', at
the intersection with the radials.
;;( 1tion, we Dark on its edge
i"? 12, 3,10,11,12. Placing a strip
rlrl
On transferring the strip of paper to the map,
matched with the rays aobo, aoco, and aodo, after which
,2 }the points 1', 2', 3', 10', 11', 12' from ria. a. ri are pricked on the map. By drawing
r!
!;,
rays from Point ao, through the pricked points marked above we obtain at the inter-
section of these rays with the sides boco and codo the wanted points lo,
20, 30,
_iloo, llo, and 12o which are the projections of points 1,2,3,10,11,12 of the photo-
,(, _..graph.
~,..) Taking the point c as the vertex of the rays, radials from the point c to
t? 47,8,9,4,5,6 are drawn on the photograph. Then, these radials are transferred
(to the sap with the aid of the strip of paper r2r2 which is now oriented by the ra-
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with straight lines, we select on the. points 1,2,3...,4,5,6..., 7,8,9...,10,11,12.
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dials cobs, coax, code. The intersection of the transformed rays (Evan point co)
2f{ransformatian are not satisfied autoisati-
yl
ll y.. ip _ the _ 1 arge p r bnx_ by n co_bijtjon of . s ep the
.4screen is tilted, so-called longitudinal eccentring of the negative is introduced
( ..__.__.._. '
jwhich consists in a linear displaceaent o the
0
,I, 1
. The
ft f
gl e
Fig. 6 3 - The Small Transforming Printer
negative is displaced until the isocenter coincides with the bisector of the an-
a' (Fig.60). The
1handle 14.
In addition
longitudinal eccentring of the negative is effected
over the
to the longitudinal eccentring, the negative ?ay also be given a
Itransverse eccentricity - a linear displaceaent along the axes 2. The negative is
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"(s
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rotated in its plane by the handle 11.
he illuminator of _ the large tranafor-aing printer cn~ntiat ._,o~f_tbe lliptic ur-
ror 6., with an electric bulb placed in it$ focus. To ensure greater uniformity of
Z1l;2 b *tacf on the negative, a frosted d sh of Astrolone, celluloid, vax, or other
transparent eaterial is provided.
C. The Small Transforming Printer (FTI)
This printer (Fig.63) is designed fo* processing aerial photographs up to 30 x
x 30 ca in size at angles of tilt not greater than 9? and at scale ratios ranging
fron 0.7 to 2.5. The screen 3 of the small printer, exactly as with the 2 preceding
instruments, is attached to the base 1 ofthe instrument, while the negative and
lens may be displaced vertically by means of the pedal-operated wheel 8. The screen
may be tilted about the two mutually perpendicular axes 2 by manipulating the wheels
10'. The tilt of the screen is transmitted over the flexible shafts 9' and the cor-
Table 7
Type of
Size
A gie of
Scale
Focal
Focal
Size of
Height of
Tranaforming
of the
Tilt
Ratio
Length of
Length
the Screen
the
Printer
Photograph
the Aerial
of the
Instrsaent
?
Camera
Lens
GI
18 x 18
15?
0.5-2.1
100 - 250
150
38x 45
3.0
Large
18 x 18
45
0.7-5.0
as desired
180
100 x 60
2.8
FIB
30 x 30
and
100 X 100
Sall
18 x 18
14.5
0.7-2.5
as desired
180
60 x60
2
4
FTM
30x30
.
!; (responding transmissions to the lens 5, which also can be rotated about two mutu-
(ally perpendicular axes. The negative 4 has no tilting arrangements. The geome-
'$O-.uric conditions of transformation, exactly as in the large transforming printer are
`.' not automatically fulfilled. Since the screen is tilted about two axes, the nega-
hive also moves for its linear eccentring in two I mutually perpendicular directions.
Longitudinal eccentring is effected by the aid of the screw 14, while transverse cc-
-
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centring is performed manually. The negative does not rotate in its own plane. Opti-
cal co ation is obtained oyer_the_scalq inverter 7.
The illeminator 6? of the amall transforming printer, as in the large type, con-
The principal characteristics of theltransforming printers are given in Table 7
43. Transformation of Photographs in tie ~'ransforming Printer
Aerial photographs ^ay be transforme4 by the optico-mechanical method, either
i
from known elements of exterior orientation or from control points.
When the elements of orientation of she aerial photographs are known, transfor-
Lion can be performed by setting the transforming printer to the correaponding an-
lea between the plane of the photograph and that of the screen, and to the required
:r,
stance between screen and center of projection. In modern production practice,
however, the elements of exterior orientation are usually known with insufficient
accuracy. For this reason, the reconstruction of the perspective correspondence be-
tween the planes of the photograph and the screen (transformation) is solved by us-
ing control transformation points. Such points must be first identified and pricked
on the photograph, and then located on the system of coordinates of the map and
drawn on the plotting board placed on the screen of the printer. The plan position
of the transformation points is defined from the photogrammetric density of the plan
geodetic base.
The transformation of an aerial photograph is accomplished by the displacement
of the images of its transformation points from their position on the board.
If we project the transformation points a, b, c, d of the photograph P (Fig
56)
.
I
_I through the lens S onto the screen E and match resultant projections with the plan
f.', .
points ao, bo, ca, do, then the corresponding angle between the planes P and E will
.-Ibe defined, and the photograph P will be transformed. On the screen E we obtain an
image of the photograph P
reduced to a horizontal
hoto
ra
h and to the s
ale
f
,
p
g
p
c
o
~e
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_ltbe sup. The images of the transforaatio, points of the photograph are Hatched with
2
their positions on the _acraen by deans of ~ a) rotation of the photo ra h wand of the
4 i _
ap with the control points on the screen)! in their plane, to orient the image with
6 __.__. _
._..___.__. 1
6 d-.a
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Fig. 6 4 - Transformation Points
For transforming the photograph on a transforming printer of category I, it is
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", are recognized on the photograph. In this case, the problem consists in determining
;;&.._ sufficient to know the position of three non-colinear transformation points which
respect to the wp; b) tilting the photograph; c) changing the height of the screen
to reduce the image of the photograph so obtained to the required scale.
the spatial position of the plane of the screen with respect to the reconstructed
pencil of rays. The spatial position of the plane is determined by three points.
,.!, lAt different intersections of the pencil of rays by the plane of the screen, differ-
., jent positions of the images of the transformation points of the photograph will be
-obtained; by matching them with the control points of the board, the singular posi-
r.?, 1 tion of the plane of the screen is obtained.
In the general fora, however, when a pencil of projecting rays condensed dur-
ling photography is destroyed, as it happens in transforming printers of category II,
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points are matched with their positions on the
12.
l4-
l6
IS
0
22.
`r1
Hof transformation,
;r I
the photograph
Icess point. For
Th
e imagesf thf
oe transormed
f( I
Iscreen of the transforming printer
f2
Nations:
1r f
~i
this reason, a fifth excess transformation point at the center of
is very desirable; this is usually obtained when the transformation
Points are determined photogrammetrically.
three transformation points are insufffcie~nt for transformation of the _ PhotograPh
?-.
._ It; is...pr_eved in..proj.ective .geoaetry .that if, for t.wo_sitnallX_,?pt i~ es
f the photograph and of the map), the ^ tual perspective relation between four non-
S -J
coplanar cor din
respon g points of these plea is reconstructed thro
ugh a certain cen-
ter of projection (Fig.56.), then the perspective relationship is automatically re-
stored for any other pairs of corresponding paints of these planes, i. e., the itual
perspective relation of the planes theaseljves is now reconstructed. Therefore, for
i
transforming a photograph, it is necessary and sufficient to have four transforma-
tion points which do not lie in a single straight line.
The transformation points x are usually selected near the working angles of the
photograph (Fig.64). They are, consequen#ly, located at
the center of overlap of
four adjacent aerial photographs from two adjacent flight strips, i. e
at the
.,
cen-
.ter of their end and side laps.
1 The existence f
1
, _i
i
,1
MG I Transforming Printer
Large Transforming Printer
(FTB)
Small Transforming Printer
(FTM)
(on the plotting board) by the
following manipu-
Change scale, tilt the screen, rotate the
photograph in its plane;
Change scale, tilt the screen, rotate the
photograph in its plane, eccenter along
principal vertical (longitudinal);
Change scale, tilt the screen, about two of
its axes, longitudinal and lateral eccentricity.
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o supplementary control points markedly increases the accuracy
-J ..aa~cr of tine photograph is the most advantageous position for such an ex-
especially in working with large and small transforming printers.
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.,
44. Preparing the Phot
ographs and the Baal Plan for Transformation
Prior to transformation, the photographs are prepared sj i ITovi:
. o
paratin of lYcaat:vcs. This ~r
1Prc preparation consists in pricking the trans-
--
formation points and the field control points. The size of the punched holes is
kept
to 0.1 -0.2 mm ao that the prick marks are shown with sufficient clarity on the
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'( I
2. Coapi I ing the Transforaat ion " Bss~is ",
Due to the fact that the rigid
lotting board on which the control and transformation points of the map are
marked,
graphic
ine y placing a piece of cardboard of determined
Introducing the
Correction for De-
formation of the
Paper
generally does not fit onto the screen of the
printer,; the points are copied from the asap onto a
strip of transparent paper by prick marks and from
there onto the tracing paper. Usually, such base
composite is prepared for an entire flight strip
of the mosaic. For prominent relief of the con-
trol points of the area,
corrections for relief
are introduced. These points are marked in India
ink by circles of approx. 2 mil diameter.
3. Deteraination of "Shrinkage for the Photo-
Since, after transformation, the photograph is developed, washed
the photographic paper becomes deformed or " shrinks ".
, his
shrinkage is determ' d b
Paper
it; and dried,
jthickness under the base sheet. After transforming the photograph in this _ I position,
i; jthe cardboard is removed and the print is exposed onto a sheet of photographic pa-
;-: per, placed directly on the screen. If no cardboard is used, the length of the
t? Y
g
la cardboard having a thickness Ti corresponding to the shrinkage indicated by the
Isize increase of the image. If S' denotes the lens of the transforming
printer, E
frays from the lens of the transforming printer to the screen increases, causing the
f
(image to increase to a size of L (Fig.65). Therefore, the problem consists is
1 Hain
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3
._ the screen, and E' the cardboard liner, then:
2
(23)
where -C : L = K denotes the coefficient of redaction in size of the image when using
a cardboard liner and which mast be equal to the coefficient of shrinkage of the
4
the distance from the lens to the screen.
1
AT
1
Measuring the Sam-
ple on a Grid
q.d2 _ (k--C) . L
To;deteroine the coefficient K of the shrink-
age of tjhe photographic paper, several c~antact
prints are made of an exact grid of squares having
sides of 5 a. each and, after drying, the segwt
-i (Fig.66) is .easared for correspondence with
the knoann original Li.
Thus, the coefficient of drying can be deter-
Mined from the relation K = F~ : EL so that
eq.(23) will be:
n=dZ 1- FCC
EL
The screen is set in a horizontal position,
and the eccentricity values
are set
I, to readings of zero. The negative is inserted (with the emulsion side down) into
,:;~ithe magazine of the transforming printer, with the center of the print aligned with
,, !the center of the negative holder. The cardboard spacer is placed on the screen
I
',,; 1
hotographi c paper; ad2 is
over which the base with transformation points is placed. The negative and the base
I
;copy are rotated so that the print will lie dia
o
ll
l
g
na
y a
ong the aif th
{
xs oe screen
land the illueinated images of the transformation points would lie in a spread from
{
(the center of the base.
131
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16
the axis _af ..the admen, are
the base (Fig.67, points of the base in
0 ...___.._....__.._
By varying the scale of the israge,
2-
l8
'0
Fi g. 6 7 - Change in Tilt of the
Screen
Fig. 6 8 - Rotation of the Photograph
in its Plane
~4.
fail to coincide, the iaage trace 5 -4.shbuld be enlarged, and the trace 5 - 2 re-
;c
duced in size; this is achieved by tilting the screen toward the observer (point 4
is lowered and point 2 is raised ). Aftet tilting the screen, all image points and
O
..t : I
---___.___j
Fig.69 - Noncoincidence of Points Fig.70 - Additional Tilt of Screen
caused by Relief
the points on the base may still fail to coincide, as shown in Fig.68. In this
case, obviously the part of the image around the point 1 should be enlarged, while
~, (- .
. the part of the image around point 3 should be reduced (the sides 1- 2, 1 - 5, 1 - 4
t ng
'rotating the print (together with the base) in its plane (in the small transformi
132
jto be enlarged, and the sides 2-3, 5-3, 4-3 to be reduced). This is achieved by
he trensforsaztioa light spots 1 and 3,
then .aatched with the_ ..correponrl 4on
b]fack). If after this, the points 2 and 4
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A
the screen that had been moved upward and ;thus will be reduced in size (compressed).
ph_ne*.point_ 3..
h tog the sides 2 - 3
`3 - 4viii be
L
j
d
6
.
,
e
Prn
ec
. ontn_t.
e...pars...M
_ 4--i
printer by tilting the screen laterally). On such rotation, the part of the photo-
Op
t
o_, 0
-
~i
010
F i g. 7 1 - Longitudinal Eccentring
The part of the print near the point 1 having the sides 2 -1, 1 - 4 will be enlarged
(expanded) and shifted to the lower portion of the screen.
It should be borne in
mind that the change in the image produced by any of
these manipulations is Bore pronounced in the lower part of the screen.
Die to the fact that each manipulation some-
?1 ?1 what disturbs all previous settings, the image
DISPLACED N?
.~.._.- - -.-- _
OF NEAT VE
e.3
0? S
AXIS OF SCREEN
DI LACEMENT
OF IMAGE
#, i
.. -+ Fig. 7 2 - Lateral Eccentring
1
,
ur
orientation points coincide, but the central point will still be out of alignment
,
._.~along the principal line (Fig.69). This discrepancy is explained either by errors
i
. in the determination of the points for transformation or the influence of the dis-
placement of the picture points
due
points are matched with those of the base by
successive approximations, repeating the above
operations and correcting the scale setting each
time.
axis o
Orccasionally
relief. At the points 1, 2, 3, and 4, these
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a case arises when the fo
where the geometrical conditions of transoraation are satisfied with a sia~altaa
I8 eons
_eccentring of the '
photograph, the pattern of non-coincidence shown in Fig. 71 or 72
S 0-
will be obtained, after the above sanipul4tions have been Wade.
by tilting the screen, since this will c3dse the points 3 and 4, located in the low-
In the transformation of hot
ab p ographs4on the large and small transforming printer
yore than the aides 1 -2 and 3 - 4, the screen is given a tilt (raising the part with
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._ 's elongated along this line, if it is displaced to the lowered part of the
screen
?6 . and is compressed during displacement into the raised part of the screen. In this
y.~;..
(case, the displacement of points (Fig. 71) is acc lished b
(' ~P by
longitudinal eccentring
._. in the direction shown in the diagram (with the screen tilted toward the observe
`2 r),
Ifollowed by a change in scale. In the position shown in Fi.72 however
: g , the dim-
placement of the points is accomplished by application of transv
::(... Brae eccentring, as
,~ lindicated in the diagram for the case of tilting the screen on t
he side of the oh-
.+' - -__- ---
.
At longitudinal eccentri
yf, ng of the negative along the principal line, the i~nge
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the points 3 and 4) until the position sbcfwn in Fig.70 is reached. By changing the
l2 anging he
i
scale (enlarging it) a better catching of the points is accomplished.
l~.
._ tQ. fQ1-CQiDctdCnttot_ the point 5. leis non?coincidfl._say be so~e*hat oyed
I i~P,r
A
Jerrora any be inaccurately eliainated, thi4s leading
to errors in netting the tilt, _
O
Bred part, to be dim 1
paced faster, i, e, he aides 1- 3 -and 2 - 4 will be chanced
server. In lateral eccentring, a torsion of the image occurs since, during dis-
placement of the ima
e al
h
g
ong t
e axisf th
oe screen, points 3 and 4 located in the
',
flowered part of the screen, will be displaced faster than
!' points 1 and 2.
-l When transforming the photographs on the lar a trans
;,,t
, 8 forcing printer, no later-
eccentring is used or only on a small scale, in vies
!f_ of the lack of centring of
!the negative in the holder.
. t The above manipulations will cause the is a int
f. +~ Po s to be Batched with the cor-
! (+
responding points of the base by a series of Successive approxications. Due to er-
rors in the position of the transformation points and due to the displacement of the
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2
.. the transformation points asst be checked for accuracy.
l C-
12
During exposure and developing, all photographs on the plotting board are aade
-nni fora
aai
in tone, i.e., the images of the same contours are produced at equal photo-
raphic density.
2O
I
22._I46~ Application of Corrections for Relief
. _!
is achieved
i' lof polyconic projection for the case of photographs with a tilted b
plane, by pro3ect-
ling then to a horizontal plane. This method of transformation compensates for the
~pictnre
i points caused by relief, it may be iepoaaible to achieve complete coinci-
. deuce. .of...the points. these siaalianaents 'aunt not exceed D.3 am. _At..larger _errcrs,
After the photograph is transforaed,`the base and cardboard liner are reaoved
frogs the screen, the lens is covered with a red filter, a sheet of photographic
paper is placed on the screen and the photograph is exposed after reserving the fil-
ter..
Fig. 7 3 - Correction for Relief
distortions of the photograph caused by tilt
but not for distortions caused by ground re-
lief.
Assuming that photograph P (Fig.73) con-
tains an image a of the terrain point A, and
that aoa denotes the distortion of the image
point a due to ground relief. An orthogra-
phic projection of the point A is ?ade onto
the screen E at the point Ao. During trans-
formation, as indicated in Fig.73, the ray
aS will not coincide with the ray S A o. The point a will form the image A' on the
screen, which is displaced from the map location Ao of the point A by a distance of
^h. This is a direct result of the distortion aoa of the point a caused by relief.
