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The Inst. of Natural Sciences Nihon Univ. Proc. of The Inst. of Natural Sciences Vol_ 29 (1994) pp. 25~35
Theory and Practice of Simple Mleasurement
Methodology in Photogrammetric Education
Kiyoo SAZANAM11) and Mitsuharu YAMADA2)
(Re'*ived october 31, 1993)
Determining the accurate object distances is always important in simple photogrammetry. In
the photographs of mountainous area, however, the determination is a difficult problem. In order
to solve this problem, the following equation is proposed for the photo scale number mE at the
10wer elevation of the two end points of the ground line :
m~ ' 2 - (v'Ahlf)2 + d' Ah/f]/sb [ = J (sk m,~ )
With this mB , accurate object distances can be computed. To keep the accuracy better than
1/100, sk'mk ;~ 7v 'Ah/f is defined as the necessary condition.
The methodology of simple photogramrnetry with non-metric photographs is described in this
paper. The method of taking horizontal-normal photographs and necessary conditions for three
dimensional measurement in simple close-range photogrammetry are also discussed.
The results of measurment by parallax-meter are compared with the results of measurment
by analyiical plotter PA 2000. The results of PA 2000 are adjusted by the bundle method with
self -calibration.
This comparison proves that the parallax-meter measurment is effective. In addition, this
paper describes the several points to be ameliorated about parallax-meters and spiral parallax
measuring boards.
1. Intoroduction
Mirror stereoscopes and parallax-bars are commonly used as the student practice materials. As
they are relatively expensive, one intsrument cannot usually be allotted to each student. To overcome
the expense, one of the authors designed a simple parallax-meter with moderate accuracy. This device
can be handled easily, and it can also be purchased by individual students. The automatic contouring
technique by means of stereo-matching has been recently studied in the laboratory. However almost
all actual mapping works are still done by using analog plotters, so it is important for the students to
master the technique of setting floating mark on the model exactly with practice of parallax-meters.
This paper describes test works of simple measurments with parallax-meters using aerial photographs
and non-metric hand camera photographs.
~ ;4c j~~f=~~~~~~~iS,~;;~1 ~~~P~~<4
7156 ~~:~~~~~~t~EI~:l~~;~J~;'(3-25-40
1 ) Department of Earth Sciences, College of Humanities
and Sciences Nihon University, 25-40, Sakurajosui 3
Chome Setagaya-ku, Tokyo 156. Japan 2 ) Topcon Corporation, 75-1, Hasunuma-cho, Itabashi-ku,
Tokyo 174, Japan.
~ 25 - (1)
Kiyoo SAZANAMI and Mitsuharu YAMADA
~~
2. Accurate Equations for Determining Absolute Flying Heights
Accurately determining absolute flying heights is essential in simple airphoto measurements. Dr.
P R Wolf m the textbook "Elements of Photogrammetry" describes the flying height H in the following
mannerl) .
(~I~)2 = (XE - XA)2 + (YB - YA)2
(~~)2 = [xb (H- hB) /f- x~ (H- hA) If]2
+ [yb (H- hE) /f- y~ (H- hA) If]2
where, XA. XB and YA. Y~ : ground coordinates of points A and B.
x~, y. and xb, yb : photographic coordinates of points A and B.
hA and h~~ : elevations of points A and B.
H: flying height above sea level (absolute flylng height).
Since this equation is difficult to apply in practice, the author had deduced the following simpler
equation to obtain the elevation h, corresponding to mb which is determined by using a sloping ground line2)
h.= h +d Ah/sb """"(1) where sb = ab and d is the distance between t
(perpendicular points to line ab from principal point
p) and a (the higher point of A and B on the
O photograph) and A h is the elevation difference : Ah=hA - h~.
O f The photo scale number mB at the elevation of the lower point B can be derived from the
a d~i following equation3). VJ t~~ p b mB = (s,~ ' mk + d' Ah /f) /sb """""" (2)
The distance between two oints rs re urred to A
O
~i ,¥__I
~ r
l lh
~(
Fig. 1
(2)
B
P
b
tr v p
Method of determining accurate number of aerial photographs.
scale
points is required
satisfy the condition. sk ' mk ~ 7・ Ah
m~ : Photo scale number at the elevation of
the lower point B.
mk : map scale number.
s,~ : distance of two points on the map.
f : camera focal length.
