close range photogrammetric systems and their...
TRANSCRIPT
CLOSE RANGE PHOTOGRAMMETRIC SYSTEMS
AND THEIR APPLICATIONS IN OPHTHALMOLOGY
by
Kresho Frankich D i p l . Ing . , University of Zagreb, Yugoslavia, 1959
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF
MASTER OF APPLIED SCIENCE
in the Department of
CIVIL ENGINEERING
We accept this thesis as conforming to the required standard
THE UNIVERSITY OF BRITISH COLUMBIA
October, 1973
In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r
an advanced degree at the U n i v e r s i t y of B r i t i s h C olumbia, I agree t h a t
the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study.
I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s
f o r s c h o l a r l y purposes may be g r a n t e d by the Head o f my Department o r
by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n
o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my
w r i t t e n p e r m i s s i o n .
Depa rtment
The U n i v e r s i t y o f B r i t i s h Columbia Vancouver 8, Canada
Date
Abstract
Photogrammetry as a measuring t o o l has been applied
mainly i n topographic mapping, although from the very be
ginning of i t s development there have been a s u f f i c i e n t
number of attempts-to apply photogrammetry i n various
f i e l d s of science.
However with the exception of the u t i l i z a t i o n of
photogrammetry i n architecture, criminology and invest
i g a t i o n of t r a f f i c accidents, which has been a standard
procedure i n many European countries, a l l other applications
have remained i n the experimental stage.
There are many reasons for the fact that non-topographic
photogrammetry has not obtained general acceptance. The
methods, instruments and ample potential of photogrammetry
are p r a c t i c a l l y unknown to s c i e n t i s t s . Fortunately
developments i n recent years have been changing the s i t u a t i o n
s l i g h t l y . A rapid increase of intere s t i n the ap p l i c a t i o n
of photogrammetry i n various branches of science cannot
be satiated with metric cameras only. Standard amateur and
professional cameras,television systems, holography, x-rays
and many other "nonconventional" photogrammetric systems
have been serving as non-metric data a c q u i s i t i o n systems.
Very concentrated investigations i n numerous photogrammetric
centres a l l over the world are now underway to evaluate
the q u a l i t y of non-metric data a c q u i s i t i o n systems.
A s p e c i a l problem i n the determination of very accurate
measurements from photographs taken by non-metric cameras
represents the camera c a l i b r a t i o n . The standard laboratory
methods used for metric cameras are not very suitable f o r
non-metric cameras because of t h e i r unstable parameters
of i n t e r i o r o r i e n t a t i o n . This thesis includes a great
va r i e t y of approaches i n the camera c a l i b r a t i o n describing
and assessing many methods that are used or suggested by
various s c i e n t i s t s a l l over the world.
In the r e s t i t u t i o n of photographs taken by non-metric
cameras using standard existing p l o t t i n g instruments photo-
grammetrists face the very serious problem of rather sign
i f i c a n t and i r r e g u l a r r a d i a l and decentering d i s t o r t i o n s
which cannot be e a s i l y eliminated. Another problem i s the
p l o t t i n g instruments which do not have s u f f i c i e n t range of
p r i n c i p a l distance. P l o t t i n g i n such cases must be per
formed i n an a f f i n e model with an exaggerated p r i n c i p a l
distance and v e r t i c a l scale.
A l l these problems can be avoided by the a p p l i c a t i o n
of a n a l y t i c a l p l o t t e r s . The a n a l y t i c a l approach i s especial
advantageous i n the most general case of close-range
photogrammetry where the elements of i n t e r i o r and exterior
o r i e n t a t i o n as well as the c a l i b r a t i o n parameters of the
cameras are simultaneously determined with the object space
coordinates. I t can only be hoped that i n coming years
instrument manufacturers w i l l be able to produce a small and
inexpensive stereocomparator with automatic coordinate
r e g i s t r a t i o n .
The f i e l d of ophthalmology i s p a r t i c u l a r l y suitable for
photogrammetry. The eye as an object of research has very
s p e c i f i c properties which make almost any measurements by
conventional methods extremely d i f f i c u l t . The fundamental
problem of measurements i s the mobility of the l i v i n g eye.
To solve that problem photogrammetry may be the i d e a l
measuring t o o l . The l a s t part of t h i s thesis deals with
small number of attempts to u t i l i z e the great p o t e n t i a l
of photogrammetry i n ophthalmology showing that without the
combined e f f o r t s of the medical profession and photo-
grammetrists no success can be achieved.