135
As shown previously, the transformation of photographs
by
the
method
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;aary to correct for relief during transformation?
i
Corrections for relief distortion cai be made at t
e locus
h
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.. - --- --- - ---
LA. t c tranaforma-
f
h
-_7lion points on the photograph a (correction b
J(~.._ b) or at the locus of the tranaforma-
.,.Jtion points Ao on the base (correction A) The
.J
12 h magnitude of the correction is dc-
ter?ined by eq?(12), except that its sign ;will be opposite to that
" . i obtained from
seq. (12).
1ti, .
'
18
Dh
H
(25)
2#'- ` In ra L
c
..!If the relief is negligible, these distortions are insi ificant
- 8'n and can be disre-
'gardrad (up to 0.3 s). Ho*eTer, at higher disc
onion it b! omes _ ahaolutely_ necea-
Therefore, for correction we have:
i
I p
xce it is inconvenient to make corrections for relief on the negative,
'since this "ill result in pin holes,
so the corrections for relief are usually made
i~ +at the locus of the points on the plotting board.
In the case that the correction of the point has a positive value of relief
correction, the mark on the photograph is moved toward the nadir point, and
the mark
:on the plotting board away from the nadir point. For the case of negative correc-
tion, the opposite procedure is used, and the correction on the photograph is made
'away from the nadir point
I the plane of transformation. For example, if the elevations of the points on
a
photograph vary from 200 to 400 m, then the factors of compensation are calculated
and on the plotting board, torard it.
To keep the relief distortion of a transforsed image to as low a value as
pos-
sible for a given scale of transformation, the correction values h are calculated
by eq.(25) from the average height of ground relief. This average height wil
1 be
from the average plane of elevation, which is at 300 m, so that these c ensatio
omp ns
will fluctuate from - 100 to + 100 ?. The survey elevation H will then also be cal-
culated from the mean plane of elevation.
The correction at the locus of the transformation points, to cospenaate for re-
136
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-r a
er
al Pht
oo r hs
of 8o~d ~ Zones, for Arena
'lief distortion, does not eliminate the distortions of the
photograpl-ic rages bnt
does.- pe>aut the correct truusfornation of the print.
Corrections for relief distortion are made for
Purposes of transformation of
printR and also for solving other hot ~P o8i'+~ametric problems , e g tbs. .'._.._.__._~_ .
__.
?
e involved in
determining the true location of points on a photograph or
oints on a
p
y zones or sections of various elevation
(planes permits elimination of this defect and reduction of the relief distortion to
the desired degree of accuracy,
Let P (Fig.74) be the photograph of the area of bold relief T
Divide the
ar
1 i ?1? Tranafortion of A
i
J
,
J2 I
.1
l6
po
nts on
a
-;transformed photograph with bold relief still excee
tl ~ d the limits of 0.3-0,4 eew, i, e. ,
yi ireduce the accuracy of the Rap,
stortion allows the trana
5G_ -formation of prints for any type of terra'
Vin, but the distortions of the
i
i
ea
into various sections by elevation intervals equal to h', as shown in F'
;the change in elevation from one section of t 18.74. Then,
he area to the next can be observed as
;the general height fluctuation for the mean plane of elevation of the area T. The
;deviation in the height of individual points from the
mean plane of elevation, for a
, ~given section can be observed in relation to the boundary limits Y s of this aection,or
,, as particnl_ar elevations h which cause relief distortion of points on
the print at
;the scale of the particular section of the
photograph. This scale is deterRined at
the average plane of elevation, Therefore, in the phot h
08rap given in F1g.74, the
scale of section 3 will be larger than that of section 2, while the scale of sec-
i
t
on 2 will be larger than that of section 1.
The transformation of the photograph by sections is acc lis
amp hed by converting
the sections (average planes of the sections) to the scale of the map,
137
p
~
have a projected relationship with the print. .
and Helref
The correction of transformation points for relief di
-
The transformation of the photogra
h b
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l o
Let is take any section, say section 2, as the starting point. The transfor~a-
-tion points are corrected for relief, with the corrections calculated. fros~ the arer-
age plane of elevation for section 2, which cowpletea transformation of the print.
-..Tus, section 2 of the print will
appear on the screen E" at the specified scale.
~`The distortion of individual points for this section will not exceed # 0.3 to t 0.4 mo.
12, .
1!
:i (
-s-i
___F9
REPRESINTATIOM OF 'ME
RELIEF
Fig. 7 4 - Transformation by Zones
responds to the position ao. Then, the scale for the third section will appear on
the screen E'" (average plane T3), equal to the specified scale at which section 2
was transformed. In this position, the distortion of the photograph prints for the
third section will not exceed the specified limits.
By increasing the scale of the image (wing the plane of the screen to loca-
tion E'), a scale equal to the specified scale is obtained for the first section of
STAT
138
Point A on the mean plane of elevation for section 3 will appear at a", when
it should have appeared at point ao . Consequently, if the scale of the image is
decreased by moving the screen from position E" to E", so that point aTT would be
reduced in size by A, then this point will appear at the position a", which is cor-
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I.
4
._
t
e aver
gage elevation plane of the initial section. The ad'uat.ent to
E .. __....... .. J the average elevation
plane of the other sections is done by changing the scale or, in other
words, by
;the photograph.
3
Ac~uall h
t
c1-anging the value of the sections by A.
In this case, A represents the difference in correction for relief o
f carious
sections, at an arbitrary elevation of a more distant point A. These va
l4. lees are de-
.~ termined by the elevation of point A, froN the average plane of elevation
XC of the
varioas sections. In practice, all corrections for point A are marked on t
lS he plot-
.-- Ling board and, after transformation of photograph along its points corr
Q-- ected for
the first section is coipleted, only the scale is changed for the other
21 ? sections, by
ans of displacing the image of point a by the correction value, corres ndi
tf~..
.L._ PD n$ to
25
'Ills ZOOC.
.-. For each position of the screen E" and E", a photograph of the print
is made
1
'"d ik
d b i
s mareyts zone nnh
er.
_ T
l ._!
-.when there are three sections or less to a print.
:{
f
r.. I
J
The assembly of a photomap consists of: placing the transformed prints
on a
mounting board in accordance with their transformation points; trimmi
ng off the
overlapping edges of adjacent prints; and cementing the rints to t
!; P he board.
I Prior to assembly, the tonality of the photographs is check
I ed for uniformity.
.INext, a hole of 0.5 ms is pricked thro* h each transformatio
n and contr
l
o
point by
I s of a punch. The punch comprises a needle mounted in a cylindrical bushing
When the relief of the terrain is very bold, no photomaps are made; Instead a
graphic plan is prepared.
with tapered ends. The needle is kept in the extended position by spring pressure
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48? Assembling the Photomap
e
y,
tran$forsat1on of the photograph by sections is
donf
h
-
ransformation by zones or sections is very complex and is used in production
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.r -
hole in the print.
center of the tramaLor tion point, pressure is .
applied to the ~~6,.._shzch._.panches
Epoint.
)2_
i tion dots
)4_
Icide. The
The center of this hole is the location of the transformation
Before asseably, the transformation as well as the effects
.# prints are
not
of coincidence
limit is exceeded,
18 1
lE
them ~pust
not
exceed
0.4 to 0.5 mm. If this
or if the tonality of the photograph is
foraation mast be repeated.
SU ~
y~
of drying of the
uniform, the trans-
is started after the checking is completed. The first
int is put in position on the base, followed by the remainder of the prints,so as
to have the centers of the punched holes coincide with the corresponding points
`r;
..marked on the control network or so that the variations in alignment of the holes
rE;.__ _
.land the dots are kept to a minimum. (Misalignment of the corresponding dots and
(,
-hole centers must be equal and in opposite directions from the center of the hole.)
cm from the center of overlap. The direction of cut is
.selected under the following conditions: a) both prints should have the same ton-
jality along the trim line, b) the trim line must intersect a minimum number of con-
hour characteristics and not come close to relief boundary outlines (e.g.,roads)or
(individual objects (houses), c) the trim line must not intersect contours or PoPula
-
-.Next the print is fastened down with weights to prevent shifting. The second print
'1 I
is located on the base in the same way and is fastened down too.
Next, the line of cut along the end lap of both photographs is marked. This
jtrim line is marked within 1
'tion centers at an acute angle.
-{,..!
(
Coincidence of relief lines along the cut is checked for proper fit. For this
purpose, characteristic points (angles) of the contours of the upper photograph are
(pricked by pins to check whether the prick coincides with the corresponding contour
140
': ..
,1
for
!and is retracted into the bushing under pressure. After placing the needle on the
j Assembly of the prints
checked. To do this, each print is placed so that the narked transforaa-
are at the center of the punched holes. These dots and holes must coin-
error
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on the lower print. The cut is made where (taking the above Condit'
ions into ac-
'count) the agreement of contour$ of adjacent photographs is beat,
... The_.daiaGrapaacy
b
-
etween the contours and the cut lines should not exceed 0.7- 0.8 ss
In no case
#should the photographs be cowed away from the transforms
( f-1 txoa points, in order to re-
duce the discrepancy of contours.
weep the prints and the mount and both prints are cut along the trim line
)4 with a
_;acaipel. The edges of the prints muat be even, amooth, and mat coincide
l c -.' with each
other. The trued-off overlap strips are saved for
IH_ correcting the photom~ and are
4aarked with the number of the photograph.
e __I
The edges of the trued prints are raised (the other part being held .-4 8 down by
weights) and the mounting board is coated with amyl acetate cement (at the spots
r!'_'
where the photographs will not be trimmed); the prints
~` - are cemented to the mount
~carefull
y smoothed down, especially along the trim line, and are cowered with
rb I
.weighted glass plates. The third print of the fli ht
1
:,o _
: g strip is mounted is the same
way as the second, and the same procedure is used f
or all remaining photographs of
the strip.
=u~ ~v.e conaitaona being satisfied, a thin strip of celluloid is placed be-
2 J
I It
The second flight
:": I
!t
C
14 t
p
s
rst be
trimmed along the line of end lap, while the side lap is tried after all photo-
Jgraphs of adjacent flight strips have been
mounted. Daring this operation
as in
,
J
the case of cutting along the end lap, the terrain alignment is checked on adjacent
J Potographs and the overlap is trimmed along the line within 1 cm of the center of
-aide lap. After this trising, the complete print is
cemented down and smoothened.
(The trimmed edges of adjacent photographs must coincide
l
exact
y Thehld b
.re soue no
I0Te1ap or space between the edges.
All other
t
alight strips are mounted in the same way. To prevent glueing of the
]:t8 along the borders the
mount is covered with wax per up to the frare line.
(After the complete photorap is mounted, the overlap along the edge of the borders is
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strip is mounted in the same way, with the
rint
fi
ing
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3
cut off, uaing a straightedge. Prior to glneing down the corner prints of the
h
t
p
o
o-
*.p, the fra.e coz,rera are wrksd at the end points of the line~e of the e
captrol net-
(,. work and are pierced with a punch. A this atrip of celluloid is laced
P under the
._.jprint to avoid a second prick at the eatah~lished
t _ ? position of the frame corner.
.I After completing the assembly of the.pboton the
aP, prints are left in position
...;under pressure of the weight for two or three da s
i 2 Y ,after which time the excess glee
_...u s wiped off with acetone.
), t
In cases in which the prints had been transformed b s
1 1 y ectiona, the laying of
4the prints on the mount is also done by zones according to the relief
J
J`
of the terrain
shown in Fig.74. In this case, only the scaled part of each rint is
-1 "o p used, i.e.,
only the second zone is cut of the print for the second zone, and onl th
`r y e third
_1 Section of the print for the third zone. The cuttin be
!~ -~ 6 tweea sections is performed
-.after both prints of the adjoining zones have been aligned with the trans
!` formation
2f. --points punched after correction for relief with r
.~ espect to the plane of mean eleva-
1tion of the given section of the print.
ca
T_
f I
:;'% f
a
c and
photomap it occasionally becomes necessary to assembl accurate
:;
"~ Y cartographic mater-
the geodetic data for the prints are not available. In this case, it
JIS impossible to assemble an accurate photomap, which means that
nnoriented photo-
-
lmaps are prepared instead, which are sometimes ca
!r, ~ !led semicontroll_ed mosaics. The
-method of composing them does not dif
!; I fer from that used for photomaps. In such
-cases, the control points for transformation an
~` and scale determination are established
IbY the photoetric method, after which the rints
~'~ prints are transformed and mounted,
(Thus, unoriented photomaps are somewhat la s
s accurate than controlled mosaics pro-
. -lduced from geodetic data but the method of c
amera work is the same.
`'' ;49. Patti the Photoma into Final Shape
I
Finishing the photomap comprises the following steps:
STAT
addithe de
ion to tscribed steps of assembling ai; unco
ntrolled mos
i
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a) The corners and sides of the frame are marked in India ink by a square with
2-? sides.
92
r,
b) The trigonometric points and coaitrol points are marked in India
ink with
comes nd
Po ng conventional a
yebc~ls. The symbol mast be centered at the
side of the line and not of the punch hole.
c) The corners of the frame are marked by their rectangular and geographic
coordinates.
d) The ends of the kiloeeter grid are entered and numbered.
e) The entries made outside the fra~e include: the nave of the trapezoid en-
tered over the northern edge of the map, at the middle; the numerical scale
designation, below the southern edge; the date of preparation of the photo-
map and the signatures of its compilers at the right; the sch
eme of the
l frame with the diagonals of the photomap and an indication of their theor-
etical dimensions at the eastere border.
1
(3._ 50. Proof checking and Correcting the Photomap
The proof checking of a photomap consists in checking and determining:
curacy of entry and outline of the frame of the photomap and ends of the kilometer
grid, b) accuracy of coincidence of the photographs with the transformation points,
'.f
Ic) divergence of the contours at all cuts between the photo ra hs
I
/_(
g p d) divergence of
lthe contours at the borders of adjoining mounts,
These corr
ti
._,.~erance for deviations on the sides of the frame and the ends of the kil
ometer lines
Iis 0.1 ?, and 0.2 nm for the di
~ agonals.
s ar
checked by commonly accepted method of the use of a straightedge.
The maximum toI-
The corrections are made, observing the following requirements:
I
1. The frame si d
ec
ons are etd
nere on a special correction sheet.
-= I
es, the diagonals of the board, and the kilometer grid end
e
2. The accuracy of superposition of the photographs on the transformation
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_. _-.. ----S --
e
meter. These deviations must not exceed ~
3. The divergences along the contour !lines at the lines of cut are determined
by matching the cut-off edges of the printfs, saved at the time of assembly of the
hotoa
P ap?
A diagram of cuts is reconstructed o the correction sheet (Fig.76), on which
are recorded the location and aeount of misalignment. The misalignment is checked
points is determined from the deviations of the centers of the punched holes from
the~ricka_of the corre ndingpoants oa ~, ? a
~- -----
all points is plotted on the correction s eet (Fig.75) on which the deviations of
are
it---k-
vw vva ~i ~a ilk {.CJl W1S 01 a ?lill-
t 3-4 cm intervals along the line of cut. To determine the degree of misalignment
V
r' ------w
I.VMO
e
o? 0 0
f4qi 45
K~ 4, 'tI 43 4
Fig.75 - Correction from the Points
Fig. 75 - Correction from Cuts
he corresponding cut-off of one of the adjacent photographs is placed along the
oint, and then at intervals of 3-4 cm the most distinct contour points located as
-close as possible to the line of cut are selected and ricked. The pricked. The cut-off part is
hen removed, and the deviation of the prick from the corresponding contour point of
/c
he photomap is measured and recorded on the correction sheet.
The misalignment of contours must not exceed 0.7-0.8 mm, and even these maximum
(discrepancies are permissible only in exceptional cases.
I
4. The correction for match along the borders of adjacent photographs when the
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photomaps are it along the line of the
hdrder, is done as in the corrections along
the cuts) by layinj~the~cutoffs of one photograph on the other and superimposing
them with the lines of a kilometer grid. By pricking corresponding contours as close
as possible to =tbe borer; tfidiscrepaocy between
If a flap is left in cutting off the photomap (usually 8 men on the scale of
cartographic work), the contour from one photomap is transferred to the other with
the aid of compasses, after determining t$e distance of the contours from the frame
and the length of the perpendicular to they border. The distance between the contour
the Frame
so transferred and the one on the photomap gives
the 'v ted deviation.
Tl4e deviation of the contours along the bor-
der mush not exceed 1.0 mm.
Tile data of these corrections are entered on
a special correction form (Fig.77), on whose mar-
gin the places and results of measurements, ac-
cording to the kilometer grid, are noted.
Correction Along
If discrepancies exceeding the established
tolerances are found anywhere during the correc-
ion, or if the number of discrepancies should reach the maximum tolerance, the cor-
esponding places on the photomap must be re-laid.
Map Phototriangul at ion
r _ Fi.g.77
To expedite the transformation and assembly of aerial photographs in making a
~hotomap, the map location of four control points on the prints must be known. This
,
4c an be done by a geodetic survey of the area or by the photogrammetric method, with
.,t)
he aid of plan aerial triangulation and photopolygonometry (see Sect.112). This
ermits to greatly shorten the difficult work of field surveying. In the last case,
only two points have to be field-surveyed, and these separated by several prints.
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2J
and these can be deteriained by 1ustrua~ent1.: The purpose of_pian aerial triangulation
is to determine additional control points,` and thus to define the position of contour
points y laboratory lnstruaKnts.
Aerial phototriangulation is a oethod of determining the position of points on a
hotograph by deans of constructing a netr~ork of triangles whose dieensions are eeas-
red on the aerial photographs.
To construct such a network of triangles, the angles of these triangles lust be
asured (not less than two angles per triangle) on the aerial photographs. In the
alysis of angular distortion of prints, it was established that the angles in-
cribed by lines on a photograph are distorted due to the tilt of the photograph and
he tilt of the terrain, and are not equal to the angle inscribed on the terrain.
.
e ar
_ istortion only in the directions not passing through the nadir point.
;~a..._
It is on these remarkable properties of the isocenters and nadir points that
.
the method of phototriangulation is based.