Because satisfying the above conditional equation
in large-scale mountain photographs is difficult, a
more exact approach and stringent checking must
be used (Fig. 1). By the theorem of three perpen-
dicular lines
~O t a = !A A"' A" = 90'
Consequently,
AO ta cr) AAA"' A", AO p t cO AA A' A"'
- 26 -
Theory and Practice of Simple Measurement Methodology in Photogrammetric Education
From these similar triangles, the most accurate and practical equation for det~rmining the photo scale
number mB is derived as follows :
mB - (sk m;~)2 - (v'Ahlf)2 + d'AhlflJ/sb' -[ - . (3)
where, v is perpendicular length to the line ab from principal point. As long as the following limitation
sk ' mk ~; 7v'Ah Ifis satisified , then the term of (v'Ah lj)2 is negligible and m~~ maintains the relative
accuracy higher than 1/100. The accurate absolute flying height Ho is consequently obtained from the
equation :
Ho = m~ ' f+ h
3. Some Examples of Determining Absolute Flying Height by Equation (3)
Photographs used for this test are photo-number No. 4 and No. 5 of course C1 of Yamakawa district
mission in Shikoku. The orientation elements by analyiical aerial triangulation are as follows :
'el = 105.73 gon, c1 = 103.218gon, a)1 =99.114gon in photo No. 4
'~2 = 105.62 gon, c2 = 101.020 gon, (D2= 99.178 gon in photo N0.5
b. = 159.375 mm, by = 100 mm, b. = 96.729 mm, fl = 152.66 mm, f2 = 152.66 mm
In Fig. 2-1 and Fig.2-2, the number on the ground line shows the absolute flying height determined
from the ground line, In Fig. 2-1, all absolute flying heights are approximately equal because No 5
photograph is kept in the limit of I gon in both c and (o.
In photo No 4 because c ' m th 3 gon the absolute flying heights show the quite big differences . , rs ore an ,
and the ground lines near the diagonals should be selected.
Finally, absolute flying heights are dertermined as 3,480 m and 3,507 m for No. 4 and No. 5, respectively.
These determined heights agree well with the results of analylical aerial triangulation.
Flg 2-1 Absolut~ flying heights (unit : m) corre-
sponding to each ground line and the frame of photo No. 5 (Yamakawa district,
Shikoku).
27
Fig. 2-2 Absolute flying heights (unit : m) corre-
sponding to each ground line and the frame of photo No. 4 (Yamakawa district,
Shikoku).
(3)
Kiyoo SAZANAMI and Mitsuharu YAMADA
~!~~~;~~~'~ '~~f'~il~~:~!~~~! IL : I o'o(~l r:~ 1~: E~T~JI~ 5 n mm ~~~ _ :-~ ~~1 vOO :tiirl~~l~~}¥~;~jii&i' ~~"'::t'~~~~~' x ' ~ E~~l~c::]~i ; 0'50 i
I
~~i' ~f~ ~~~~T89 4'_~il:~____'=~~" ~;~!~~:
.] : j :!' 5 :'oo ~ - -' "~ ~" ~;~: '~ ~~1~~~7r~~~'L?~~i~~J~~~i"~r~~~~ilr;:~'~~ ' " t: ll P
; ~~~T ~'~ij ~ ~_)' " i:~.~~~~~~ ~~4~~'f;~l'~r*_~~);~:~~:~~' Q?1;:~'f~}T~{!ji'Ji'--'~~i~}~' ' R: ~f~i
sl 50 ~ I 1'50 j
I
; 2'00 ~ ~i {
~i}ri~~~'~~~~i~~~~~~f~~~~2'~~~~~/~~!~~~:(~)~j) ~!~l"'~~;~~:~~~!/;2:~' :~;~
i : 2'50 I ~i ~~: :~f ~~~~ f
~ 3'00 ~~~'(~1s;;'~(b ' ~~- ~~
~~ ~~'_"'_~~:t~_~
i];.・ .~~_~~ Ij: i_'~~~~~- x _ j it ji;fi~i9 oj '~.j'. ji;~it:17f~~j~~~:~'~~~~i:_j:J~;~~(:~~~~rfl~'~~~c~~~'J~!~]!rF~r-r~~~rf:r _ '~ '
; ~3'50 J
[
lil ; ;'jii i JS4'00 _ _'~~~j. . - " _ L I '~~~: ; _~~~-~~ ~ ~ f ; 4'00 l ;!:iil " !