V
TABLE OF CONTENTS
Chapter I
1) H i s t o r i c a l Development of Nontopographic Photogrammetry 1
Chapter II
2) Close-Range Photogrammetric Systems, Introduction 21
3) Data A c q u i s i t i o n Systems 23
4) C a l i b r a t i o n of Cameras 28
5) H a l l e r t ' s Grid Method 38
6) Jacobi's Method for Non-Metric Cameras 47
7) Brown's A n a l y t i c a l Plub Line Method 58
8) Abdel-Aziz's C a l i b r a t i o n Method 73
9) Abdel-Aziz-Karara C a l i b r a t i o n Method 77
10) Conclusion on C a l i b r a t i o n of Close-Range Cameras 84
11) Data Reduction Systems, Analogue Plotters 85
12) A n a l y t i c a l P l o t t e r s . 96
Chapter III
13) Application of Photogrammetry i n Ophthalmology, Introduction. 99
14) Measurements of the Front of the Eye 101
15) Measurements of the Optical System 107
16) Measurements of the Retina 113
17) Summary and Conclusion 123
18) Bibliography 126
VI
LIST OF FIGURES AND ILLUSTRATIONS:
1-1 De v i l l e ' s automatic p l o t t i n g instrument 5
1-2 Phototheodolite of I t a l i a n Army from 1889.. 7
1-3 Phototheodolite by Finsterwalder and P u l f r i c h 8
1-4 P u l f r i c h 1 s stereocomparator 9
1-5 P l o t t i n g of the Interior of the Dome of Santa Maria del Fiore i n Florence 11
1- 6 P l o t t i n g of waves i n the harbour of Hamburg 14
2- 1 Modern phototheodolite, Wild P. 31 24
2-2 Stereometric camera, O f f i c i n e G a l i l e o 25
2-3 Object and image bundles 31
2-4 Perpective centre 32
2-5 Image coordinate system 35
2-6 Grid and Projection planes 39
2-7 Image of the Grid 41
2-8 P r i n c i p a l point... 48
2-9 Transformations of coordinate systems 50
2-10 D e f i n i t i o n of p r i n c i p a l point ....51
2-11 Plane of d i s t o r t i o n correction 52
2-12 Distorted and undistorted rays 64
2-13 The image of a plumb-line 69
2-14 Abdel-Aziz' t e s t object 74
2-15 Vanishing l i n e 75
2-16 Construction of the nadir point 76
2-17 Determination of the p r i n c i p a l point and the camera constant .76
2-18 P r i n c i p l e of o p t i c a l projection system. 86
VII
2-19 P r i n c i p l e of mechanical projection System 87
2-20 P r i n c i p l e of optical-mechanical projection system 88
2-21 Elevated a f f i n e model.... 92
2-22 Decentering of photograph 93
2- 23 C-scale for decentering... 95
3- 1 Schematic representation of the normal eye 102
3-2 The section of the c i r c u l a r shape of the eyes 10 3
3-3 The horizontal and v e r t i c a l cross-section of the
sc l e r a 105
3-4 Refraction of a l i g h t ray i n the anterior chamber 108
3-5 Projection of a refracted ray i n the xy-plane I l l
3-6 P r i n c i p l e of observation of the r e t i n a .....114
3-7 Binocularophthalmoscope 115
3-8 Fundus camera 117
3-9 Stereogram and p l o t t i n g of the fundus ....122
V I I I
Acknowledgment
The author wishes to express gratitude to a l l i n s t i t u t i o n s
and persons who by various ways contributed to t h i s t h e s i s .
Wild of Canada Ltd. gave a photograph of t h e i r l a t e s t model
of t e r r e s t r i a l cameras. Zeiss-Jena sent the paper by
Dr. Rzymkovski about the measurements of the radius of
curvature of the sc l e r a , Dr. Drance and A. Nelson permitted
the p u b l i c a t i o n of one of t h e i r stereopairs and the corres
ponding p l o t t i n g of the fundus of the human eye.
The author's h e a r t f e l t thanks go to a f r i e n d William
Tupper for many f r u i t f u l discussions about various photo
grammetric problems and p a r t i c u l a r l y to Prof. H. B e l l who
c a r e f u l l y reviewed the whole text, found innumerable errors
and made many suggestions.