.(,
If the photograph was horizontal during exposure, its isocenter and nadir point
ill coincide with its principal point. In the case of a horizontal or plan survey,
owever, which is the only one that will be considered in the following passages,
hen the angles of tilt of the photographs are small (a < 3?), the isocenter and
nadir point will be close to the principal point, and if they are replaced by the
principal point, or even by any desired contour point close to it - tested "central
point" - no practically perceptible distortions will result (as proved in Sect.34).
,- __~
! (
photo raph.
The nost that are ever needed are four points per photograph, as for tranafor.ation,
Consequently, the angles can be measured on an aerial photograph, or radials
]drawn on it, for the construction of a phototriangulation grid only fro+a these base
-
points (principal point, nadir point, isocenter) or from the central points of the
The value of the angles of a tilted photograph and terrain are described by a
adial drawn from the isocenter of a flat plane
The relief of th
ea creates
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-, - --- - - -.--- ---
I.
In processing the photographs of a mountainou8 region, when the distorti
an of
directions due to relief is very considerable, the nets should be G
oa..st..ted from
the nadir point; since the true nadir points are unknown, they are determined as the
so-called arbitrary (moat probable) nadir
points. (see Chapter XII).
The construction of phototriangulati m nets may be carried out by various oeth-
ods, either on a single flight strip or for several flight strips together. The
~e
t widely used, simplest, and at the sage tine fairly accurate fore of
hototri -
p
angulation net is what is called a rhomboid chain, which is usual) constru
usually cted
within the limits of a single flight strip.
A phototrian8ulation rhomboid chain is constructed in the follarin
8 earner.
Given is the flight strip of air photographs 1,2,3...(Fig,78), with a 60% end
lap, on which every three adjacent photographs mutually overlap. I
In this case
the
,
the central point (or nadir point) of each photograph will be represented
on both
?adjacent photographs. For example, point 2 of the second photograph is ea
pped as
;point 2' on the first and third photographs; similarly, the contour points a
and b,
termed tie points and chosen in the zcne of triple overlap, are mapped on all
pho-
tographs. Consequently, for each photograph we may measure (or graphically con-
;struct) the angles y and E, formed by the radials from its central point
the
cen
tral points,
?Fig.78.
Let us assume
Photographs
twice by resection from the angles y3 and w4 and E3 and E4.
p
-
o
graph, the position of the central point of the third phot ra can
a' og Ph be determined
mapping them on adjacent photographs, and the tie points, as shown in
"-a' w%LLuuLesx thl
coot mates of the central points of the first and second
- oe centra points of the first and second
to be known. Then, knowing the angles yl and ~-2, we may, by direct in-
i
.?tersection, determine the coordinates of point a. In exactly the same way, the
,angles 41 and E2 can be
?,:-, the coordinates of the points a and b, and the central
point of t
he second
hot
The figure formed by these four triangles (1a2, 1b2, 2a3, 2b3)
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used for determining the coordinates of point b. Knowing
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rhomboid,' therefore such a scheme of a phototriangulati
On net
cb* in .
For the photographs 2, 3, arid 4, a
ca
racT.Cd by the
of the aid
point c and d, after which the distance b -
3? and so on can be determined for
7 C
Fig.78 - Rhomboid Phototriangalation Chain
any number of photographs of the flight strip.
By
: teat, the radials from the central points can be laid to
Photograph, e.g., to point x (Fig.78) and determine
tion. In this
!
be determined,
constructing such a rhomboid sys-
any
desired points of the
their new position by intersec-
way, the horizontal position of four points for each photograph can
as required for transformation and mosaic
assembly
.
From this scheme of constructing a rhomboid phototrian ulat'
B ion net, and from
the condition that the tie points belong to three adjacent
photo
h
grap
,..e
s ie th
'condition that there be a zone of triple overlap, it follows t
hat a 6end lap
1 (between the aerial photographs on the flight strip is re
'" ~ quired for constructing a
;rhoaboid phototriangulation net.
The construction of such a grid may be made either
analytically, for which
148
can
an be
be
is termed a rhomboid
new rho.i,,,;a
rhomboid
_
t
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purpose the angles y and E are measured with special inatru?ents, or graphically, by
copying the radials from the photograph onto tracing '
papers Which is termed a cen-
tral radial tracing. A central radial tracing is shown in the lower part of Fig.78.
As a result of the great aaount of work ihwolred when using the analytical method,
the net is usually constructed graphically.
To construct the nets, either the negatives of the aerial photographs or con-
tact prints made from then say be used. The former have the advantage of being less
subject to deformation, while the photographic image is better viewed on the latter.
When negatives are used, the points of the net are pricked on them and copied onto
;the central radial tracings. When using contact prints, the central radial tracings
may be copied from the points pricked on the photogra jc, or the radials may be drawn
directly on the back of the photographs, by which the net is constructed. In pro-
Idactive operations, negatives
The graphic construction
.following processes:
are usually eoployed.
of rhomboid phototriangulation nets consists of the
a. Selection and pricking of the points on
the photographs;
b. preparation of the central radial tracings;
C. construction of the net;
d. reduction and connection of the net.
52. Selection and Pricking of the Points
The pricked contour points must be distinct, sharp, and easily recognisable
on the photographs. Such points,
;tracts, the intersections of roads
e.g., -y be plowed fields or other agricultural
or ditches, the corners of low structures, small
shrubs, or haystacks (pricked in the center). It is forbidden to prick: blurred,
i
(unclear, indistinct, or rounded outlines; outlines intersecting each other at an
angle of less than 30? (ur more than 150?); corners
of shadows or the shady sides
. of objects; high buildings or trees; shrubs and haystacks more than 0.3 mm in di-
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(i:
meter on the photograph, incised water channels; variable outlines (boats and rafts
an _the water, autoshobiles and trains on roads, etc. ) Points e*n stee e.l s
P Qpe. are al -
so unsuitable.
The pricking of
points, on the accuracy of which the accuracy of the phototri-
:angulation depends to a great extent, gnat be done with extreme care and re
p caaion.
the center of the prick siust exactly coincide with the point to be
pricked, which
'mist be represented in the form of a geometric point. The prick must be small, with
. a diameter of not amore than 0.1 mm.
a. The Pricking of Central Points
2C
?1 Is
-.--7
oincide with any marked contour points.
i ;
j points, e.g., if it coincides with a la
. r
e and b 1
The central points must be pricked at the beat contour point located clos
eat to
the principal point of the photograph (and not further from it than the radius de-
ters~ined by the expression r fk : 50). A special transparent sheet is rena
p red
or selecting the contour of the central point: The coordinate induces of the
pho-
:tographs are pricked on the celluloid, and the opposite points are connected by
straight lines intersecting in the principal point of the picture; then, a small
circle with this point as its center and with a radius off k50, is cut out of the
:celluloid. The ca~ntour point taken as the central point must be easily identified
y entified
on both adjacent photographs of the flight strip, on which the point is also
;pricked. On the photographs (negatives) the prick is surrounded with a s uar
q e in
India ink.
In constructing the nets for subsequent stereoscopic Processing of the photo-
:' grapha, rather than pricking the central points, the nadir points are pricked re-
~
gardless of whether
j If the central point (or the nadir ~
point) does not coincide with any contour i
cannot e recognized and pricked on
k
the adjacent photographs of the flight strip, then the initial radials f
' (the radials 4
to the central points of th
d
e a
jacent photographs) on these photographs are drawn
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"artificially" (cf. Sect.53).
b. Pricking the Ground Pointa of Control
, ..Ground w
_ points o control serve to orient the phototriangulstlon ae v on-the-
.;plotting board and to reduce them to the a4asigned scale. The location and density
- of the points of ground control are dictated by the required accuracy of
triangnla-
tion, based on the laws of cumulation of lrrors in the nets. Ordinarily the points
:of ground control are given in each of a fa~ober of photographs (from 6
, 8, and up to
2O photographs, depending on the scale of the flight strip and the scale of the ma
P
Hto be prepared) in the zone of aide lap between the flight strips and, wherever
J1aible, in a zone of triple overlap of thephotographs in one flight strip. After
-`determining the points of ground control on the ground, they are identified and
i
;pricked on the contact prints, putting a sketch and description of the contour point
;so selected on the back of the photograph.
s
The pricking of the points of ground patrol in the process of pl-ototriangula-
Lion consists in pricking the fixed contour point on all negatives of
both the giv-
en and the adjacent flight strips, on which the identified contour is shown. In
the identification and pricking of points in the negatives, the field rick o
prick on the
;negative, and also the sketch and description on the back of the photograph are used
as a guide.
The prick points on the negatives are marked with triangles in India
C. Pricking of the Tie Points
It follows from the principle of constructing a phototriangulation net and
from Fig.78, that the tie points a and b should be selected on contour lines
I lying
ion the center line of the triple overlap of the
' photographs of one flight strip
land as far as possible from the center lines of the photographs, but not closer
than 1 ca froo the edge of the photograpb (Fig.79). On the end photograph 1
_
and
these points are located at approxi~ateiy equal distances 1 frau the edges of the
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photographs.
The tie points are pricked on each iQdividual flight strip independently, and
are not repricked on the adjacent flight stripa. On the negatives they are en-
)
14
16. .
" . _;
20
2'
its
circled in India ink.
d. Pricking of the Transformation Points
The transformation points are also narked on the contour points of the photo-
graph, located at the center of the quadruple (end and side) lap of four adjacent
F i g. 7 9 - Tie Points
photographs of two adjacent flight strips (Fig.64).
If four such photographs are placed side by side, as shown in Fig.80, then the
transformation points must be selected at equal distances 11 from the end edges of
the photographs and at equal distances 12 from the side edges of the photographs.
The rectification points are pricked on both flight strips, when viewing them
:)) simultaneously. They are encircled in India ink on the negative, with the sub-
The total number and position of the points pricked on the photograph is shown
f
in Fig.81. In addition to the points given in this general scheme of their loca-
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o ___.. _.._... _..........- _ _
--~ bons the
points of control are a ri-
ground ~.so pricked on a few
photographs
2j4 i53. Plotting the Initial Radials
~a te ats iii iihIcb the central points or the nadir `
.rem is __ on
po~"ta are not
the adjacent.photographa, the initial radials are plotted "artificially".
Fig.80 - Selection of Transforma- Fig.81 - Location of the Points of
tion Points the Phototriangulation Net on the
Photograph
; Artificial drawing of the initial radials is based on the fact that a straight
line on the ground is also represented by a straight line on the photograph; con-
,
sequently, if the terrain is flat, contour points lying on a straight line on one
Fig. 82 - Plotting the Initial Radials
photograph must also lie on a straight line on the other. In broken terrain, this
postulation is valid only for an initial radial
passing through the nadir points of
'both photographs. If such straight lines, containing corresponding contour points
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0 , r-_.-__.___.---- ._--._. -_ .............
-j pass simultaneously through the
nadir poidt (or the central point) on each of the
-i phat aigrapha , then . these _s tra ight 1 incs
4.~
will form a at.ra.ight _.line _ in~srcmc~t.pg_ the
Fig.83 - Plotting the Initial RjIuLdials by Successive Approximation
~4---1nadir points (or central points) i.e., they will for the initial radial (Fig.82).
?1: -
a. Plotting the Radials
!;}_.
1 First case. Cne of the nadir points (or center points) is identified on the
adjacent photograph.
point I' and coinciding with the line xx, this point is then identified on the sec-
ond photograph. Placing a second strip of celluloid, with a straight line etched
celluloid.
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Let the central point I be identified on the second photograph, while the cen-
tral point 2 of the second photograph does not coincide with the contour and can-
!not be pricked on the first photograph. Then, taking a strip of clear celluloid
"t ;film with a straight line xx etched on it by a fine needle (Fig.82), this line is
I
~) ;then superimposed on the pricked central points 1' and 2' of the second photograph.
,~ All the contour points of the photograph coinciding with the line xx lie on the in-
itial radial 1' - 2, After selecting the contour point a' most remote from the
S '1
it, on the points 1 and a of the first photograph, the required initial radial
is obtained, which is marked on the edge of the photograph by a prick through the
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_. -
Second case.
The nadir
points (or central points)
3*ceat photograpl~___
are not identified on ad-
In this case, the initial radial is determined by the method
of successive a
-
p
proximations.
The line xx of the cellulod templet is placed on the first
photo-
graph in position I (Fig.83) and is matched with the prick of the
central point I;
the contour
line of the
Fig.84 - Tracing the Initial Radials on Rotating the
~ Photographs
through 90
1Cl
t o --~
the contour
point a is selected in the region of the central point 2, on the
assumed
initial radial. In this position of the templet line, we select on it
point b in the region of the central point 1 or, preferably th
___
e
t
`i for partfh i
o tenitial radial which increases
tions.
the accuracy of the determina-
Setting tiLe second line xx in the positier, I' on the correspondi
'
ng
,
b' of the second phatograpll, we note that the d points a
ash does not pass through the cen-
tra 1 point 2. We then rotate the line around
point b' into position II' to its co-
i
id
nc
ence with the prick of the central point 2, and mark t
~ he new contour point
on the templet. Then, he line xx on the first photograph is rotated about the
;central point 1 into the position II, to coincide with the contour point c. The
1
C,
contour point d is then
l
se
ected
.
The line xx is rotated cn the second photograph about the central point 2 into the
position III', to coincide with the point d, on which, in the region
of the center 2,
ine nowd
coincies with point b, on which a new
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.. __ ___?r .T_.---- _
q
a new contour point a is selected. Next;, the line xx on the first photograph is
J rotates.__sbswt.. t~.e. cc traJ. _point_ 1 into position_ iIL aatckst_sc _
_1 point e. This rotation is, in practice, o small that the point d does not lease
-~ the templet dine. This results in a '
position ui which the line xx on the first and
each photograph by a prick through the celluloid.
i
b. Stereoscopic Plotting of the Initia Radials
The stereoscopic plotting of the initial radials gives wore accurate results,
14
second photographs passes through a aeriep of corresponding contour points d, k, e,
(d', k', e') and through the pricks of this central points 1 and 2. These lines are
consequently the sane and, since they pass through central points (or nadir points),
they are initial radials. The initial r4lial so obtained is noted on the edge of
16 -
,.', --4 ------- I__ -
since tde stereoscopic method
H
I wvuocuiar-.
in For
i
j
2 of one
j i
I
stereoscopic
flight strip
'and are placed
the
under the stereoscope
f
of
observatjon
plotting of the initial
are rotated through 90?
considerably more
exact
than
the
radial, the adjacent photographs 1 and
with respect to the normal position
position shown in Fig.84.
In this position they are viewed
and shifted ntil the images of the two
merge into one distinct stereoscopic
the
earth' s
aerial photographs
image. In this position of the photographs,
surface will be perceived as a plane.
If the photographs are then superimposed with fine lines
traced on glass or
(rlexiglass plates (Lobanov rulers), these dashes will likewise be perceived stere-
oscopically with respect to the contours of the photographs. Thus, if the line on
the left photograph passes through the contours al,
on the right photograph does not pass through these
respect to them through a certain angle y, then the
i perceived not as lying in the apparent plane of the
bl, cl (Fig.85), while the line
contours and is rotated with
line will be stereoscopically
ground, but inclined to it in
' The principles and sethods of stereoscopic vision are discussed in Chapter VIII.
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ade to peas ^-
through the pricka of the nadir points (or the
central points), then the position of the
lies will gi,e the required initial radial,
whi4ch is then pricked by a needle through the
special openings K on the ruler (Fig.84).
as shown in Fig.87.
The radials must be fine (0.1 mm) and must pass exactly through the centers of
the pricks of the points. At the central point, the photograph reference number
is
entered.
In accordance with the general scheele of constructing; a phototriangulation net
(Fig.78), each succeeding central point (e.g., the center of
photograph 3) is de-
I termined with respect to the preceding ones (centers 1 and 2) by resection along
three radials (at the points a, 2, and b) on a single straight radial (2 - 3) -the
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, rotated instead,
l
marks are used.
To obtain in graphic form the radials from the central point
points
pricked
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to all other
all points are caref
ll
u
y copied
on
,
;encircled with a pencil line, and marked with subscripts as on the hoto ra
P g ph. Then,
I from the central point, the radials are traced to all other points b a a
by c librated
ruler, with India ink or ordinary ink,
,!
the photograph,
tracing paper
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-i initial radial. For this reason, the projcedure of graphic construction of a plane
L.pkOLOtriangnlatiQII rkombic net is as foUiws.
---1
__J On a certain coai.crcial base (tracing paper, Goanak paper, Astrolon), on which
(:
the construction is pricked through to the points or the vets, the ft re~ial
"
- -
.
I I ..
._ y
Fig.88 - Constructior. of the Rhombic Net
tracing of central radials is placed. This is superimposed by a second tracing, in
such a way that the corresponding initial radials 1 - 2 of the two tracings will
coincide (Fig.88).
The distance between the central points of these tracings, which is termed the
first base b1 of the net, determines the scale of the entire net. If, after match-
ing the first two tracings along the initial direction, the second tracing is
shifted along the initial radial iithout distrubing the coincidence so obtained,
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r . .~
-_~ then the base will be shortened (or lengt~tened); at the sa~se time, all the triang es
2 -1
4 reduced or enlarged.
third tracing is matched
radial 2 - 3 (position
net. In so doing, the radial
tracing.
with tie initial radial 3 - 2 with the corre-
I
3 " , Fi.88) which has already been obtained in
3 - a and 3 - b need not necessarily pass
through the points a and b previously obtained. Since these directions ist pass
through the tie points a and b, the tracing 3 is shifted along the superimposed in-
Ylfi__i
!itial radial 2 - 3, moving along the rays 3 - a and 3 - b, toward the points
_.1
12 _
1 a .