1!!! i l:54' 50 ' Ji !i!55'50 f I l f[ ' ~~-_~;jt oe c~ ~ : ; ~l'~ ~Tr~;'~ ~~:~~~~;--:t~-' '. ~~l
; :r f 155'00 ~'I: 1;~~:~~F~~~~~~~~~~~1 ~ ' ' J:~~ ~~ ~ " ~~:_ 1 5'00 i]i'{ i: i ' r~ ~' _ !~~~'_/:~~~~;i~f'=_(:' c= _ ~"~~~'~=/~~
~~J: ~ :~' _ ~l _ /~'~~~~~]c~]~= ~+:*'~~~1'~~~; --'~L' ~ ;! ~~~JJ~~~!~T{~{~ ~ '[~ ' ~' IL ! - ~ ' a;~ ~ ' ;~lt~~cl]c~T~~~ _ :~~~r'=J~l~~~~Ir'!"r f
~i - ~ :~"~' _~(! - L_!"~~il~(~t~~~~~~-s
~ -- ' ~=_ -~ - - -~ - -- ;~ ~ -S :~ ~lj~~~50 ; 7'00 ' __ i~r~~~~~ ' (T~~ ~=- ~ 6 ' 50
~ * I ~L;' ~ ':~~;~~~ 'l~ I~1;~ " ~i" --- -~ _ ~~~- ~ ' '~ ~i~T'I"/_~3~1'~:~~~'_''~f'_' ~~~ ~~~: ~rh;:;;~ ~ '~~:~f/~~ff~~~~':r~~!'_'__;<~vfr'f' ~' - ' ; ; !_ji~8'00 ~ 8'00 ~l'~: ~{ r~ ~ ~~~~ -- ~1~ _ ' h ' _ ~ ~;;~~~~/j~~/~~ ; 58'50 ~ 8'50 tcl5 5 ~:~~ I " J ~ s _ ~f: '-~~~ ' _~Jrrr"/ 'h -*-' ~~r -F _ _ ~~~~ **' ~( ~~~~s!' 71 = ' ~ r~'~~~I ~~ ~~~ 1~ ~ ~~~ ~~;~ ~"~'r~1~~~'T~A~!il_~~~~~~~~~/~~" _! - "~ :~'r {{~ ~:~~_
i - 5q'oo ~ q'oo Fig' 3 Absolute flying heights (unit : m) correspond- ; 5q'50 ; q'50
ing to each ground line and the frame of ; -60'00 i 0'00 Photo (C15-5)' (Gifu district)' ; 60'50 ; o'50 The broken line designates the boundary of ; : I 'oo ~ I 'oo the stereo-photo (Fig' 6)' ; 1 6 1 '50 ~ I '50 i!
: 2'00
64'50
s'oo
5 ' 50
66'00
6'50
67'00
67'50
8'00
8'50
q'oo
q'50
70'08 spiral parallax measuring board which the author has
recently developed were used' See Fig' 4 and Fig' Fig' 4 parallax-meter' 5' The former had the measurement accuracy of i
(0'05/'vO'03) mm ; the latter' that of i(0'05!~0'02) mm'
According to the usual height formulae' AH::: H' AP/ b' AH== H' AP/ (b + AP)' Where H iS the
flying height above the object ground' It iS also a variable' Therefore a series of orderly A' B' C'
D and E measurements must be made by using these formulae :
AHA~~ =: HE ' APA~~ / PA' AHBC := HB ' APBC I Pc' AHCD =: (H~ + AH13c) 'APCD /P AHDE := (H +AHCD) 'APDE /PE
(4) - 28 -
Theory and Practice of Simple Measurement Methodology in Photogrammetric Education
s:d5',o
a: ~~ *o
(~!J
'1cL.
c~)
Q1
,)
~,
(i. b'
.b/'?
,~ 'bl)~ S:o.O ,,of .~)b ~
S3. o-
58.5: ・50.
1;O ・S:
1;9 ・e' 1~1,~'
ej
4;q
,~
・r'
'o
(s ,~ lo o
j62・5 5:3.a-51・5 :5S.5: 58.s-
~l '62. O 'o '$S ~~
Cr / 'O
*o 'cTl
*S
1~9 ・ol_ '~1~
l~ V~
(~;$
.c.
c~-
~,o ・s:
,~
Y* ,; ,J)
e5q'
~ b
C1
・50.0
e,
~!
~
$t
1,,
'a (i, b*
.b~'?
.1~b ~
・51.5 .55.5
'~~.o
(r/
~ 'O O
.b~)~
'fl.S
:62.s
' d 2. o
Fig. 5 Spiral parallax measuring board. (unit : mm)
In simple close-range photogrammetry, these fonnulae are very well matched. For these
measurements, the direct measurement of the parallax by the parallax-meter is superior to the parallax
bar. Parallax bar measurement requires the parallax corrections between principal points and object
points. Also the measuring marks are likely to move back and forth.