Kresho Frankich
CHAPTER I
HISTORICAL DEVELOPMENT OF NONTOPOGRAPHIC PHOTOGRAMMETRY
A c c o r d i n g t o t h e "Manual o f Photogrammetry" p u b l i s h e d by t h e
American S o c i e t y o f Photogrammetry, "photogr amine t r y i s t h e
s c i e n c e o r a r t o f o b t a i n i n g r e l i a b l e measurements by means o f
photography."* Under measurements we i n c l u d e t h e g e o m e t r i c a l
c h a r a c t e r i s t i c s o f t h e photographed o b j e c t s , such as s i z e , form
and d i m e n s i o n s . Photogrammetry has been u t i l i z e d i n many
d i f f e r e n t f i e l d s , b u t i t s most i m p o r t a n t a p p l i c a t i o n s a r e i n
geodesy and s u r v e y i n g i n t h e p r o d u c t i o n o f v a r i o u s k i n d s o f
t o p o g r a p h i c maps. D u r i n g i t s development photogrammetry h a s ,
however, p a s s e d t h e bounds o f t o p o g r a p h i c s u r v e y s and has been
a p p l i e d i n many o t h e r b ranches o f s c i e n c e , such as a r c h e o l o g y ,
g e o l o g y , m e d i c i n e , b a l i s t i c s , a r c h i t e c t u r e , c r i m i n o l o g y , a s t r o
nomy, m i c r o s c o p y , and many o t h e r s . I n r e c e n t y e a r s a new
co n c e p t o f c l o s e - u p photogrammetry has been i n t r o d u c e d , i n w h i c h
t h e o b j e c t s a r e s m a l l , and t h e i r p h o t o g r a p h s a r e t a k e n a t
r e l a t i v e l y s h o r t d i s t a n c e s from t h e camera. Under n o n t o p o g r a p h i c
photogrammetry we g e n e r a l l y u n d e r s t a n d t h e a p p l i c a t i o n s o f
photogrammetry i n a l l f i e l d s o t h e r t h a n t o p o g r a p h i c mapping.
The h i s t o r i c a l development o f n o n t o p o g r a p h i c photogrammetry
p r o g r e s s e d p a r a l l e l t o • t h e development o f photogrammetry i n
g e n e r a l . I t i s u s u a l l y u n d e r s t o o d t h a t t h e h i s t o r y o f photo
grammetry b e g i n s w i t h t h e h i s t o r y o f p h o t o g r a p h y , a l t h o u g h t h i s
i s c o r r e c t o n l y t o a c e r t a i n e x t e n t . The b a s i s o f t h e whole
photogrammetric s c i e n c e i s c e n t r a l p r o j e c t i o n and i t s l a w s ,
* [ 4 ]
- 2
a n d s i n c e t h e F r e n c h m a t h e m a t i c i a n L a m b e r t (1728-1.777) i n h i s
book " A b o u t F r e e P e r s p e c t i v e " o f 1 7 5 9 , d i s c u s s e d t h e f o r m a t i o n
o f t h e p e r s p e c t i v e image w i t h o u t h o r i z o n t a l a x i s , we c a n c o n s i d e r
t h e b e g i n n i n g o f p h o t o g r a m m e t r y t o be e a r l i e r t h a n t h e i n v e n t i o n
o f p h o t o g r a p h y . A more o b v i o u s b e g i n n i n g o f t h e s c i e n c e c a n be
a s s i g n e d t o a F r e n c h m a n , B e a u t e m p s - B a u p r e s , who i n 180 8 made two
p e r s p e c t i v e d r a w i n g s o f a t e r r a i n f r o m two d i f f e r e n t s t a t i o n s
by means o f "ca m e r a c l a r a . " F r o m t h e s e d r a w i n g s a n d k n o w i n g
t h e d i s t a n c e b e t w e e n t h e t w o s t a t i o n s h e made a t o p o g r a p h i c
p l a n o f Cape S t . C r u z .
However t h e m o s t i m p o r t a n t f a c t o r i n t h e d e v e l o p m e n t was
t h e i n v e n t i o n o f p h o t o g r a p h y by D a g u e r r e a n d N i e p s e i n 1 8 3 9 .