If;
I formed ~
by the resections at the remaining points of the net will be ,proportionally
Is this way the selection of the
struction scale of the net.
value for the first bnse deter lm es t e con=
After laying the first two tracings,
the positions of points a and b are ob-
tained at the intersection of the correspsonding radials, which positions are neces-
sary for determining the position of the third tracing with respect to the first
_j two, and the initial radial 2 - 3 on thk central point of the third
I( t
-4 The
-4 sponding
!a and b, until they coincide. If the ray 3 - a has been made to pass thrcugh the
!point a(always being careful to
prevent the
o!mittsl radials from be
i
.
cm
ng separated,
, and being sure that they remain superia~posed), then, as a result of the existence
Hof errors in the radials, ray 3 - b may perhaps not pass through the point b thus
forming a small triangle of error (position 3 in Fig.88). The altitude of the tri-
i
tangle of error, measured from the base of its side along the lateral radial 2 - a
;must not exceed 0.3 mm. If it does, the existence of a gross error in the radials
'must be asau~ed, which will have to be corrected by verification, first of the in-
itial radials and then of the radials to points a and b.
I If the altitude of the triangle of error is within the permissible range, the
;third tracing is shifted along the initial radial, with the coincidence of the in-
itial radial being maintained under all circumstances, to the position 3, until the
ray 3 - b passes through the center of the triangle of error obtained in the po-
160
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0 --
- sition 3'. In this case, the
7
~__ trian_gle of error arises
triangle of1error at point b will be halved, but the
at point a. These connected trianglea of error at
~!points a and b mmst be equal in size, but opposite in direction i.e, w
_.r _ with respect
to the ateral-rays 2 a and T- b;e vertexes o t e rlan~ s~must a turned
in opposite directions
neCtlon must not
stances coincide.
(position 3). The altitudes of the triangles after the con-
exceed 0.15 mm. The initial radials -~ere must under all circom-
The closure of the
triangles
by rota$ion
f
lithe initial radials, is categorically foridden si
h
nce t
is would bkh
,rea up te net.
18-
8
r establishi h
t
20
e
,
ng
Position of the hard tracing, the positions of the
points
c and d and of the initial radial 3 - 4 are obtained, which are required
for de-
iter~ining the position of the fo
low in f
g "4 ourth tracing. The fourth and all suc-
l
~4-,
_lceeding tracings are laid in the sale way as the third one.
_i This results in a phototriangulation net of arbitrary scale, which is termed a
R
? ; -- .1
"free" net, i.e., one which has not been reduced to the scale of the plotting board
and is not oriented on it.
The points of the net obtained at the intersection of radials and also the
central points, are pricked with a needle into the base, on which a sheet of tracing
;paper has been placed.
At the points where permissible triangles
;obtained, the points are pricked in
the
abase are encircled with a bow compass
r
should be 1.5 ram) ; the
central points
of error have been
center of such triangles. All points on the
(its diameter
in the image,
on reduction
in addition are surrounded by a square, with
a subscript showing the reference number of the photograph, while the ground points
of control are surrounded by a triangle bearing a number or place-name as subscript.
The name of the trapezoid and the number of the flight strip are inscribed on the
i base.
It is recommended that the laying of free phototriangulation nets be performed
on a mounting board with transillumination. Otherwise, especially under field con-
161
of the tracing involving a shift in
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of the Base
i
.-.!ditions where the plan position of points in difficultly accessible areas is to be
_idetermined, the nets of plan phototriangulation are constructed direct4 on the
{
12.
22
. ! Fig.89 - Construction of a Net at the Scale
;.z
plotting board to the assigned
Scale.
The construction of nets at
the scale of the base (the plot-
ting board) is done as described
above, while the position and
length of the first base (i.e., the
first two tracings) must be found
f ran ground points of control de-
termined on the terrain itself
(Fig.89).
The position of the first
tracing is determined by the Bolo-
toy method, i.e., the tracing 1 is placed on the plotting board in such a way that
the central rays to the ground control paints 23, 24, 25, and 27 pass through the
pricks of these ground control points on the plotting board. The position of the
first tracing already characterizes the orientation of the net on the board, since
the initial radials to the adjacent photographs thus are given an accurately de-
fined position.
The second tracing is matched with the corresponding initial radial from the
first tracing and is then moved along it until the radials to points 25 and 27 pass
also the entire net, now has a scale equal to that specified. The technique of the
further construction of the net does not differ from that described above.
through the pricks of these points on the plotting board. Since, in this case,
the resections of the ground control points in the net coincide with the position
of the points of the field control on the board, it follows that the base bl , as
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m=t0.358b_: X2..3 _z_2 r..
'J
r
Ifi where n is the number of bases from snits l
~ to final; mE is the error in the radial
I ~' --~ expressed by the ?alue 4 -5'
R ~s the scale ratio, equal to the ratio between the
2ai:ii
l
Passing now to the construction of a?net on -one side (right), and then also on
_Qt>I?.sAa1 (tbe_ left) to the field
n
co
trol poit f
ns,or exaiple to oint 34 0
.tracings 3 and 4, we may obtain a positioq where the intersection of the field con-
y- ~
. 1 trol - .. _ _. ___ _
point in the net does not co1ncide with its position. on the 6oard-
allowance of the error of closure m so obtained is defined by
0
12J
ph otograph, in millimeters.
?'A. I
;be started from the
[_i The error of closure is eliminated by gradually shifting the tracings in the
~" direction of the true position of the ground control
,2:; i point, but in so doing we at-
" Etempt not to disturb (within the limits of graphic accuracy) t
i he coincidence of the
' jinit.ial directions and the intersection of the rays of the tie points.
After connecting the region of the net on the right side from the first bas
1the e,
''. construction of the net left of the first base is Continued until closure at the
' minor field control points. After completing
the construction and closure of the
net, we prick its points on the plotting board.
In those cases where the extension of the nets is performed
~ on an assigned
scale (as described above for a construction directly on the board
~,: ), the laying must
center, extending the net to both edges. This will result in
the smallest deviation from the specified scale and also furnish proper orientation
of the net. For cases of free net construction
i.e., nets at an arbitrary scale
and with arbitrary orientation followed by reduction on the plotting board t
i he
;laying of the net is usually started from the edge (left); the accuracy of t
Y he net
will be the same in either case.
163
sca
e of the survey and the scale of the ap; and b is the value of the base on the
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.r -
O_1_;; -_-__ _..___ .._ _ ___
K Reduction ay be performed either by~an optico-graphical method, using special
projectors known as reducin
~~ K printers, or by the graphical method.
1211 The principal method used is that ofoptico-graphical reduction.
pv. neaucLlon or uorizonLal rfOtotrlangul tlon Nets
4_i__ ____----,die process -oD ric_ing free nets t~ aca1t aad orienting tttc-bo-or inserting
l
t ii_e_net et between field control points is t+.rmed reduction of phototriangulation nets.
2_I
14 Figure 90 shows a scheutic diagram 4f a projector reducing printer, where 2 is
i
16 the holder carrying the phototriangulatio net (on wax paper or Aatrolon) and 3 is
s -
18 the lens projecting the image of the net,
O_- 13t316 illuminated by the lames, onto the screen
try ;_!I_________. 1. Tie planes 2 and 1 must be para11e1-
~4 UI that case, the ,wage on the screen will
-..:._.,
\ If the position of the screen is
_:8 , ' shifted from position 1 to position 1',
f
Fig. 90
Scheoatic Diagram of a
Reducing Printer
then, as indicated by the sketch, the im-
age a0b0 is reduced to the size AB. The
problem of changing the scale of the net
is thus solved simply and simultaneously
for all points of the net. To preserve the sharpness of the image, the lens 3 must
be advanced slightly.
If a plotting board on which the points A and B (field control points) have
been plotted is placed Oil the screen, then the line AB may be placed along the
line ab of the image by rotating the board on the screen. By changing the scale of
the image still more, the projection of the points AB can be ?atched with the
points A and B of the board. This solves the problem; the image of the net is re-
duced to the scale of the board and is oriented on it by the two control points A
and B.
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0
aalus, 6o reauce the net it is essent al to have not leas than two control
2 I To lay._ x _ nstL,_ the P 1QtQgrephe _.*re s_o selscte _. e_ minor f i~ld _con -
Jtroj points are located along the edges o the net (for soae interaedi'ato nets or
~ ..---._,
....--- - - -__
flight atr i _ _.__..~_....__.._ _ 4__ _
- ps points in conmon with ad'a ent nets are Sometimes used as minor cone-
1
12 _;
20+
_I 7-
1 -S
trol points).
After matching the minor control pouts of the image and of the board, all
pointa of the isiage of the net are transferred to the board with a ahar
p hard pencil,
Fig. 91 - Popov Reducing Printer
the screen
1 of this instrument, in contrast to the dia-
gram (Fig.90), is fixed, and the scale is changed by shifting the holders 2 with
shown in Fig.90. However,
i.e., all the rectification and central
points are so transferred.
The nets can be reduced on any pro-
Ijection instrument (reducer, rectifier,
projector) which allows the scale of the
image to be changed while maintaining its
sharpness and assuring similarity of the
image to the projected net; this latter
condition requires that the planes of the
negative and screen are parallel. How-
ever, the transforming printers and the
projectors now in actual production have
holders that are too small co accomodate
a net, and this requires a preliminary
photographic reduction of the net, while
still preserving similarity. This in-
convenience is eliminated in a special
instrument, the Popov reducing printer.
The Popov printer (Fig.91) consists of a projector whose schematic diagram is
165
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the screen, and by shifting the lens 3 to maintain sharpness.
subject to reduction, are pricked into the tracing. The control points 1 and 2 are
connected on it by a straight line which will serve as a base. In addition, to ob-
taro optimum intersection of the points near line 1-2, the arbitrary auxiliary
point A is selected on the tracing and is connected by straight lines with both
control points. For long nets several auxiliary points are selected.
0
STAT
- ahif~i
(change of scale while
preaery,ngcharpHass) are
esde. -autonat~,cally~ .using.
the special device 4, termed a rhombic sc*le inverter which is actuated by the hand-
y
_I wheel 5.
The holder consists of a frame with ? cut glass plate 60 x 60 cep, on which the
net is placed, covered by a cover glass, mnd illuminated by the electric laps of
Fig.92 - Gr*phic Reduction
the illuminator 6. The scale factor of the instrument can be varied from 0.6 to
2.55 m.
; 4.
56. Gra
Graphic reduction is used in field work when no reducing printer is avbilable.
:The principle of graphic reduction consists in the intersection of points in the
net with the control points, i.e., with a certain assigned base.
,, : Let the problem posed be the reduction of the free phototriangulation net I on
the plotting board by the control points 1 and 2 (Fig.92). The points of the net,
is Reduction
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_
The tracing is then placed on the board in such a way that the 2-4
points 1 of the
traeing..and the-- board..eoincide, while i
}
-t . the+.rial 1 - _2 .. Hof thy-'tsacing-.~.e_
_. through point ? of the board. After oriedting the traci
ng in this way, all of its
--
points-. the auxiliary point A are pricked auto the board and the radial drawn to
again pricked on the board. The new pricks are then connected with
18 point 2. The
intersections of corresponding radials fuknishes the wanted position of t
he points
them from point 1,
10
The tracing is then advanced along line 1-2 so that the control
12 points 2 of the
tracing and the board coincide and the ratIial 2 - 1 of the tracing passes through
14
1 of the board, after which all points ofithe net and the auxilia
16 - ry point A are
of the net at the scale of line 1-2, on t1ie
22 j plotting board. The saw intersectim
t
his obtained on the board for the position of the auxiliary point A.
The points of the net lying near the line 1-2 intersect poorly with points 1-2.
G
.
To obtain a reliable intersection, point A of the tracing is matched wi
8 t6 the pos i -
tion of this point on the board, and the tracing is so oriented that the
''`I points 1
._ land 2 of the board lie on lines A-1 and A-2 of the tracing. After
~ pricking all
_J points of the net in this position on the board, the new pricks are
r '~ ! connected with
point A. The radials from point A to the points of the
net yield reliable inter-
sections for such points.
.; f; I
i
t
(
t
1, 7
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-
1
j? e
I
CHAPT*R VI
TOPOGRAPHIC INTERPRETATION
Basic Principles of Topographic Inte.'retation of Aerial Photo r hs
_ = Oae of the basic processes in making a topogr hic ^
fro i aP ap ao the information
~i ._..jgathered through aerial surveys is photogtsphic interpretation;
-~ is other words the
i! 1j recognition of the characteristics of the area as recorded on the aerial
photograph
f~ _and which are vital for oakimg a ^ap of the area. Depending on the
-t purpose for
i;- lwhich the oap is intended - for topographic, ground surface, eolo
' 6 gical, agricultur-
#
l
a
, or any other
Purpose -the corresponding
opo-
:, ;graphic, surface, etc. In this study, intended for topographers only
. y the b
a
C
si c
P
: principles of topographic interpretation are discussed.
:( As is known, the various elements of an area such as:
roads, forests, cul ti-
Jvated areas, populated areas, etc., must be indicated
I
on a topographic map. All
, these topographic details must be placed within their respective positions and
boundary limits on the map, and must be given identifying marks and designations.
!' For example, in drawing a road into a to o r
P g aphic map, it is absolutely necessary
!;" _i to describe the character of the road by an '
Y identifying symbol which could indicate
= .}whether the road is an I expressway , an improved dirt road, aside road or what other
'"' JtYPe
and
l
~
a
so to indicate the populated ar
{ egg
`?/ Ioutlines of a
forest it is
interpretation will be called t
which it joins. In drawing in the
necessary to indicate the type of trees
d
an
to identify
`.'clearings and burnt over areas. Ail the other elements are also described in ajj-
~.'- flat bre
kd
a
owns, The number of separate elements as well as the degree of detail in
168
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.Y-
i data. Therefore, topographic surveyors provided with aerial photographs, go over
the photographed terrain, marking all elemental boundaries required for map prep-
aration on the prints. He also marks on the prints
objects which were not recorded
by the photograph and inserts the names of places. In practice the
! ;~ I field survey
is usually combined with a photointerpretation. For example, aerial photographs
!
at a scale 1:50,000 to 1:70000 000 cannot be interpreted to show, nor is it possible
!, I
._~to identify on them, lines of communication. It is
i.;_ difficult to determine the na-
! Lure of a forest, etc. Even with prints at a larger scale it is i ssible to
~ es-
_ tablish the type or the functional use of a photographed building. Is the building
',:t --
-. of stone or of wood? Considerable additional data has to be secured.
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which each element is described depends on the scale of the map being prepared and
--- , a
..oa the_natural features of the area. For example, a foot trail does _not _hare such
(.. significance in the Central European region of the Soviet Union but is very iapor-
.... ......
j~ i tact in the relatively inaccessible regiobs of the North and Far Eaat. Thevphya.-
_ cal elements, entered on the topographic map, are defined by means of a specially
1(.._
...~ developed key chart; by the naming of populated areas, by boundaries and landmarks,
1
by waterways, etc.
Many different objects are recorded on the aerophototopogra
hic surv
h
p
ey c
art
,
itt _1
e objects which have to be drawn into the topographic map. This great detail recorded
1c.
_.j on a photograph raises the problem of defining where certain parts of the landscape
appear on the print and for determining their characteristic features. If this
2i
problem could be solved completely in studying aerial photographs, the field survey
,! I
!would be limited to compiling the names of towns etc., and all of the inte
?'. t rpreta-
! Lion would be done with instruments. However, the small scale of aerial 2r ~ photographs
and the necessity t terrain which cannot be recogni or re-
to secure .. data ,~ on ? the ~ terrain which cannot be recognized d or re-
corded by an aerial photograph, require additional field surveying to obtain such
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58. Identifying Features, which can be Used in Photointe!retation
r
!. All identifying features, used in laboratory interpretation of aerial al pho to-
t . lgraphs, are classified into two groups
the f'
,
Irst group co~prlsing direct data and
~ _.:4ti1e second group indirect data. The first
?_.~ group, as used for the photointerpretation,
~;,.~contains the data that Positively identify the object in
1
--
_ J question, its shape
siz
,
e
,
re
ative
) 4 ,osi tion of - obj ect wi th respect to the surrounding obj ects
J the interpreted clas-
) ;; _iSi fi cation of the landscape as a whole, and to s
upplemental data obtained fro exist-
I._"ling statistics and descriptions.
--3
(.4 The shape of an object is one of the most iaQortant facts in identification.
Y__,~ a object is presented on prints without any distortions of its shape when the opti-
Y'? _~cal axis of the caioera is exactly vertical and the object is on a horizontal plane.
Y' }'or exau0ple, buildings appear on prints as
rectangles , roads appear as developed
i,~ . ~ibbons which represent improved
highways if they are rather straight
i ~ and railroads
:j ~ ~f they are
g
nes, etc. If
?,
~he optical axis Is slanted, the shape of the image of an
object on the photograph
;;: differs from the actual shape.
his distortion is very small on prints used for m
:G baking. The
?'A5&&
-.
of an object, however, has a great influence on the ch
ange in
hape of an i
mage. This is so because the higher elevations
of
an object will be
r r; on the image (relief distortion),
? jdistorted as in the case of an aerial photograph
!: f a town, the high buildings may not only make the adjoining streets
appear narrow-
? r than they are, but may in places hide the street completely
; d-i sable to judge the shap - therefore, i t i s
a of a high building from an aerial
PhotPgraph only on
? the basis of stereoscopic examination
I (Sect.69), when the interpreter is able to see
so~ he depth of field of an object, with the aid of a stereo Pair. It is often possi-
''' _ ~le to draw correct conclusions as to
the shape of as object ho. only one print,
-~ut in this case
the shadow thrown by the object, as recorded on the
real assistance, print, is of
170
..:
1-----ate'., +?~u color. the indirect group refers to data that establish the
l
qu
R
te Straight.ivers and streams
~ appear as
windin
li
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focal length of the camera and the altitude of flight during photography) and the
C
approximate dimensions of the actual object, it is easy to determine the actual size
._a of the object as shown by the print on a reduced scale. This permits amore accu-
.' _(
rate description of the object to be interpreted. Thus, e. g. , rectangles on the
prints represent individual buildings, gardens, agricultural areas, and some other
4:
`elements of the landscape whose dimensions can be calculated by their representa-
1c '
_J tive size. At the same time, on large-scale prints (1:5000 to 1: 10,000), individual
_ i buildings often appear larger than large agricultural areas on small-scale prints
(1:50000 to 1:70,000).