The parallax-meter, on the other hand, measures stably. It can be operated quickly and easily.
In addition, it improves the reliability of measurements by comparing adjacent floating marks. The spiral
parallax measuring board which has gentle slopes of floating marks offers superior approaches to
measurement.
4.2 Preparation of Prallax Correction Graph
Using stereo-photo in Fig. 6, the parallax correction graph was made. As shown in Fig. 6, about
20 points were selected in the overlapping area and the elevations of the points were taken from the
topographical map. The lowest point, No. 5, was selected for the datum and parallax differences, A P1-5,
A P2-5, the others were calculated from the following formulae,
APl-5=P5 H1 5/H AP2 5 P AH251H
The parallax P5 of point No. 5, however, was measured by a parallax-meter. The flying heights
above ground : H1 = Ho ~ hl' H2 H h "-', elevation differences : AHI 5 hl - h5. AH2-5 = h2 - h5 " " ', and the others were all known values. Next, actual parallax differences AP~-5. AP~-5
and others were measured by a parallax-meter. Then v = A P - A P'is a correction of parallax difference.
The absolute flying height Ho = 3,897 m ; the distance between the two principal points L = 144.5
mm ; the reading values of the parallax-meter at No. 5point 15 = 66.50 mm and P5 = L - 15 = 78.0 mm
were all obtained. Table I shows the results of measurement and calculation. Fig. 7 shows the parallax
correction graph.
- 29 ~ (5)
Kiyoo SAZANAMI and Mitsuharu YAMADA
Fig. 6 The stereo-photograph of Gifu district which were taken by a RC 20, May 17, 1990. The flight line is oriented north-south.
O (O)
O (-D ~.)
(-o. 3)
(-a. 4)
(-u 5)
(-o G)
(-o T)
( -o. ~)
(- L~. ~])
-O ~g
O
Fig. 7
5 (-n 1~(-Ll'~~_o's~-[]'~l (r~~J~/il 3 [] ooO
O (-o' [) (_u' [~) o IY L-Q '2) i
(i} 1~ L i] ?) (~) c-u' :]~ /] (-tl ~) O O (_[1"E) (_[i 1) -o ' O -o' o~
(_t] t~ / (j,~") Il") -o E~ o ~ -o' 2) (~{f' d) / ( tl'7~ /
/ ~-[]' :~1
/H'I_ //./~'1,J,7(r~} 11 t / O / {-ll ~J//
/-{" IT ~/ ii IT I , / ~/r} 1' ! ILL1 L u 2') ~ {] j l ・,(:- 3~~
-t) 32
9
¥ (-m J] {-ii 4) ' -l ¥ ~-~ ¥~ i] ~) ~-[] ~
~¥¥_(_¥: fi}
L (-v' [il iO -[] GX -) 37 (-[1 1)
(-LI s) ~[] i] ((O O 71 c-LI D) f-1~ :1' ( u' 4) .///+
t-o 2) " {-[1"~ l
-o 13
-c] !]" -- Za O~h~ ' -l L fi LT L~ Ll~~-0'40u :14
parallax correction graph' (unit : mm)
O : Vertical control point'
(-C'6) : Interpolated value'
(6)
Table I Parallax Corrections.
- 30 -
Theory and Practice of Simple Measurement Methodology in Photogrammetric Education
5. Three-Dimensional Measurement of Non-Metric Photographs
5.1 Parallax-Meter Method
To use the parallax-meter in non-metric photos, it is necessary to keep the camera axis exactly
in the horizontal plane and nonnal to the base line. This maintenance is accomplished by sticking tape
on the objects at the same height as the camera. This tape should then coincide with the central lateral
line of the camera viewfinder. This coincidence maintains the horizontality of the photo-camera axis.
In normal photography, the problem of convergent and divergent camera axes may be avoided by using
two targets and by pacing off the base B measurement. Marking the diagonal intersection of a photograph
with a needle to know the deviation from the exact horizontal and normal photography is a good practice
as seen in Fig. 8.
Before the actual photograph is taken, an article whose size is known should be placed alongside
the object. A book or a pack of cigarettes would a usable article, but longer distances from the object
would dictate larger articles.
This article can then be replaced as control points. The article itself should be parallel to the camera
axis, not oblique to it.
