theory and practice of simple mleasurement methodology in ... · theory and practice of simple...

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)


~!~~~;~~~'~ '~~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 -


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)


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 -


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)


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 -


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 )

theory and practice of simple mleasurement methodology in ... · theory and practice of simple...

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