9
One of the important factors of interpretation is the height of objects, which
y% l
. _ ' is determined by their shadows or through stereoscopic examination of the prints.
,.
I To determine the height of an object by its shadow, it is important to know not only
i,.
,the direction of sunlight at the time the photograph was taken (which can be deter-
. 1
!mined by the direction of the shadow) but also the height of the sun above the hori-
1
surest way to fudge height of objects is by stereoscopic examination
Color of an object is a very important factor in interpretation or, to be more
i
. specific, the ability of the object's surface to reflect ranges of the color spec-
true. An object absorbs some rays of the sun and reflects othe
Th
rs
e refletd
ce
sultant effect on the film is well known (Sect.ll). This light-sensitive surface
STAT
171
~zon. It is definite that any variation in the height of the sun will cause a vari-
1
ation in the length of the shadow of an object. This makes it impractical to judge
I shadow. The
J of a pair.
rays have a certain range within the spectrum, giving an idea about its color, by
its image. Any light reaching the light-sensitive emulsion of a film first passes
through a thick layer of atmosphere and then through the camera lenses. The re-
For a comprehensive interpretation, the size of an object is a desirable cri-
ten~ion. Knowing the applicable scale for the print (the scale being governed by the
height by shadow alone. Furthermore, in many cases, high objects do not throw a
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sity on the composite image. This makes it possible to judge the color-reflecting
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172
{
p
ble to interpret with greater accuracy.
'. ,- !
covparing the aerial photographs, with respect to their geometric (shape and size)
i and optical (tone qualities) characteristics. with develo
ed samples it is possi-
I
invariably will study its geographic characteristics to be prepared for the type of
_,,%t
- features he might have to face during interpretation. Data obtained from rosters
'~,, -
and lists in larger towns of the region and lists of names greatly facilitate the
process of interpretation.
-l populated area indicate the presence of a well at that point, etc. In addition,
j supplemental practical data are of importance as is also a geographic study of the
I entire terrain. For example, a topographic surveyor working in northern regions
Factual data of interpretation give a basis for indirect data. For example,
i a road ending at a river and continuing on the other side of the river indicates
the existence of a bridge or a ford, numerous paths converging at one point in a
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._. ability of the corresponding object.
:_i different coefficients of color sensitivity. d b usin tical filters
an by g op of differ-
_-i print. this variance of tone, in photographing the same objects, is advantageous
.__j and tones of shading. For example, when using panchromatic file, water surfaces
.__1 appear as dark tones (appearing in light tones on the negative), whereas infrachro-
I G _-
vatic film will cause these save water surfaces to appear in light tones on the
1 .-i
I ent color, the isiages of variable objects on the prints are not reproduced in stand-
a- for interpretation, since it permits better distinction between objects, which
'! -
reacts differently to the different rays of the light spectr. Thus the variable
tpaantity of the reflected rays and their spectral eoaposition create a variable den-
would be reproduced in the save tone on one film but not on another.
The ability of terrain features to reflect colored light, the spectral sensi-
- tivity of film, and the use of optical filters were used as basis for special refer-
~:
ence charts published, which are composites of samples for photointerpretation. By
;:: i
By using different types of 1l, which have
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The Sequence of Steps in Photointerpretation
the day's entry on the photographs permanent by going over them with India ink. If
Prior to interpreting an aerial photograph, the topographer makes a study of
the region fro. literature data and deteratines the basic characteristics of the re-
- '" gion he will be confronted with during interpretation. If the scale for the ^ap
'... ~j
j coeposite is to be larger than 1:100,000, the topographer will make a detailed ater-
12-I eoscopic examination of all
!surveying. This route at
printa where in
j r ` l of elements and
7(may be accurate
the interpretation is being made from contact prints or from enlargements, each
start of the work with the boundaries of the +ark areas,
which progress approximately along the center line up and down and across the com-
i
:l1
,, distinguishable
these photographs and which are needed for making the topographic
lines, wells, bridges, etc.). The surveyor also draws in the
~. -~tablished boundaries of elements which includes the collected list of pertinent
posite. The interpretation is done along these working areas of a print. Simultan-
eously with plotting the interpreted objects on the photograph, names are inserted,
photographs and ?ark them with a route for future field
include all populated areas and all sections of the
by instruments will be uncertain, such as boundary areas
also their composition.
enough,
certain areas for which photointerpretation
still absolutely require a field survey.
Field surveying consists in recording objects on the photographs, which are not
jmap ( couni cation
names. The elements which were not distinguishable are drawn on the photograph,
es-
fixing their location by distances measured from the distinguishable objects.
the course of rivers is indicated, and all other specified data are recorded.
t
J
All identified objects are drawn into the photograph in the field, using desig-
mated key charts. Every day, after returning from the field, the topographer makes
hotograph is marked at the
When making a map
a scale 1:10,000 of an area
which
is difficult to pene-
trate, it is senseless to attem
t a field
v ey b the abov h d
t
I
---
, e .e
o
n such cases,
p
!after a comprehensive study of the prints obtained, the topographer goes into the
44
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11
field with only the prints which are eost representative of the general area. After
.!the field survey, these prints can be studied as standard exa.ples and.. used as refer-
_-.1 once indicators for an interpretation of the rest of the prints. In this case, geo-
r f
. igraphic observations recorded in report f?rm are of great assistance.
E.4
i
i
I
.
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1;
CHAPTER VII
TOPOGRAPHIC_ GEODETIC 11ORK IN VERTICAL- COMBINED
AEROPHOTORUAV.EYING
60. Tying in Aerial Photographs on the Plan
Tying in of aerial photographs consists in defining the plan
position of
sev-eral contour points of the terrain which can be recognised on the aerial photograph
(identification points).
The number of plan identification points and their distribu
tion on the photo_
graphs depend on the scale of the map being prepared the scale of flight, the pho-
togra?etric method of filling in or densifying the control net
that is being used,
and also on the physical, geographic, and economic characteristics of the terrain.
To compute the number of identification points, the formula
for cumulative errors
is used which, for a plan phototriangulation series, takes the
form:
?E
m = ?0.35 Rb
n3 + 11.3 n + 6.5 1 + 33
II
(27)
iwhere m denotes the mean-square error in the position of me "
dean points of the pho-
totrian
l
i
gn
at
on series at the scale of the ^ap; R is the reduction
the scale of flight to the scale of the map); b is the size of the base at the
scale of the photograph; mE is the mean-square error in one direction; and a is the
umber
f b
o
ases between identification points. The allowable
error in th
of points on the plan is given in the resPectiye east a Position
ructions so that, in computing
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t (.
the density of the geodetic base, it can be assumed that ita ^
etude is known.
`Than, knowing the distance b between the principal p ointa o
..f the photogra~6a, the
scale of the map being cospiled, the scale of flight, ... ...... . .
and the mean-square error in
one di rection ~, the equation
n3
9 .2 p2
U R2 b2 net
(27a)
t ,_
-will yield the permissible number of photographs between lan cont
t ( ~ P rol points, and
~oonsegaently, the distance L between bench marks. This distance is
I :-~ - ~ obtained from
-the eguatlon
%i
L = B (n-1) (27b)
+ 11.3n + 6.5 1 + 33
where B is the length of the photographic base on the terrain.
61. Drawing a Plan for Tying in Identification Points
Bearing in mind all of the above conditions, a plan for positioning geodetic
tie-in contour points (or identification points) can be drawn up.
The Planning is carried out by rough mosaic mounting of the aerial
photographs
on which all known points of the geodetic grid are entered (approximately or exactly,
depending on identification) along with the proposed plan identification points.
The plan identification points are usually so selected that they fall in the
center of the side lap between flight strips; then each identification point can be
used for two flight strips. ThR plan identification point mast not be located
along
the center line of the photographs since, in that position, it will be
very diffi-
cult to incorporate into the phototriangul ation grid.
In planning, the topographic features of the terrain must be taken into
con si d-
eration to draw up a project easily reduced to practice. When
marking off a point,
not only the ease and reliability with which it can be identified but also the
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PROVISIONAL P4 RK
OF CENTRAL PRINT
? PLAN IDENTIFICATION
POINT
~zanaard scheme of Locating Plan Identification Points
on a Trapezoid at a Scale 1: 25, 000
C
A
possibility of deteraining its geodetic coordinates must be considered. Therefore,
!in drawing up a plan, stereoscopic methods for Viewing aerial photographs area re-
4_4 P
regniai te.
E..
The photographic representation of contour points Bust be clear and sharp.
-.( Die following ^ay be selected as identification points: crossings of roads or
l o __._I
paths, intersections or corners of tilled fields, foundations of buildings or struc-
12 ._
(turea not covered by shade, unshaded bases of isolated trees or bushes, etc.
II R
,_~ Selection of identification
points on poorly defined contours or contours that
dare circular in fore should be avoided since they cannot be accurately identified.
1L
?
s
?
O
A
iFor example, identification points in ravines, among trees and bushes, in the deltas
r '
. Hof rivers
or brooks, or at the crowns of trees are unsuitable.
I . From the viewpoint of geometric location, the identification points should be
I
positioned so that they can be intersected by no less than four central points of
the Photographs, i.e., they should be in the center of the zone of side lap of ad-
jacent acent flight strips, and should preferably be in zones of triple end lap. The den-
sity of identification points will depend, as indicated above, on the scale of
the
map and other conditions. Thus, e.g., for a map at a scale 1:100,000, the intervals
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9 urn. Aerial photographs with insufficient end lap and toning should be tied in with
Sadditional identification points" (Bib!. 17 and 18).
After a plan is drawn up, all points selected for t
i
i
d
y
ng
n an
all behk
nc mars
1
are plotted on the reproduction of the rough mosaic and designated by conventional
"
symbols.
betaeen plan identification points along the line of flight may be as large as
60-100 1cm, while for maps at a scale 1: 25, 000 or 10, 000 (Fig. 93) it has been
estab-lished that "plan identification points should be located at intervals
of 4.5 to
The aerial photographs and the reproduction of the rough mosaic, with the se-
lected points narked on it, are turned over to the personnel charged with tying in
the aerial photographs.
is
ii 62. Performing Topographic-Geodetic W rlc for Tying in Aerial Photographs
The task of tying-in aerial photographs to points of the geodetic bases consists
of the following operations:
1) Identifying the contour points (identification points), marking them on t
8 he
aerial photographs with pin pricks, and sketching the identification points (con-
tours);
2) Fixing the identification points on the terrain;
3) Topographic-geodetic surveying to determine the plan position of the
identification points.
Before tying-in is started, a thorough reconnaissance of the terrain should be
made to confirm the choice of geodetic methods and to check the disposition of
planned identification points.
. Identifying, Pin Pricking, and Sketching Points
The process of identification consists in collating and matching identification
points with the corresponding points on the terrain, of marking them on the aerial
photographs with pin pricks, and of sketching their position. These are all ample
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c;
but very important operations.
The process of identification requires great care and full
attention, since
.;the possibility of oversights in identification must be avoided at all cost. hi in-
correctly identified point, even if its geodetic coordinates are correct, is con-
pletely useless.
Identification on the terrain should be carried out with an error not exceeding
)2
6
the graphic accuracy of identification on the photograph. It may be taken for
S C'
i%
i'
Fig. 94 - Marking of an Identification Point on a Photograph
and its Contour ketch
granted that a pin prick can be made on a photograph with an accuracy of 0. 1 yam.
i, Therefore, errors in identifying contour points on the terrain should not exceed
!0.1 m? relative to the scale of the photograph. When identifying a point on the
(terrain, the topographer should carefully compare all contours on the photograph
, !near the selected identification point with the terrain to make certain that the
`point he is about to pin-prick on the photograph is the point he is sighting. Such
a comparison is mandatory, since one photograph may contain several identical con-
tours, so that the wanted point can be positively identified only by comparing the
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A
image of the contours next to the point with the terrain. After the contour of ter-
rain selected as an identification point has been positively identified by comparing
the terrain with the photograph, the point is pricked on the photograph. Soee kind
of fire backing such as celluloid should be placed under the aerial photograph when
pin-pricking points to ensure proper coincidence. A thin, sharp needle should be
used so that the pin pricks are round, small in diameter, and visible against the
light.
The pin prick should be encircled on the reverse side of the photograph and
signed. Here also a sketch is entered of the identified point at a scale larger
than that of the aerial photograph, for
easy reading. When sketching a contour,
p the image of the contours on the photo-
7 - _\ should be used as guide and the ter-
PLAN 1.5K - --f
PROVISIONAL MARK
O - "IDENTIFIED"
- DITCH
Fig. 95 - Marking an Identification
rain as a control, to achieve maximum co-
incidence with the sketch of the aerial
photograph. Nhen hatching the sketch of
the contour, the relative degree of dark-
Poi nt on the Terrain
ness of the photograph should be retained.
Terrain contours which do not show up on the photograph should not be shown on the
contour sketch. Brief explanatory descriptions should be made on the contour
Fig. 96 - Digging for Reference Marks
sketch, e.g.
(Fig. 94).
corner of a field", "bush", "cross roads", "corner of a house", etc.
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The contour sketch should be drawn with an ordinary black pencil, clearly and
accurately, indicating the date of identification and the name of the sketcher.
;Careful and accurate sketches of identification points are helpful as a control of
identification and in transferring identification points from one photograph to an-
other.
I . _ib. Marking Identification Points on the Landscape
i
J
2t, E
i
f oral
2,:. I
Ication
Identification points are marked on the landscape with a stake about 1 ^ long
:and 0.1 m thick which is driven into the ground to a depth of 0.6-0.7 ^. A spot is
smoothed off
j
point
on the upper part of the stake, and the name or number of the identifi-
is written on it.
Identification points are
triangle with
also marked by ditches dug in the form of
1.5 ^ sides or a circle with a radius no smaller than
an equil at-
1 ^tFig.95).
The ditch should be one shovel-width wide and deep (0.2-0.3 m); see Fig. 96.
(The earth removed from the ditch should be piled outside the ditch so that it does
pot interfere with the setting up of the instrwsent.
I
i 3
Various methods of topographic-geodetic measurement are used depending on ter-
' rain conditions.
A surveyor's stake may be placed on the identification point to facilitate
Sightings from other points.
i
I If these reference marks must be preserved for a long time, they should be re-
~inforced in a more permanent manner.
I
I
pC. Topographic-Geodetic Measurements
The analytic grid (small triangulation grid) and the graphic (geometric grid)
most widely used for locating identification points when mapping open or semi-
(concealed terrain, and the transit traverse is primarily run through the concealed
terrain.
i
Combined use of both these and other methods of tying-in are often met in
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4
(p i
practice. Constructing a control survey net by graphic methods is permissible only
for maps at a scale 1: 100000.
Since the majority of plan identification points are isolated points, it is
-'Rost convenient to locate then by direct or reverse intersection with triangulation
i..
1?
iditional geodetic measurements.
ipoints (Fig. 97. )
However, identification points cannot always be obtained directly by tri la_
jtion or intersection; in such cases some point near the identification point must be
iselected and the identification point must be tied in with this point by i making ad-
s
I
(.
\
1
DIRECT INTERSECTION G's
REVERSE INTERSECTION
Fig. 9 7 - Locating Identification Points by Intersections
, w
irect measuresoent
Hof the line to the identification point the
so-caller, tying-gin by points (Fig.98).
This method may also ue used when some point of the
e
d
ti
g
o
e
c gridt b id
cannoeenti-
/ ,
:1 jfied on the aerial photograph. In such cases, the known contour adjacent to the
Jt which cannot be identified is also tied in by a point.
Vhen direct measurement of the distance to the identification point is i s-
/. fsible, the distance can be determinea geodetical!y by constructing a triangle and
jmeasuring the elesaents necessary to determine the plan position of the identifi-
!cation point.
,? i
As noted above for con 1 d
ce
;run.
IDENTIFICATION
Thus, e.g., the polar method of tying-in can be used
ith d
a a terrain, transit or tachymetric traverses
Tachymetric traverses for tying-in identification points
are
are run for small
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Fig. 98 - Polar Method of Tying-In
scales of photography (1:50,000; 1:100,000) or for cases where it is difficult to
measure lines of the strip, e.g., when the land is concealed, intersected, or swampy.
Transit traverses are run:
a) Between two geodetic points, in the fore of separate elongated traverses;
b) In the for of a system of traverses based on geodetic points and foroin
g
one or several j unction points;
c) In the for of closed polygons based on one geodetic point (Fig. 99)
Q)-?`___
Fig. 99 - Diagraa of Transit Traverses
"Hanging" traverses should not be pereitted, the traverse should be tied into a
geodetic base point or into the extension of an earlier traverse.
Graphic (plane-table) tying-in of identification points is carried out by ex-
panding the geometric grid.
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In analytic, and even more so in graphic tying-in, there may be opportunities
for locating additional identification points. Advantage should be taken of such
t
o^mron methods, indicated above, various forms of tri-
_ay be used, their choice depending on the specific conditions encounterea.
sagular circuits, complete and incomplete central systems, and combined intersections
For the analytic tying-in of aerial photographs, the basic measuring instrument
lerses, allowable errors of closure, etc.), depending on the scale of the map and the
77t
ca to erances (configuration of grids, length of tray-
1 1
~ethod of tying-in, are contained in corresponding
I
i(
fopportnnities if this can be done simultaneously with carrying out the basic task
C R
~lthe tying-in of planned identification points.
.j In addition to
he most c
Jis a theodolite of 30" accuracy; for graphic tying-in, a plane-table with a tele-
j ._f
_Isoopic aiidade is generally used.
The technical methods of making angular and linear measurements for tying-in
l`r .I
Iof aerial photographs are the same as for ordinary geodetic work, while the f
7. ' .
few spe-
J
ific requirements and tec}uii
~tion of
1 7
4) A survey record.