D a g u e r r e p r e s e n t e d t h e i r new p h o t o g r a p h i c p r o c e s s b e f o r e t h e
F r e n c h Academy o f S c i e n c e s . T h e y h a d p e r f e c t e d a v e r y s o p h i s
t i c a t e d p h o t o g r a p h i c m e t h o d u s i n g s i l v e r i o d i d e a s a l i g h t
s e n s i t i v e m a t e r i a l . The o l d p r o b l e m o f " f i x i n g " t h e p i c t u r e
was s o l v e d b y t h e a p p l i c a t i o n o f a c h e m i c a l known a s s o d i u m
t h i o s u l f a t e w h i c h d i s s o l v e s l i g h t - s e n s i t i v e s i l v e r compounds
b e f o r e t h e y h a v e b e e n t r a n s f o r m e d i n t o a v i s i b l e image b u t n o t
a f t e r w a r d . T h u s , t h e y e x p o s e d a p l a t e and b e f o r e a n y o t h e r
l i g h t s t r u c k t h e p i c t u r e b a t h e d i t i n s o d i u m t h i o s u l f a t e t o
h a l t f u r t h e r a c t i o n by l i g h t . The l i f e o f d a g u e r r e o t y p e p h o t o
g r a p h y was n o t v e r y l o n g . O n l y a f e w weeks a f t e r D a g u e r r e
a n n o u n c e d h i s i n v e n t i o n t h e E n g l i s h s c i e n t i s t H e n r y F o x T a l b o t
p r e s e n t e d t o t h e R o y a l I n s t i t u t i o n o f G r e a t B r i t a i n h i s n e g a t i v e -
p o s i t i v e s y s t e m , w h i c h i s b a s i c a l l y t h e s y s t e m we s t i l l u s e .
- 3 -
To the i n v e n t i o n of the photographic process another v e r y
important i n v e n t i o n must be added. In 1846 a French chemist
by name of L o u i s Menard d i s c o v e r e d t h a t c e l l u l o s e n i t r a t e would
d i s s o l v e i n a mixture of e t h e r and a l c o h o l to produce a h i g h l y
v i s c o u s l i q u i d t h a t d r i e d i n t o a hard, c o l o u r l e s s t r a n s p a r e n t
f i l m . He c a l l e d the substance " c o l l o d i o n . " The i d e a of u s i n g
c o l l o d i o n as a photographic emulsion was f i r s t advanced by
Robert Bingham, a B r i t i s h chemist i n 1850.
Very soon a f t e r the d i s c o v e r y of photography Arago and
Gay-Lussac p o i n t e d out t h a t between the photography of t e r r a i n
and the t e r r a i n i t s e l f t h e r e e x i s t s a pure p e r s p e c t i v e r e l a t i o n ,
which might i n i t i a t e the a p p l i c a t i o n o f photographs t o mapping
purposes. They suggested t h a t photography c o u l d be s u b s t i t u t e d
f o r ground surveys wherever t e r r a i n was i n a c c e s s i b l e .
The main c r e d i t f o r the i n t r o d u c t i o n of photogrammetry
belongs to an o f f i c e r i n the Engineer Corps of the French Army
Aime Laussedat. He i s known today as the "Father of Photogram
metry." He c o n s t r u c t e d the f i r s t u s a b l e cameras i n 1851. Using
two photographs he made a few maps by means of photographs
taken from a b a l l o o n . The b a l l o o n photography was f i n a l l y
abandoned s i n c e i t was d i f f i c u l t to expose a s u f f i c i e n t number
of photographs from a s i n g l e s t a t i o n because of problems i n
o r i e n t a t i o n of the b a l l o o n . Laussedat's remaining r e s e a r c h was
concerned w i t h t e r r e s t r i a l photogrammetry. Photographs were
taken with the f i r s t p h o t o t h e o d o l i t e which was a combination of
4 -
c a m e r a a n d t h e o d o l i t e . I n 1898 L a u s s e d a t f i n a l i z e d h i s r e s e a r c h
o f many y e a r s w i t h a book i n w h i c h he d e s c r i b e d p h o t o g r a m m e t r i c
i n s t r u m e n t s a n d m e t h o d s f o r p u r p o s e s o f m a k i n g t o p o g r a p h i c maps. r
The b o o k " R e c h e r c h e s s u r l e s i n s t r u m e n t s , l e s m e t h o d e s e t l e
d e s s i n t o p o g r a p h i g u e s " i s s t i l l r e g a r d e d a s a v e r y v a l u a b l e
b o o k , b e c a u s e t h e m a i n p r i n c i p l e s l a i d down a n d e x p l a i n e d a r e
s t i l l i n u s e .