It should be placed near the lower part of the object. If the position of the article is higher than
the camera, the depth of the article cannot be photographed.
Unlike those of aerial photographs, the photo bases of close-range stereo-photography are generally
Fig. 8 The stereo-photo for simple close-range photogrammetry. The discrepancies between the crosses of tapes and the scratched crosses show the deviation from the horizontal
norrnal photography. The book on the table can be used as control points.
= 31 - (7)
Kiyoo SAZANAMI and Mitsuharu YAMADA
Fig. 9 The stereo-photo of test targets taken by the non-metric camera (lens :
f = 50 mm). NIKKOR
very short. Principal points do not have to be transferred to coincide on the same base line. As shown
in Fig. 8 orientation can be easily accomplished by using objects with horizontal lines like a blackboard
and by keeping two corresponding points about 60 mm apart.
Fig. 9 shows the test targets taken by a non-metric camera (1ens : NIKKOR 50 nun). Ground
coordinates of the intersection points of tiles were maintained within the accuracy of i 10 mm. Object
distances were regarded as unknown. They were found by using the depth of the known article. In
the formula Y= P'A Y/AP, the depth AY is known. Then, Y is determined by measuring P and AP
with a parallax-meter. The same equations as those used in large-scale mountain photographs (Section
4.1) can be used. Fig. 10 shows the discrepancies between Y coordinates obtained on the basis of the
given distance A Y (A17-A37) and the ground Y coordinates. The accuracy of A2-. A3-, A4- points
is rather good. The accuracy of the forward depth can be improved by increasing the known A Ydistances
on both sides.
Fig. 11 shows the errors of Ycoordinates in the case of the given distance A Y (A17-A87). These
results have proved to be fairly effective. That means the known base line length must be given on
the photograph and it can be defined as the line of the same depth as the object.
Fig. 10
(8)
Discrepancies between Y-coordinates calcu-
lated in the case of the given depth A Y (A17-A37) and ground Y-coordinates. Non -metric photographs (f= 50 mln) were meas-ured with the parallax-meter. (unit : mm)
Fig. 11
32 -
Discrepancies between Y-coordinates calcu-
lated in the case 0L the given depth A Y (A17-A87) and ground Y-coordinates. Non -metric photographs (f= 50 mm) were meas' ured with the parallax-meter. (unit : mm)
Theo脚d Pracdce ofSimple Measurement Methodologyin Photogra㎜ethcEduca廿on
≡_、._. 「1tllll
・調lr1・T・r11蝉!抽コm’鷹1」1 t!1.1 11「 一一 、-」一 一
一…一
一LL.
~一 塑望鰍8襯繍臓認需謂耀篇專零織3PHOTOGRAMMETRICSCALE 一 二L、T、. l
Fig.12 Photogrammethc scale consists of both large and small wedge.(unit:mm)
Fig。13 The stereo-photo Qf test targets taken by the non-metric camera(lens:
MINIWIDE∫=28㎜)SIGMA
A12 12 一12 82 一46 25 一11 o 61 77 10 11 99 56
A11 12 一12 53 一45 26 11 1 29 45 47 50 38 2
A10 11 一32 78 一23 5 3 41 了o 62 60 63 50 11
ん9一 68 一3a 31 o 18 29 39 26 荊 57 61 51 M
へ8一 一18 一2了 19 ” 26 19 11 55 68 li7 62 61 25
A7一 30 一24 5 1 16 31 2段 34 5 32 27 42
丁 25
良6一 14 一22 一7 4 呂 7 3 37 34 31レ 21 15
『
2
鳥5一 1 一15 24 一1 1 3 9 30 16 18 15 21 2
八4一 8 一5 11 9 5 9 6 15 16 28 26 21 18
A3一 7 一9 3 1 一4 10 3 G 13 5 8 9 4
A2一 3 一2 8 1 7 2 1 5 1 6 6 9
A1 へ 2 A 騒 A-4 盈 5 A-6 汽 7 A8 A 9 A l 轟1 A1‘ A ll
Fig.14 Discrepancies between y-coordinates calculated in
the case of the given depth」y(A17~A127)and
ground}二coordinates。Non_metric photographs(∫=
28mm)were measured with the parallax-meter.(unitl
mm)
33 (9)
Kiyoo SAZANAMI ^nd Mitsuh^ru YAMADA
To find the length A X (lateral direction), the principal distance c for the enlarged photo with service
size must be calculated. The measured ground distance AX(A16-A17) was 150 mm. The distance
Ax on the photo was 14.Imm which was measured with the large wedge scale of the Photogranunetic
Scale (Fig. 12). Here c = 202.7mm can be calculated from Ax/ AX= c/ Y (O-17). The term Y (O-
17) in this equation is the distance from projection center (exposure station) to the point A17. Then
AX of the points A46-A47 was given as 150 mm by using the equation Y (O-47) = Y (O-17) + Y
(A17-A47), Ax = 10.0mm and c = 202.7 mm. The error was I nun in this case. For the large wedge scale, using stereoscope of 4 magnification is better. For a small object less
than 5 mm, a small wedge scale. This scale needs a 15 x magnifying glass. Fig. 13 shows the stereophoto
of test targets taken with super wide angle lens (f=28 mm SIGMA MlNl WIDE) and Fig. 14 shows
the discrepancies between Y coordinates obtained on the basis of the given distance A Y (A17-A127)
and the ground Y coordinates.