For graphic tying-in (in
control points marked on it;
3) A diagram showing the tying-in
contours marked on them;
2) A reproduction of the rough mosaic with
the rough mosaic):
identification points and geodetic
of identification points.
addition to the aerial photographs and the reproduc-
1) The plotting board with points located on it;
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be consulted in carrying out the work.
instruction manuals, which should
On completion of the work of tying-in aerial photographs, the following mate-
rials should be submitted.
For analytic tying in:
I 1) The aerial photographs (contact prints) with identification points and
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63. Surveying Relief on Photon s, Aerial Moaaica, and Photographs
It is known that a photomap is a mosaic of transfor
d
i
me
pr
nts g1ue4 tiff
o a st mounting; the photographs are usually printed on glossy paper. Such a photomap is
1inconvenient for work under field conditions, so that the photomap is usually re-
placed by a reproduction on sat paper, cemented to a rigid support (aluminum or ply-
~wrood).
aerial mosaic, or photograph differs as follows.
p
g
ap
~' 'weaning that the surrey of relief is based on known contours; se
condly, the photo-
!
7{.
ated points, etc. ), contains contours related to the relief of the terrain, e.g.,
t I
es of ravines, lines of water courses, cliffs, water holes, etc., i.e., elements
i
which form the skeleton of the relief.
The base lines of the relief or its skeleton, i.e., the lines of water courses,
iidges, summits, etc., plotted by the topographer during the plane-table survey in
the form of broken lines, are
# I
2) Data on the margins of the plotting board of the plane-table;
3) Topographic records.
Compared to plane-table survey, in which the topographer enters on a blank sheet
^pf paper contours of his own choice and the relief, the survey of relief on a photo-
raphs, in addition to the contours of the locality (estate boundaries, roads, popu_
i
tease, these lines need not be plotted, since they are already given in such greater
detail on the photograph than on the plane-table survey.
Ina
i
g
ven
The basic methods of plane-table surveying (Bib1.19), in their application to
plotting horizontals and sketching relief on photomaps, aerial mosaics and photos
r;
remain unchanged in principle. However, there are certain
specific differences
~rhich have a noticeable effect on the nature of the work.
Before beginning the field work, the accuracy of the photomap reproduction must
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rriaariiy, the contours of the earth'a surface are depicted on the
hoto
r
h,
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! the trapezoid should not exceed 0.2 0.
!',..j
The photographic reproduction of the photomap should be of a nniforn grey or
must also be checked. Deviations in dimensions of the borders should not exceed
,10.3 mm, while errors in the position of control points with respect to the border of
(1
..`be checked. The borders and the kiloeeter grid of the eoordi~ates can be checked
;with a precision ruler or a beam compass by comparing the dimensions With their
w..
theoretical magnitudes. The accuracy with which geodetic points have been plotted
E
j light-brown shade and of normal sharpness and density, so that lines drawn in by
Scale !:2OCflo
Fig. 100 - Determining the Plan Position of Halting Points by
Measuring the Distance along the Contour with a
Leveling Rod
fi pencil will be readily discernible on all parts of the photomap. At this tile, the
r, elevation control points, elevation reference marks, and the descriptions of their
i
I,
In addition to the photomap, a set of aerial photographs with 606 end lap of
f
d
'position should be checked.
the given strip of terrain is required for stereoscopic study of the relief.
" (64. An Elevation Control System for Surveying Relief on Photomaps
If a photomap of scale 1:25,000 to 1:10000 has 20 to 30 elevation control
;Points which are uniformly distributed over the plotting board, there is no need to
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ROAD
INTERSECTION
_j Fig. 101 - Determining the Plan Position of Halting Points
' .1 by Measurement from Two Contour Points
expand the elevation control net, since this number of control points will permit
'accurate determination of the elevation of any intermediate point. If the dens
and distribution of elevation control points is inadequate, the elevation con
1 trol
tnetwork will have to be densifiea.
s
i
i
UNDER$Ru
RAVINE
..;
~....
I Fig. 102 - Determining the Plan Position of Halting Points
t
b I
n
yersection from Two Points
'. ' iJensification of the elevation network is carried out either by expanding the
geometric grid, or by extending the basic plane-table elevation traverses. The
most convenient method of constructing an elevation grid is selected on
the basis of
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the nuaaber and distribution of elevation control points on the plotting board, and
also on the basis of terrain features (density of forests, irregularity of relief,
,.sand other characteristics). Actual inspection of the terrain along with a stereo-
(H
Iscopic analysis of the photograph will help in selecting the most eonvenieat method
V ._
that the distance
of constructing the elevation grid.
The most con method of constructing the elevation control network is by using
the basic plane-table elevation traverses, whose points can generally be identified
p
s c
l _ J
(distance hetw.. n i.:o..*: c; ...i -
on the photomap.
If it is
2`? ..
directly from the photomap as the
rather than measuring them with a range finder.
impossible to identify points of the traverse in
._can be fixed by the distance measured
2#.._E
2'
2
if
rse, while orienting the photomap by
the plan position, these
with a ruler from a contour point of the trav-
a compass
checking the orientation with other more
distant
In addition to the method described above,
or by the contours on the photomap,
contour points or geodetic points.
many other combinations of methods
pay be used to determine the plan position of points. Several
nethods are given below.
I
1. By measuring the distance along a straight contour from
of the most typical
its turning point
hvi th a leveling rod,
~ontrol (Fig. 100).
.i
using another angle along the line or another contour for a
2. By measuring the distance from two well-identified contour points of the
hotomap with a leveling rod. The point will be found at the intersection of these
(radials, laid off to stale with compasses (.Fig. 101). The photomap is oriented by
I... i y
. Compass or by contour points, using distant objects as controls.
-l `?
I
3. By intersection from two or three well-identified contour points of the
hotomap, which points
4. By reverse int
are oriented in advance (.Fig. 102).
ersection from geodetic control or identifying contours, with
r reliminary orientation of the photomap.
STAT
188
It is one of the characteristics of vertical-combined surveying
between
oint
an be determined
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e e
evat
on traverse i btl
s runeween eevation control points
{(control points, reference marks, triangulation points)- and also bet
i
In addition to these methods, characteristic for vertical-combined surveying,
5 -;
(plane-table survey sethods (a geometric grid, based on the plane-table traverse, and
;a graphic solution o? reverse intersection) are also used. The latter is chiefly
C !
used in parts of the photomap with an insufficient number of identifiable points.
The basic plane-tabl
l
i
ween po
nts of
I: I
(tied-in basic plane-table elevation traverses, by using a telescopic alidade or
(transit with a vertical circle that reads to 1' or 30" accuracy or a t
l
i
e
escop
c
, l .
L
idade equipped with a cap-altimeter designed by engineer G. Vu.Stodolkevich.
J... i
C-
The transfer of elevations with a telescopic alidade is generally carried out
py taking readings in two directions to obtain direct and reverse elevation, while
9'e
2' 1
I
i
Fig. 103 - Sighting on Landmarks for Orientation
IIn observing such landmarks, the horizontal stadia wire of the telea..ope tube of the
The elevations transferred from points of the traverse by numerous sightings
Jon local lancearks, used for orientation, may be used later in sketching the relief.
!
ovation. The distance to these objects is taken from the photomap.
,y dangles are measured in the two positions by the vertical circle.
{
,. I I~hile running the basic elevation traverses, observations are made on points
Iof the trigonometric grid and on other local landmark
s which have significant ele-
189
f.
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. alidade is sighted on proeinent characteristic points or lines of the object, such
as the top of a chimney or tower, the base of the spire of a windmill, etc. The
;sighted place is then entered in the record, with a sketch (.Fig. 103).
Points of the basic traverse, used later for plotting the relief and for tying-
Jin of surrey traverses, should be narked with a wooden stake and capped. For the
" i
)%
Iscales of topographic maps compiled by vertical-combined surveying (mainly 1:10,000
d 1: 25, 000), published instructions are available that give the respective toler-
i
l lances for lengths of traverses and lines, errors of closure, and other technical
. ;rules to be used as guides. In the given case, greater lengths are periaitted for
lane-table elevation traverses than for plane-table surveying, since in running
j
thea off, the plan position of points is determined from the photomap.
This fact is important, since it makes it possible to have a less dense geode-
tic base on the plotting board which, in turn, affects the organization of the work
?. i
as a whole.
;
After computing the average increments in elevation between points of the trav-
. ~erses and drawing up a diagram of observations, the heights of points of the basic
lane-table elevation traverse are equalized by the vanishing point method or by the
jpolygonal method. Then other adjacent traverses and connecting points are tied in.
I
Elevation points are plotted on a tracing of elevations (Fig. 104) which con-
tains also their numbers and elevation.
1
I Also plotted on the elevation tracing are geodetic control points, reference
j
{marks for geometric leveling, survey base points, survey traverse points, and iso-
dated points for Which observations have been entered on,record (local landmarks,
r
jcharacteristic points, etc. ). Magnetic declinations are also recorded on the trac-
1
(ing.
I
1 ~nnin of elevat' t
n
d
.i
g io
raverses is
one unaer various conditions, depending on
the existence and location of elevation control points and on the physical, geo-
.j
graphic, and economic character of the region surveyed. All. these affect the trav-
STAT
190
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l'
!,.
9;
I
S
i
1
6c 24
1940 I1LOVSK OBLASf
JL?
'77
'.'.
Chief of Party
I
05
r
y I'
'b
26
F43
Drawn by Topographer 1'L Class
Scale 1: 25, 000 IVANOV between 5 May and
15 Septe?ber 1940
Magnetic declination + 7`1$'; Correction after comparing with compass -
Corrected declination + 5.45'
STAT
191
TACING OF LIEVATIQ S
N-37-86-V-a
-a ii i ~ -~i. r7~
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erse and the nature of work performed. For example, depending on the availability
of points and the nature of the terrain, it may be expedient to extend the elevation
grid in parts, but not over the entire plotting board at once. In open and treeless
cterrain, the work is different froo what it would be in .noded terrain If t
r
e
e
C
la
di
- are
b
rge
o
es o water on the terrain, the water surface can be used as a reflec-
lr
?tor for transferring elevations, etc.
)2.!
All these and other individual variations in the terrain should be considered
d put to good use in running basic plane-table elevation traverses.
i
Full use should be made of points of the basic elevation traverses as transi-
l ; " i65. Transitional Survey Points
,', ^tional survey points in plotting relief. Besides these points, the elevation and
position of other transitional points, necessary for the survey, should be defined.
2: frhe density and distribution of these ints will depend
Points on the skill of the topog-
?:: rapher and on the nature of the relief and density of trees in the area. In open
"laces, the number of transitional points will be smaller than in wooded sectors
.` Jirhile an area with broken or sharp relief will require more transitional points than
level area.
Transitional survey points may be located on the photomap in various ways.
In the plan position, these are located by:
a) Identifying a contour point. Any contour, its angle, or the intersection of
r,
ontours identified on the photomap, can be used as transitional survey points;
b) Identifying lines on which the point is located (landmarks, roads,
the point will then be located at the intersection of the radials, read from the
staff and laid off to scale on the photomap with compasses (see Fig. 101);
etc.),
jnd measuring the distance from one, two, or more identified contours (see Fig. 100);
i
1 c) Measuring the distances from two or more identified points located near by:
(see Fig. 102);
d) Intersecting with two or more identified contours at a determined point
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e) Reverse-intersecting from geodetic control or identified contours with pre-
liminary orientation of the photomap;
I
f) Any of the methods used in plane-table surveying, or a combination of them.
3
A frequently used method of locating points is by reverse intersection with orienta-
tion of the plotting board by means of sketched-in bearings. For example, assume
!;
. }that a traverse is run along a boundary which is poor in contours (swamp, tundra,
.
(
l f
meadow, etc. ). From the last positively
Ito a transition point not identified
salting point of the plotting table
1; r
f
t
the leveling staff).
1
Vertical
different points of the staff.
oriented by a
are measured twice in each direction, on two
Survey elevation traverses are run between elevation
control points (triangulation points,
bench marks, points on basic elevation tray-
verses) and tied in. Traverses consisting of no more than two points, not counting
kite starting point, do not have to be tied in.
'r I
,,
ional points for further use by driving a stake and capping it, blazing a tree, or
I
angles
identified contour point, a bearing is taken
the photomap. On this transition point, the
is
line drawn to this point from
he preceding point, and the point itself is reverse-intersected with surrounding
eodetic or contour points.
In orienting the photomap, besides using control points, use prominent distant
ontour points and identify them carefully.
With respect to elevation, transitional survey points are obtained:
In some cases, it may be preferable to mark the terrain position of transi-
Elevations of the tied-in transitional prints
d also marked on the elevation tracing.
should be entered in the record
P i bering of all points on the elevation
racing, in the record, and in the catalog should be the same,
ether method;
j b) as isolated points - by sightings on two or three points, whose distances
I
're taken from the photomap.
a) Primarily, by running survey elevation traverses through a point (through
to avoid error. In
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fl-
addition, it is advisable to number all basic n .a
""`s 4u+?ay translzlonal points with
'serial numbers, starting with "one". Thi
s methodfb
o numerin rec
,' 8 P ludes the possi-
,.bility of giving the same number to two
( E points.
c
E 66. Snyiog Belief
),
To depict relief with horizontals el
i
evat
on pointlld
,s, so-cae st
l ` P went on the corresponding scales.
rhe relationship between the linear dis placement of one ma
. rk and the a
!placement in depth of the wandering mark is read' pparent dis=
ily established from FiR.128.
Let the left mark coincide with the point a of the left photograph
1 and the
'right mark with the point a2 of the right photograph. Then the floating mark will
*ppear to coincide with the point A of the model. If
both marks are displaced by
the same quantity a lc 1 = a2,c'
2, then the wandering mark is shifted to the position C',
!located at the same distance from the observe
.. 1 r as the point A. In order to displace
the space mark from the point C of the model the
'I , right mark must be displaced, in-
~ !dependently of the left mark, by the
quantity c2c2. On the basis of FiA.128, we e~ay
write:
i
f
a1 `1 ?1 cl 01 a1 x~ -
,I 1 1
if a2c2 = o2 c2 ?2a2 x -
C= x~!
- z -
~= - (xC
231
Cl $1
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(37)
STAT
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A cosparison of egs.(37) and (32) indicates that the independent displacement,
by c2c2, of the right-hand mark is the absolute-parallax difference, which can be
determined in this way. Consequently, to determine the X-parallax difference be-
tween the points A and C, the wandering mark must be successively displaced from the
points A and C of the model, and the value of the independent displacement of the
right (or the left) mark mist then be measured. The difference of elevation between
these points can then be calculated from eq.(33).
The variations in parallax difference obtained by this method must be measured
very accurately as indicated by eq.(33). Assume that photographs, 180 X 180 mm, in
size, with a 60% end lap were obtained in aerial surveying. Then the photographic
base at the scale of the photograph, (distance between principal points) will be
72 mm. The flight altitude was 3600 m, and is used as the initial altitude, while
the relative elevation to be measured was lm. In this case, the horizontal-parallax
'difference will be
72mmx lm
P
3600m-lm
= 0.02 mm
Therefore, in measuring the parallax of up to 1 m, this must be done with an accu-
racy of 0.02 mm. This indicates the importance of accuracy in measuring parallax.
It also is necessary to measure accurately the abscissas of identical points with
i
special measuring instruments. This is particularly true when the points are lo-
,
~cated on contours that are not too clear.
Despite the convenience in using topographic stereoscopes to determine relative
elevation from prints, the method has not received wider use in the USSR. The
eason for this is the fact that the horizontal-parallax difference,
measured on the
photograph, depends not only on the elevation difference of the points but also on
the elements of interior orientation of the photographs, thus mking a calculation
;of the elevation difference from eq. (36) pgssible only. for cases of ideal photo-
STAT
232
7'
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graphs, when the optical axis of both prints are strictly vertical and the projection
centers are located in the same horizontal plane. In all other cases, the correc-
tions for the difference between the actual conditions of expoaure and the assigned
conditions must be applied to the measured horizontal-parallax differences. The
corrections for horizontal parallax are correlated with the elements of exterior
orientation and also with the current coordinates of the control points.
;74. Elements of Exterior Orientation
The elements of exterior orientation of prints determine their position with
r~apCC`L GO a
given system of space coordinates and are characterized by six quanti-
ties. The system of space coordinates is
usually described by the vertical planes
r (Fig.131) xz and YZ and a horizontal plane
0
l Xy. The outlines of these planes are the
S directions of the axes of the system of
space coordinates. The first three elements
of exterior
1
orientation represent the linear
coordinates
of the center of projection and
Z:? rts ~
are denoted
by X$, Yc, 7.c. The position of
'N
i
the optical
axis of the camera is defined b
Fig. 131 - Elements of Exterior
Orientation
while the angle
tion onto
t
y
the angles ax and c. The angle ax is the
projection of the angle of tilt a of the
optical axis to the coordinate plane XZ,
represents the angle formed by the optical axis with its projec-
the plane XZ and is, therefore, measured in the tilted plane.
the sixth element is the angle of
and is measured on the photograph
I
of the photograph. Consequently,
rotation y of the nhnrno - h
between the path of the plane XZ and
there are six elements
each photograph, of which three are linear and three are
the xx axis
of exterior ~rlirw~at?nw
?~??? . ..as r.aars Vii
angular. Therefore, the
233
Finally,
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spatial position of two photographs is determined by twelve eleaents of exterior
orientation.
75. The Coordinates of Photograph Points
The position of any of the image points on a photograph is determined in ac-
cordance with a previously selected rectangular system of coordinates.
Since the elementary object of processing in a stereophotogrametric survey
consists of a pair of photographs, it follows that the axes of coordinates are
selected simultaneously for two photographs. The principal point of the photograph
is often selected as the origin of such a system of coordinates, in view of the
fact that its position can easily be obtained from the images of the coordinate
marks. The direction of the axis of the system of coordinates is given by a line
:connecting the principal points of the two photographs, while lines perpendicular
to the xx axis and passing through one of the principal points are taken as the
.yy axis. In this way, each pair of photographs has one axis of abscissas, xx and
two axes of ordinates, yy and y'y'.