L a u s s e d a t 1 s i d e a s d i d n o t f i n d a g r e a t r e s p o n s e i n F r a n c e .
O t h e r E u r o p e a n a nd N o r t h A m e r i c a n c o u n t r i e s , h o w e v e r , i m m e d i a t e l y
r e a l i z e d t h e i m p o r t a n c e a n d a p p l i c a b i l i t y o f p h o t o g r a m m e t r y a n d
l e d t o i t s t r e m e n d o u s d e v e l o p m e n t i n A u s t r i a , Germany, I t a l y ,
R u s s i a a n d C a n a d a .
E d o u a r d G a s t o n D e v i l l e i n t r o d u c e d p h o t o g r a m m e t r y t o C a n a d a .
As S u r v e y o r - G e n e r a l o f C a n a d a he s t a r t e d a p h o t o g r a m m e t r i c s u r v e y
f o r m a p p i n g p u r p o s e s i n m o u n t a i n o u s t e r r a i n i n 1887 a n d i n 1889
he p u b l i s h e d h i s h i s t o r i c a l b o o k " P h o t o g r a p h i c S u r v e y i n g , " i n
t h e p r e f a c e o f w h i c h he w r o t e : "The o r d i n a r y m e t h o d s o f t o p o
g r a p h i c a l s u r v e y i n g w e r e t o o s l o w a n d e x p e n s i v e f o r t h e p u r p o s e ;
r a p i d s u r v e y s b a s e d on a t r i a n g u l a t i o n a n d on s k e t c h e s w e r e
t r i e d a n d p r o v e d i n e f f e c t u a l , t h e n p h o t o g r a p h y was r e s o r t e d t o
and t h e r e s u l t s h a v e b e e n a l l t h a t c o u l d be d e s i r e d . " * I n o n l y t h e
two s e a s o n s o f 1893 a n d 1894 t h e C a n a d i a n - A l a s k a n B o u n d a r y
C o m m i s s i o n c o v e r e d some 14,000 s q u a r e m i l e s u s i n g p h o t o g r a m m e t r y .
D e v i l l e was an e x t r e m e l y i n t e l l i g e n t s c i e n t i s t a n d he r e a l i s e d
v e r y s o o n t h a t t h e a p p a r e n t s i m p l i c i t y o f p h o t o g r a p h i c s u r v e y i n g
* [ 1 4 ] -
- 5 -
was a delusion. Professor E.H. Thompson i n the D e v i l l e Memorial
Lecture* i n 1965 wrote: "After eight years' experience of
photographic surveying, D e v i l l e asked himself why such an
apparently advantageous method should be accepted so r e l u c t a n t l y
by the surveying profession generally. He was writing i n 1895;
i f he were wri t i n g today he might s t i l l f i n d his question not
e n t i r e l y out of place." De v i l l e r e a l i z e d that the advantages
of photogrammetry must be emphasized, but also that i t s d i f f i
c u l t i e s must not be minimized. In 1902 D e v i l l e made an addi t i o n a l
contribution to the science publishing a paper i n the Transactions
of the Royal Society of Canada e n t i t l e d "On the Use of the
Wheatstone Stereoscope i n Photographic Surveying." In the
history of photogrammetry th i s was the f i r s t d escription of an
automatic p l o t t i n g instrument. The o r i g i n a l drawing of D e v i l l e ' s
instrument i s shown i n F i g . 1-1.
C
F i g . 1-1. D e v i l l e 1 s automatic p l o t t i n g instrument
*[70]
I n 1858 M e y d e n b a u e r , a German a r c h i t e c t , u t i l i z e d p h o t o
g r a p h i c s u r v e y i n g f o r n o n t o p o g r a p h i c p u r p o s e s f o r t h e f i r s t
t i m e b y o b t a i n i n g r e l i a b l e m e a s u r e m e n t s o f i n a c c e s s i b l e d e t a i l s
on h i s t o r i c a l b u i l d i n g s f r o m two p h o t o g r a p h s . I n h i s a r t i c l e
o f 1896 "Das D e n k m a l e r a r c h i v u n d s e i n e H e r s t e l l u n g d u r c h d a s
M e s s b i l d v e r f a h r e n " * he s u g g e s t e d t h e f o u n d a t i o n o f a s p e c i a l
p h o t o a r c h i v e o f monuments f o r t h e p u r p o s e o f t h e i r m a i n t e n a n c e
a n d r e s t o r a t i o n . T h i s i d e a was l a t e r r e a l i z e d by The I n t e r -
n a t i o n a l A r c h i v e o f P h o t o g r a m m e t r y ( Q u a t r i e m e c o n g r e s i n t e r -
n a t i o n a l de p h o t o g r a m m e t r i e t e n u a P a r i s . P r o c e s - v e r b a u x d e s 1 V
s e a n c e s d e s c o m m i s s i o n s , 1 9 3 6 , pp. 3 1 1 - 3 1 3 : D o l e z a l , E.:
"Uber p h o t o g r a m m e t r i s c h e D e n k m a l a r c h i v e " ) . M e y d e n b a u e r was
a l s o t h e f i r s t s c i e n t i s t who u s e d t h e w o r d " p h o t o g r a m m e t r y " i n
one o f h i s many p a p e r s o f 1 8 9 3 .