5.2 Results of Analyiical Plotter PA-2000
The correction for camera lens distortion was not applied, because inner orientation elements are
usually unknown. The points A24, A26, A29, A42, A44, A49, A64, A66, A69 were used as the control
points for the absolute orientation.
The standard deviations of coordinates derived from measurements of 91 points were o:* = i36.0
mm, o~ = i45.2rnm, o:. = dl 13.9 mm in f= 50 mm normal camera.
The standard deviations of coordinates derived from measurements of 132 points were o:*= ~31.9
mm, OY= i45.2 mm, o:. = i43.9 mm in f=28 mm super wide angle camera. Fig. 15 shows the discrepancies of Y coordinates in f = 50 mm nonnal camera and Fig. 16 shows
Fig. 15 Discrepancies between Y-coordi-nates obtained by analyiical plotter
PA-2000 and ground Y-condinates. (f= 50 mm). (unit : mm)
Fig. 16 Discrepancies between Y-coordinates ob-tained by analytical plotter PA-2000 and ground Y-condinates. (f = 28 nun). (unit :
mm)
( 10 ) - 34 -
Theory and Practice of Simple Measurement Methodology in Photogrammetric Education
the discrepancies of Y coordinates in f = 28 mm super wide angle camera.
5.3 Results of Analyiical Method
The results by the bundle method with self-calibration (camera : f= 28 mm) are as follows : (unit :
mm) (unit : gon)
Principal distance : 28.791
The coordinates of central projection points Ax = - Axp-~ (R0+R1+r2+R2'r4) + (pl '~+ p2' ~ + p3'xy+ p5' ~ 2)
Ay = ~ Ayp~~・ (R0+R1'r2+R2'r4) + (P4'~y+p6'~2)
where
The orientation elements of camera Correction coefficients of lens distortion :
Ro =0.217E-02 Rl = ~O.880E-04 R2 = -0.182E-08
Correction coefficients of film warping :
P1 = ~O.337E-02 P2 = -0.203E-02 P3 =0.115E-02 P4 = -O.334E-03
The inner orientation elements P5 = - 0.833E-03 P6 = - O.324E-04
The displacements of virtual principal points ~ =x-xp y = y~yb r2=~2 + y 2
The standard deviations of coordinates derived
from measurements of 23 points are a*=i
3.7mm, ay=il4.7mm and a.=:t3.9mm and maximum errors are AX*** = 11.4 mm. A Y
***=-27.6mm and AZma*=11 7mm
6. Conclusron
In parallax wedge measurement, measurement accuracy is determined by the minimum measuring
mark interval, because interpolating a fraction of adjacent measuring marks is difficult. The author
proposes that both side lines of the parallax-meter should be changed to zigzag lines with I cm pitch.
The right side zigzag lines should be angled at 45' to the horizontal line. The minimum measuring
mark interval of both parallax-meter and spiral parallax measuring board should be also changed to
O.02 mm.
The authors express the heartful thanks to Asia Aerial Survey Co. for the analytical works by bundle
method with self-calibration.
The authors also wish to thank Professor Oshima of Hosei University who made many valuable
suggestions.
References
1) P. R. Wolf, "Elements of Photogrammetry", MCGRAW-HILL INTERNATIONAL BOOK COMPANY. (1983) pp. 135-136.
2) K. Sazanami, Simple Photogrammetric Devices, Journal of Forest Aerial Survey; 66 (1968), pp. 6-11.
3) K. Sazanami, "Simple photogrammetric Instrumentation" (Text Book : JICA) (1978) pp. 2-4.
- 35 - ( 11 )