In processing a second pair of photographs, the direction of the xx axis will
change, since it will be given by a line connecting the principal points of the
second and third photographs (instead of the first and second) so that the direc-
tion of the ordinate axis yy will also change. For this reason, there may be two
idifferent directions of the coordinate axes on the second photograph, depending on
whether it is paired with the preceding or the following photograph.
In accordance with the system of coordinates selected, the position of each
point of the photograph may be expressed in a linear or an angular forn:. In the
t
! former case (Fig.l32), the wanted data are the quantities x; x', y, and y', of
i
I which the coordinates x and y define the position of a certain point al of the left
photograph with respect to its_orinc rieLpoints, while the coordinates x' and y',
in turn, determine the position of the corresponding point a 2 of the right photo-
hi
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234
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graph with respect to the origin of the coordinates at its own principal Point.
If the position of a point on the photograph is ex pressed by angular coordi-
natee, then the quantity sought will be the angles ~x and (Fig.133), which are
Y
. ,~ r
Fig.132 - Linear Coordinates of the Photograph Points
the projections of the angle formed respectively by the projecting and principal
rays on two planes. Q e of these planes is the plane containing the projection
center and the abscissa axis of the photograph,
S while the other plane is an inclined plane pro-
. duced by the projecting ray Se, whose locus on . . . 11ik! . - the plane of the photograph is perpendicular to
. .fk ' e_
the abscissa axis.
--- -~aLll -y V L.UD11SfCd, bearing in wind the fact
' Points of an Ae- that the distance between the projection center
rial f Photograph and the principal point of the photograph is the
focal length. Solving the triangle Soa, formed
after Projecting the o
R point a of the photograph onto the abscissa axis, will yield
lar coordinates of the points of the photograph
:.:::ix. a! ._~ By solving the right triangles Soao and
g Saoa, the relation between the linear and angu-
FiDi
; natea of the
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(39)
By analogy, the following equations are obtained for the second photograph:
tans' = f ; tan ~' y' cos ~r
k fk x
Knowing the linear coordinates of the points of the photographs, this hakes it
:easy to obtain their angular coordinates, and vice versa.
76. Horizontal-Parallax Difference
of ideal exposure conditions results in a change in the val
f
h
o
ue t
e abscissa for
;identical points on the photographs and thus in a
change in the
difference. Consequently, the horizontal- rallax
~ Pa difference is defined by the
equation:
I
tan ~ = x
x f i Saa = fk ? cos ~x
(38)
Since the angle at point ao in the triangle Saoa is a right angle,
it follows that
or, after substituting the value of $a
o
y
Sa
0
= __coax
tan sr y
I
Then, as a result of the
OP=x111 - x
a: - x`' xCs
change in the abscissa, we have:
YP=x.1 -x?-x' +x
s ?
ci c=
(32)
(40)
236
~.r
The deviation of the elements of exterior orientation from the specified values
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Taking into account tha t
e,p ep + bp- xa
and x., = v
-`I A
Where by is the change in the hor'
iaontal parallax, while ex
denote the change in the aba a '
1
C188S, it can be atal
by=drp-'p=A~
a1 xa=
)
The values of ~
a'
of the eles+ent 1 ay, exC1 apd xCZ may be defined fx
a of exterior ~ the correlation
orientation with the change in abs -
Assume that the exp;,os ure was don c iasas .
e at a strictly Vert;,.
iCameras , but at an altitude which as -=gal camera axis, for both
a different fro* the assigned altitude, Then
(Fig.134) along the abs
cissa axis, and
!earth's surface, will between any two points on the
be represented at the assigned al
;on the photo trtude Ha by the distance
graph ? At the actual fli
h
x
g
t altitude
2
H it will be x
H
0
-X
c
ange
I in the abscissa on the photo a
,; - will be: Ph, due to a chars
B'e in heiRh
the
h
X2-1
x' _
ft
xa 1 + eza 1 ; xa a
1 C1 + ezc 1 : x' _
C2
=X
Ho
xa= + exa
t
Xc t + exc
t
eX
C
Xi
1 xc
(Ho - H)
Boll
z1
H ` H, - H )
exc1, and Q
CZ
(42)
STAT
237
! Therefore
(41
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Fig.134 - Influence of 1?ifferent
Flight Altitudes on
the Abscissa
^1
= fk tan (ax + ), x2 = fk tan B=
tan aZ + taxi R= ,
x2 - xl = Ax= = fk tan 13 - _
1 - tan a= tan Sz
fk tan ax - fk tan a; tan
238
On changes in the angle of tilt ax of the optical axis, the relation between
the coordinates 22 of the tilted photograph and x1 of the horizontal photograph is
w --
Fig. 13 5 - Influence of Longitud-
inal Angle of Tilt on
the Change in Abscissa
found by solving the triangles Soa and So'a', formed by the direction of the pro-
jected ray Sa and the optical axis So or So'.
Then (Fig.135),
tan ax + tan a; tan2~x
1 - tan a= tans
(43)
At low angles of tilt ax (ax ' 30); the second term of the denominator will be
t small and can be neglected in order to simplify the solution. Then,
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Knowing that,
tan t3 =
z
it follows that
ex2
ti
ti
- fk tan ax
t
E
n L
On varying the angle w, i.e. the
P
displaced from its horizontal position (Fig.136) into a tilted
position, while the
Fig. 136 - Effect of the Lateral Angle
of Tilt on the Change in Ab-
scissa
!between the direction of the projected
tilted photograph will be ~, while its
and aa0S will be Sy and ~X.
angular coordinate S and
The
co^sists in
! the plane containing the optical
angle ~
y is measured
projected ray Sa !oaintains its
v,nformer "direction. The projection
of the point a onto the yy axis
will be a o for a true vertical or
horizontal photograph, while the
projection of the point a', again
onto the yy axis, will be ao for
a tilted photograph. In accord-
ance with the notations, intro-
duced above, the lateral
tilt oSo' will be w,
and
angle of
the angle
ray and that of the principal ray of the
projections
x2
x2
lateral angle of tilt, the photogra h is
onto the coordinate planes a0S0
difference between the angles ~, and ~X and the
axis
the fact that the angle
y
and the radial of the yy axis,
is measured in
whereas the
in the plane containing the projected ray and its projecti
on
onto the plane Sox. Similarly; the angle ~x is measured in the plane
Sox, while the
angle az" ri the plane containing the direction of the projected ray and its projec-
239
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tion onto the plane Soy.
cular to the plane Soaoao, so that the triangles a'ao and Saab are similar. Fr
0 osi
the similarity of these triangles, it follows that
LikewiaC,
.
Thu*,
cos + Y) - cos W cos ~y - aln Y sin
y
COs
r
= xl cos 1 - xl tan sinW
a'a'
0
x2
i aao
aao
aao -
Sao
x1; Sao
coo y
i Sao
fk
cos (~y + W)
The lines
a'ao and aao will be parallel to each other since both are perpendi-
xl
Noting that the solution of the right triangle So'ao yields
_
tans'
r
ft
j considering, from the smal lnees of the angle w (~ 30), that cos w = 1 it
I
x2
xly
ft
am b
(45)
x
(Fig.137), with the xx axis of the photograph preserving its former direction, the
abscissa of some point a can be expressed as
x2 =r cos (p+X)
II.
STAT
240
s.aaw A&y, 11 Gne photograph is rotated in its own plane through the angle
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while its value, before the rotation, was
In these equations, ? denotes a polar angle, and r the radius rector to a point.
r t- cos V + cos cos X - sin sin x)
or, noting that
t
L~.
Fig.13? - Effect of the An- 1 - cos X
the Photograph on the
Change in Abscissa
At a low angle of rotation of the photograph in its own plane
Thus, the combined effect of all above elements of exterior orientation on the
!: I
I abscissas of photographed points is expressed by the equa~.ion
I
;.,. 1 ~x = exi + Ox2 + Ax3 + Ax4 = - i- (H - tio) -
i
. - fk tan ax - f tan a; f sin W - y sin X (48)
k k
i
f
This equation defines the variation of the abscissas of an
y ponies on the
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L x = - R (HZ -H0) - fk tan aY _ w?2
= fk tan as
s
sin W2 - ya= sin X
2
sin W1 - yci sin X1
where the subscript
the subscript 1(2
...I - &Jo' - ik can i _ - _ tan a_ -
refers to the left photograph of the stereo pair, while
refers to the right photograph. Substituting these values in
eq.(41), the change in horizontal parallax difference, in relation to the change
in the elements of exterior orientation and the current coordinates of the points
on the photograph can be calculated. For sioplifying this expression, we note that,
in accordance with egs.(32) and (35),
point C1 coincides
left photograph, that at low angles of tilt the difference between the ordinates
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+ 2bhp a sin 1' +
k
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of corresponding points will be very sn+all, and that the deviation of the elements
of exterior orientation fro., the ideal (axl = ax2 _ ~1 "2 = Xi = x2 = H1 - Ho `
= H2 - Ha = 0) is also small, we may write
4
A
p x?
1
(H2 - Ho) +
a' sin 1' -
ft s
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20px?1
a sin 1' + 2b a
i
1'
fx= -
s
n
k fk x2
, . - ---1 W2 sin 1' + ep a sin 1'
fk fk x=
Then, assemhling the above quantities in accordance with the coordinates of
current points, it is not difficult to construct the final expression
where
xlil
by = - f (oH+
k
fkP
2ba x2
xZ a1
P fkp az 1
Y,1 b
- ~2 - P X1 - X2 + f W2
k
2tpx
~ '1
p (H2 - Ho) - a + 2bap a
H fkP "2 fkP =i
bH = l H (H1 -112); p=
sin 1'
epya 1
s
e
p
W+
ax (50)
flip 2 fkP s
Equation (50) permits calculating the change in the horizontal parallax differ-
: as a function of the change in the elements of exterior orientation.
Let
fk = 70 mm; H = 3500 m; b = 72 mm; x
?1
70 mm; y~ = 70 mm;
1
H1 - H2 = + 20 m; a1 = + 2?; az2 P ; = - 1?; w2 = + 2?
Then,
X1 = - 3?; X2 = - 1?; Ap = 0
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6H = + 0.40 .,~:
aY - a= + 3?. ' - w
1 2 1 2
2ba=
- 2.53 as
3?
fk
W2
0?
)' i.e., the first tern will be equal to +2.13 , the second -3.60 .., the third
i
I +3.60 ss, and the fourth will be zero. Therefore, for perfectly flat terrain where
J. ? the horizontal parallax difference should be zero, it actually equals -2.13 ^.,
.1 and the elevation difference, calculated fro. q.(36), will be 109.6 .. Thus, if
2 the effect of the elements of Exterior orientation on the change in the horizontal
i' parallax difference is disregarded, the elevation differences calculated fro.
eq.(36) will show very large errors, interfering with the preparation of saps with
1- satisfactory accuracy. This fact is responsible for the liaaited usefulness of
measuring or topographic stereoscopes.
77. Plotting the Relief by Sections
An analysis of eq.(50) which expresses the change in horizontal parallax dif-
ference in relation to the change in the elements of exterior orientation, indicates
that the first and fourth terms will be directly proportional to the change in the
jabscissas and ordinates of the observed point, while the second and third tens are
I tied in with the current coordinates by a .ore cowplex relation. Therefore, if it
is ass u.ed that the second and third terms are equal to zero, the change in the
horizontal parallax difference with any change in the abscissa air ordinates of a
J
r'
current point, can be graphically represented by a straight line. For this pur-
I pose, segments equal to the corresponding abscissas or ordinates, are laid off on
.., ; the straight line representing the xx axis or,yy axis of the photograph (Fig.13$).
Along the perpendicular, erected on this straight line at the point with the ab=
scissa x = 100 ?, the values for the changes (op) in the horizontal parallax dif-
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from the ground line to the drawn line.
Construction is possible when the geo-
deti% eleYations of two
points are known,
C
i"
,i i
Such a construction can also be performed in the case where the influence of
246
ferencea, calculated from eq.(50) are laid off for the value xa = ya 100 ?,
Then, connecting the point of origin of the straight lines with the end of the per-
pendicular, a graph of the corrections for
all intermediate points is obtained, since,
for these, the corrections will be repre-
aented by the length of the perpendiculars
Fig.138 -
since the chance the horizontal
parallax
p
lationa difference (if ac:1 = ax2 and W1 = W2) is
directly proportional to the linear coordi-
Graph of Correction
for Linear Inter
o-
Dates of these points. In this case, (Fig.139), eeaauring the horizontal parallax
difference for two points a and c having known geodetic elevations on the topo-
graphic stereoscope, and comparing these elevations with those calculated from
eq.(36), the difference due to effect of the elements of exterior orientation is
R
1where 1'p is the measured hor' 1
obtained. By connecting the two points with a
straight line and measuring the horizontal-paral-
lax difference of any point (e.g., c) on this
line, with respect to one of the points of origin,
linear interpolation (as mentioned above) will
y.&ela Lne cna nge in this difference so that its
Fig. 139 - Linear Interpo- correct value can be calculated from
f lation on a
i
1 Straight Line
aaiiax ai=Ierence and
op is its difference
I izontA_
obtained from the graph.
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Ap=d'p=op (51)
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I,
the second term (i.e.,
~x1 axZ ) while the third term of eq.(50) is not equal to
zero. However, in contrast to previous statements, linear interpolation gray be per-
.formed in this case if the original geodetic points are located either along the
ordinate axis (x1 = x2), or along the abscissa axis (y1 = y2). For these points, the
change in parallax will be directly proportional to only one coordinate (y or x).
Therefore, an over-all analysis of eq.(50) which relates the change in the
horizontal parallax difference to the elements of exterior orientation, permits the
the yy axis, the change in horizontal-parallax difference of these points will be
following conclusions: If two points, having geodetic elevations are located along
directly proportional to the difference in their ordinates, which makes it possible
to determine these changes for any intermediate point by mans of linear interpo-
lation. In all other cases, the change in the horizontal parallax differen
e
a
b
c
c
n
e
k/ I
:determined by linear interpolati~.n only with a certain amount of error, which will
!be the sailer the smaller the difference in abscissas of the selected points and
the smaller the difference in the angles of tilt.
For a practical solution of this problem, the entire area of the photograph is
(divided into sections (zones), within whose limits the change in horizontal parallax
!difference will be considered to obey a linear interpolation law. This zone is
'usually provided with several (usually four) geodetic elevation marks. Picking two
?of these points for the starting points (a and b), their horizontal-parallax differ-
fences are measured
multaneously,
!some located
and compared with those previously calculated from eq.(33). Si-
parallax
differences are measured at other points as well, including
the straight line
ab. The differences between measured and calcu-
lated values are used for calculating the change in the horizontal-parallax
differ-ential. The resultant value is interpolated for intermediate points. By subtract-
ling the change in horizontal-parallax differential, obtained by interpolation, from
the measured value, the corrected horizontal parallax difference is obtained which
is used for calculating the elevation difference.
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.. -
S. tential. The resultant value is interpolated for intermediate points. By subtract-
(ing the change in horizontal-parallax differential, obtained by interpolation, from
the measured value, the corrected horizontal parallax difference is obtained which
(is used for calculating the elevation difference.
x2),
the second term (i.e., a, = ax2) while the third term of eq.(50) is not equal to
zero. However, in contrast to previoua statements, linear interpolation may be per-
forred in this case if the original geodetic points are located either along the
ordinate axis (x1
3
or along the abscissa axis (y1 = y2). For these points, the
change in parallax will be directly proportional to only one coordinate (y or x).
Therefore, an over-all analysis of eq. (SO) which relates the change in the
(horizontal parallax difference to the elements of exterior orientation, permits the
l I
..following concluaions: If two points, having geodetic elevations are located along
_; the yy axis, the change in horizontal-parallax difference of these points will be
1;
.?directly proportional to the difference in their ordinates, which makes it possible
i
. to determine these changes for any intermediate point by means of linear inter -
Po
lation. In all other case., the change in the horizontal parallax difference can be
,
ideterained by linear interpolation only with a certain ac,...~t of error, which will
,~
the the smaller the smaller the difference in abscissas
of the selected points nd
2:
Iaultaneously, parallax differences are measured at other points as well, including
,,
;the smaller the difference in the angles of tilt.
1 Fora racti al s 1 t'
p c o
h'
Iof these points for the sicarting iris (a a d
) h h = - t ? ,.
o
u ion t PL is problem, the entire area of the photograph is
f
(divided into sections (zones), within whose limits the change in horizontal parallax
(difference will be considered to obey a linear interpolation law. This zone is
usually provided with several (usually four) geodetic elevation ..arks. Picking two
P
n , t egr orLLtf1L ,.-satax Idler-
b
! I
~ences are measured and compared with those previously calculated frog, eq. (33). Si-
, 1
Isose located on the straight line ab. The differences betLeen measured and calcu-
,
-latea values are used for calculating the chen~- ie-.r6a_rr__
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247
1
s. , .,.. ,
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I'
'% 1
1
:,f
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248
I
The number of sections that the field of the photograph is divided into depends
on the required accuracy of plotting the relief and the quality of the calculation
data. For asking asps at a scale of 1:100,000, the print is divided into two or
three sections, when aerial photographs are used. Simultaneoualy, when determining
the values of elevation for a series of intermediate points of each section, the
relief is plotted together with the elevation marks located within the boundaries
of the section.
78. Densification of the Control Network by the Straight-Line Method
The geometric principle of the straight-line method; proposed by C,V,Ro noy-
skiy, encompasses the fundamental law of projective geo:s;ry that a straight line
Fig.140 -
I duced in which the corresponding points A, C, and D of the terrain are located,
re-
I gardleas of whether or not they lie on a single spatial straight line or at the
in space is m ppped by a straight line on the
picture plane. This is due to the fact that,
through the center of projection and the
spatial straight line, a plane may be drawn
that always intersects the plane of the aeri-
al photograph along a straight line. How-
ever, the location of the image of three
points of a locality along a straight line
on the aerial photograph does not mean that
the corresponding straight lines
rain are collinear.
of the ter-
,w let the three points a, c, and d
of the aerial photograph (Fig.140) be col-
Then, through this line and the
Stre;ght-Line P4e*hod linear.
Selection of Points
on the Aerial Photo-
graph for Making a
center of projection S1 a plane can be pro-
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i ~.
locus indicated in Fig.140. At the same time, the images of these three points on
the second photograph will usually be non-collinear, except for isolated cases. In
order that the images of three points of the terrain shall be, at the same time,
collinear on two adjacent photographs, it is a necessary condition that, through
these three points and the two centers of projection, two planes are drawn inter-
secting both picture planes in straight lines. This condition will be satisfied if
the three points of the locality lie on a single straight line in space or if these
two planes coincide, i.e., if the three ground points and the two centers of projec-
tion are coplanar.
The second of these cases corresponds to the arrangement of points on aerial
photographs in straight lines roughly parallel (for the case of a plan aerial photo-
r. 1
graph) to the direction of the base line. Therefore, to exclude the second case
1 roughly perpendicular to the directions of
4::
1
A
consideration, the points on the photographs must be selected along directions
_
C
N
O
. -. __._._ t_
Fig. 141
' indicates
be a
in
that
space.
result of
Letermining the Ele-
vation Difference of
a Point Located on
Straight Line in
Space
~D
the base line. In that case, the collinear
location of the three points a, c, and d on
the left and right aerial photographs indi-
cates that the corresponding ground points
C, and D lie on a single spatial straight
line. On the other hand, if on one photo-
graph three pcints a1, c1, and d 1 are col-
linear, then the deviation of the point d2
of the second aerial photo raph from the
straight line joining the point a2 and c2
A,
the three ground points A, C, and D do not lie on a single straight
In this case, the deviation of the point d2 from the line a 2c2 will
the relative elevation of the point D above the line AC. Thus, a
study of the character of the location of three points on two aerial photographs
i
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permits determination
In densification
y. r
the elevations of points A and C of the
ground are determined geodwtically, and the
elevation of any other point, e.g., point D,
on the same straight line, is then found
t photogrammetrica lly. In Fig.141, let all
t
rID three points A, C, and D be located on a
D
Fig. 142 - Determining the Excess
of a Point by Measuring
the Photograph
single straight line, and let the elevations
(f nni1 *a
-- ~~~.a aev
e sj{d C be snoRn . Then the a le -
vation of point D is found from the simi-
larity of the triangles ACC0 and quo,
whence,
AD - AA
D1 + ~2
(Ac - AA) (52)
D1
To determine the elevation of point D fro? eq.(52), the distances D1 and D2
between known and determined points must be known. These distances can be replaced
by radials measured between the images of these points on the aerial photograph.
Let (Fig.142)
p
n, an
j let the three ground points A, C, and D be located on some inclined straight line.
( Prods from the points A and C horizontal straight lines to their intersection
with the projecting ray SC at the points E and K. Then, the triangles acS and AES
i
dcS and DKS, and ACE and C DK will be similar. The similarity of these triangles
I gives
of the mutual location of the three ground points.
of a basic vertical control net by the straight-lip method,
{C
t
an aerial photograph occupy a strictly horizontal
ositio
d
AE
HA bD AC AE
- ac: Lk
f k --- f k a; 1-D
' where HA and HD are the height of the camera station above the plane containing A
i
250
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write
t
02+D1 d1 + d2 h d2
D1 dl
If we assusie that (d1 + d2): d1 = Q, then
r
or, from eq.(52),
,. i
AA = _
(.: ;
Finally,
r
and D. Noting that AC = D1 and CD = D2, and denoting ac by d 1 and cd by d2, we slay
D1 + G2
Cz
D1
D1
D'2
a a
(HA - h )d=
HAdi HAd1
HA dl
HA
_AA
I Q- (Q-Q)
)
]( A
HA
(53)
(54)
= Q (Ac AA)
h (SS)
A
1+ (Q- 1) A
HA
Equation (55) clearly indicates that, to determine the elevation difference of
. 'the int D over the int A the elevation difference between the
~ po po points C and A
located on the same straight line must be known, and the distances d1 and d2 between
the images of these points on the aerial photograph rust be measured.
If the point D of the ground does not lie on the str-ai ht line in s
~ g pace joining.
;the points A ac C, then the determination of its elevation is performed in two
stages. At first the elevation of some point D' (a fictive point) located on
251
'a
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I 1'
straight line AC is found, and then the elevation of the actual point C with respect
to the fictive point. The solution of this problem is illustrated in Fig. 143. 0>Q
the left photograph, let the images al, c1, and dl of three ground points be col-
linear, while, on the ground, let the point D be higher than the line AC. Then the
ges a2, c 2, and d2 of these sane three points on the right photograph will not be
I
i
i
., i
i
collinear,
I
I at the point
Fig. 143 - Determining the Excess of the Actual Point over the
Fictive Point
1 .e.
i d2d2. then,
point
prolong
d2 will
the
deviate from the line a2c2 by a certain quantity
line AC to
its intersection with the projecting ray S1D
D'; the resultant point U' will be the fictive point whose image on
! the right photograph
will be at the point d2, lying on the line a2c2.
the right projection center
If, through
S21 the ray S2d2 is drawn parallel to the ray S1d1,
then its intersection with the plane of the right photograph at the point d 2 will
I lie on the line d2d2, since the rays S2d2, S2d2, and S2d2 will be coplanar. If
252
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D
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LI.
then the plane S1S2D is drawn, the rays S2d2 and S1d1 will lie on this plane (and,
consequently, also the ray S2d2 which is parallel to it). The sane plane will then
contain the point D' and, obviously, also the ray S2D'.
Assuming the planes of both photographs and the photographic base S 1S2 to be
horizontal, it is logical that the trianglea d2nd2S2 and S1S2D, and also dd2S2 and
;S1S2D', will be sinilar. For this reason, the aides of the triangles have the same
jratio to each other as the focal length of the camera has to the flight altitude HD
and HB above the planes drawn through the points D and D', respectively. Thus,
SIS3fk
2
4:
'the ground point D will be expressed by the relation
Q (A~ - AA) A PHD HD
i A? = AA + (s6)
, AC - A Bfk
11
Thus the straight-line method makes it possible to determine the elevation
t
dq"d2 - didq = d2d2
8fl
SiS2fk Bfk
Ho}1b HD Hp~ (-)-h
I where ~h denotes the elevation of point D over D'. Th. quantity d2d2 represents the
}horizontal parallax difference, determining the distance of point d2 from the line
!drawn between points a2 and c2. For this reason, the elevation reference mark of
~oark of any point D whose image is located one one of the photographs, on a line
1joining the images of two other points whose elevation is knon
or
w F th'
is pu
rpose,
Jthe difference in horizontal parallaxes 0p and the radials d1 and d2 on the photo-
,.
!graph must be measured frow the known point to the unknown point.
253
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Fig. 144 - Selection of the Straight Line in the Zone of End Lap
'straight line is selected to lie in a direction roughly perpendicular to the base
'= line (Fig.144), forming an angle of not less than 300 with it. Two of the points
Hof this line must have geodetic elevations, preferably at the end of the Barked line
: ~
t
h
There are two variants for the deneification of the elevation control cetwork
by the straight-line method. In the first case, densification takes place within
the limits of a single pair of photographs in the zone of their end lap. The
In
at case Q wi 1 be less than unity, which increases the accuracy of the deter-
1
(
minations).
The photographs are placed in the measuring stereoscope and adjusted (oriented)
'so that the marked line is perpendicular to the xx axis of the instrument. The
horizontal parallax is measured at all points and will be equal at points A and C.
The horizontal parallax difference 4p of point D with respect to the two other
points is used for calculating the elevation of point D. If the straight line forms
I': an angle w, different from 90', with the base line, then the measured horizontal
f_: iparallax difference ip' will be inaccurate; to obtain its accurate value, it most
,; be divided by cos (90' -fir) or by sin ~. Then, the equation for calculating the
.'elevation of the points will take the form
AD a AA
0,
? dt
dA _ A 1
'"C _ "A'
HA
A..Vu u~
I.+~+ abab
+ LJ (57)
Bfk sin
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.' -
I;
,4
9,
case, the first of the points
seiec~cd must be simultaneously depicted on the
d
secon
Photograph of both flight strips, and the second point must be in the zone of triple
In the second case, the densification of the basic elevation control network is
perforeed withir. the liaits of a few stereo pairs, using the photographs from two
adjacent flight strips. The straight line must be located in the
zone of side lap
(Fi
1
g
45) rhlll
.ougy parael to the direction of the flight strip, and awst have
'detic elevation points at its ends.
These two points are joined by a straight
f ~ ?
0
Fig. 145 - Condensation of Straight
on which points of
are located in the
F' i g . 14 5 - Tying- in of Points by the
Straight-Line Method
!end of the straight line so marked.
I To measure the horizontal parallax
both flight strips are adjusted in the
is Perpendicular to the xx axis of the
overlap, i.e., appear on the sec-
ond and third photograp}. Thus
two points will be marked on the
second photographs, supplemented
by a third point located simul-
taneously on the third and fourth
photographs. Similar selectioe
of points is continued until the
difference,
the
two
first
photographs of
measuring stereoscope until the straight line
_.nstru;;nt. The datum
points in the densifi-
STAT
255
f
Z,
Line in Zone of Side Lap
geo-
line,
densification are selected so that not less than three points
side lap of the first photographs of both flight strips. In this
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t;
cation of the elevatoa control network obtained by the straight=line method
com-
prise s datum point having a known geodetic elevation, and the point 1 vhoae
eleva-
tion is arbitrarily assigned. From the known points of elevation the stra
fight-line
method is used to determine the first unknown and then the next, etc, until the end
of the iaarked line is reached. Arbitrary elevation values are used. The progres-
sire method is used until the last photograph is reached, so that the
elevation of
points 3 and 4 can be used for determining the elevation of point II having a geo-
detic elevation. The difference between the arbitrary and the geodetic values of
elevations
point 1.
,
fence at point II must be divided by the number of bases into which the straight line
1Cj ;had been divided, and the quotient must
~~ be subtracted from the elevation taken for
Point 1. Now if the reference mark for point 1 (Fig.146) was in error by the quan-
tity 1-1', then this error increases to the quantity II-II' at point II, while all
,; I
intermediate points are in the positions 2', 3', and 4'. To obtain the correct
.;marks of all points selected, the discrepancy
II-II' must be divided proportionally
., Jt h
i
i
!with reversed signs, as corrections to
!
the straight-line method is useful
', i
/:
Iwrth increasing number of photographs between the points of known geodetic elev -
a
I'tjon, because of the unavoidable errors in
h
p
otogrammetrii
c constructons. An
addi-
tional increase in error is caused by relief of the photographed terrain s
o that
A
only on level or slightly undulating terrain.
J79. par*1laciic Rulers
I
I The densificat' f
i
may be conveniently carried out with the parallactic sine ruler developed b
FV
y
..
)Drobyshev and shown in Fig.147. The two glass plates are provided with lines; the measuring marks of a stereoscope. One of the sides of each ,
ch plate
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o L. e distance to the points selected and the resultant quantity must be a l
pp led,
256
the elevations so determined.
The errors of elevation densification by the straight-line method increases
on o the elevation control network by the straight-line method
of point II will be the error in the arbitrarily selected elevation of
To determine the correct value of the elevation of that point the differ-
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J.:
rrain
Fig. 147 - Parallactic Sine Ruler n d
a
reading is taken on the
i5o.f..!
a spatial li
ine cuttng the model at
points A and C. In this
position, the
index of the beveled edge of the plate.
displacement of one of the plates
r
t
t
!distance between
during densification of the elevation
network by the straight-line method, the
first plate is placed on the left photo-
graph so that its line coincides with
the selected line. In the same way, the
plotted line of the second plate is
matched with the straight line a2c2 on
the right photograph, after which both
plates with the photographs are brought
together until their beveled edges coin-
cide. If a simple stereoscope is placed
over the photographs, the observer will
see a stereoscopic model of the to
has a beveled edge forcing an angle of 5?44' with the traced lines.
The beveled edge
of the left plate is graduated in millimeters, and an index line is
?arked on the
be:eled edge of the right plate. In e~easuring the horizontal
parallax difference
t
change, which,
din depth.
Jte point
the scale
the plotted lines, which retain parallel to one another, will
stereoscopically
As a result of this
D of the model, after
of the beveled edge.
!will be equal
corresponds to a displacement of the spatial line
displacement the floating mark can be superimposed on
'rich the new position of the plate is read off on
The displacement of the plate along the beveled edge
distance betwe
h
en t
e rul diidd
ers,ve 1;y the sine of
n
th
is equal to 5?44',
the line.
along the beveled edge of the other, the
--- based on rig.l4tj. Since
oiue w`iil be 1
STAT
357
e angle formed by the edge and
r
this
10, i.e., the resultant displacement
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the change
respect
j .1
i?
of the plate will be ten tiaies as great as the change in distance between the gradu-
ation lines, which is equal to the horizontal parallax difference between
n
Y
and A. Consequently, to obtain the desired horizontal parallax difference, the
! Fig. 148
;difference of the third point
0
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Measuring the Horizon-
tal Parallax Difference
with a Parallactic
Ruler
above-described method. Then,
been weasured if the
{
measured displacement of the index of the
plate must be divided by ten and used for
calculating the elevation difference.
In determining elevation by the straight
line method with the aid of a measuring ate-
reoseope or parallactic rulers, the photo-
graphs need not necessarily be so adjusted
that the straight line is strictly perpendic-
ular to the xx axis of the instrument or
cincides with the index line. In this case,
taking one of the pouts of the straight
line with a known elevation as the datum
point, the horizontal psar.~.llax difference of
the two remaining points is measured by the
by simple calculations, the same horizontal parallax
with
orientation
the two other points which would have
of the photographs had been strict, is now deter-
jmined. This procedure considerably facilitates
orientation of the photographs.
The calculation of the horizontal parallax diffe ences is performed in a record
ion the form presented in the Table given below.
In Column 1 of this record, the number of the aerial photograph with which the
measurements were made is entered; in Column 2, the number of the orientation, which
is always done twice (as a cross check); in Colun 3, the number of the point on the
straight line selected; and in Column 4, the readings on the scale of the
parallax
screw. Taking the reading at point 1 for the datum and subtracting it froa~all
258
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STAT
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10
Record for Measuring the Horizontal Parallax by the Straight-Line Method
Heir fhientatiom Point Heading
Na. No, No.
1 2 3 4
'pl
1748
1795
67.41
0
0.0
0.00
67.95
+0.54
39.6
1000
-0.54
0.00
67.87
+0.46
76.4
1.939
-1.04
-0.58
68.35
0
0.0
0
00
II
68.14
-0.21
39.2
1.000 '
+0.21
.
0.00
1;
67.33
-1.02
75.8
1.934
+0.40
-0.62
0.00
0.00
-0.60
ot;ier readings, will give the measured horizo
t
l
n
a
parallax diffhih
erences wc are
.
j entered in Column 5.~n Column 6, the distances measured on the photographs along
' the straight Tina froei the initial point to the two other points are entered and
I in
t Column 7, the ratio of these distances to the dist
ance to a sedif k
con pont onown
elevat''}
i
6pf
~
+ . I
1
on. a product of these ratios by the measured }:orizontal parallax differ-
j once of point 2 (a point of known ~PfA1 7 r i t ...._, .
Iquantity bp', which is entered in Column b. The sum of the values of Columns 5
and 8, entered in Coluan 9, represents the horizontal parallax difference which
gn, gives the
would have been measured at strict orientation of the photographs.
~
I la t ions
The same calcu-
are made for both orientations, and the average of these values is entered
u n Co luwn 10.
The calculations of the elevations of poi^ts by the straight-line method is
of the following form.
number of the aerial photograph is entered in Column 1; the
point of the straight line in Column 2; the flight altitude above the
through the datum point, in Column 3; the coefficient calculated from
given
j from t h oaeaaured horizontal parallax differences to the elevation differences; in
1
STAT
259
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the equation
the
plane psasing
in a special record
In this record, the
number of
in Column 12 is entered in Column 4 and serves for the transition
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' Ir. the case of transverse lines passing across a number of stereo pairs, the
arrangement of the record becoeaes slightly more coeaplicated, but the principle of
calculating the elevation of the points remains the same.
STAT
260
Photo- 1int
Record for Calculating Point Elevations by the Straight-Lime Method
1 2
1748 1
1,95 ! 2
3500
17.48
1P
0.00
0.00
-0.60
0.0
0.0 1.000
-10.4.1.936
10 I 11
1945 .I k
Remarks
12
HpHp
Bfk sin '
21 ~6.Q~ 178.3
-31.4 = _41.8 152,7
is
ti -
= Q (Ay-A1) x
x (c- 1) A! A1
H
Column 5, the parallax values of 0p are transcrid from the record. The product
of the data in Columns 4 and 5 is next entered i? Column 6. From the same record,
the values of Q are entered in Column 7. The known elevations of points 1 and 2
are then entered in Column 11; the elevation of point 2 with respect to point 1 is
next calculated and entered in Column 10. The resultant elevation difference (in
this particular example -16.2 m) is multiplied by the value of Q and the result
entered in Coluew 8. Since the calculated quantity represents merely the numerator
of the second term of eq.(56), the correction 6' is applied to it at differences in
elevation of more than 50 m, to allow for the deviation of the denominator from
,, ' unity. The correction is calculated from the equation in Column 12, while the re-
suit of the calculations is entered in Column 9.
The sums of the quantities en-
i
, tered in Columns 6, tt, and 9 Rive the values shown in column 10; by adding these
, ! to the reference marks of the datum points, the geodetic elevations (Column 11) of
. i the points to be determined are obtained.
I
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