The e n d o f t h e n i n e t e e n t h c e n t u r y was c h a r a c t e r i z e d by
t h e d e v e l o p m e n t o f t e r r e s t r i a l p h o t o g r a m m e t r y , w h i c h was a p p l i e d
i n many m a p p i n g p r o j e c t s . The p h o t o t h e o d o l i t e i n v e n t e d by
L a u s s e d a t o b t a i n e d i n i t s v a r i o u s c o n s t r u c t i o n s t h e s h a p e w h i c h
h a s r e m a i n e d u n t i l t o d a y . T h i s i s o b v i o u s f r o m F i g . 1-2 a n d
F i g . 1-3 i n w h i c h t h r e e o l d e r p h o t o t h e o d o l i t e s a r e shown.
U s i n g p h o t o t h e o d o l i t e s , J o r d a n a n d Remele i n 1874 made a
map o f t h e L i b y a n o a s i s D a c h e l a t a s c a l e o f 1:5000.** A t t h e
same t i m e S. F i n s t e r w a l d e r p l o t t e d A l p i n e g l a c i e r s by means
* A r c h i v e o f h i s t o r i c a l b u i l d i n g s a n d i t s f o u n d a t i o n s by means o f p h o t o g r a p h y .
* * [ 4 0 ]
F i g . 1-2. Phototheodolite of I t a l i a n Army from 1889
of photographs. In 1898 he also published a book e n t i t l e d "Die
geometrischen Grundlagen. der Photogrammetrie" (Fundamental
Geometry of Photogrammetry). In that work he solved the problem
of determining the p o s i t i o n of the two camera stations indepen
dently of t e r r a i n measurements from four points i d e n t i f i e d
on both photographs.
- 8 -
(a) P h o t o t h e o d o l i t e by (b) P h o t o t h e o d o l i t e by F i n s t e r w a l d e r P u l f r i c h
F i g . 1-3
A t the t u r n o f the century a r e s e a r c h s c i e n t i s t of K a r l
Z e i s s - J e n a , P u l f r i c h , d e s i g n e d the f i r s t modern photogrammetric
instrument, a stereocomparator ( F i g . 1-4) which used the
p r i n c i p l e s of stereophotogrammetry and a f l o a t i n g mark. Inde
pendently of P u l f r i c h two members of the Geographic I n s t i t u t e
o f Vienna, A. von Hubl and E. von O r e l c o n s t r u c t e d a s t e r e o -
comparator and a stereoautograph r e s p e c t i v e l y . These instruments
- 9 -
meant a r e v o l u t i o n i n photogrammetry and p r a c t i c a l l y s o l v e d the
main problems of t e r r e s t r i a l photogrammetry. •*
The I n t e r n a t i o n a l S o c i e t y of Photogrammetry was e s t a b l i s h e d v
i n 1910 w i t h Dr. Edward D o l e z a l as i t s f i r s t p r e s i d e n t . Three
years l a t e r the s o c i e t y had i t s f i r s t congress i n Vienna.
The c o n s t r u c t i o n of the a i r p l a n e s p u r r e d the development of
a e r i a l photogrammetry. Between the F i r s t and the Second World
Wars Hugershof i n v e n t e d M u l t i p l e x , w i t h the a n a g l y p h i c p r i n c i p l e .
During t h i s p e r i o d the g r e a t m a j o r i t y of s t e r e o instruments such as
the S t e r e o p l a n i g r a p h , Autograph, Stereotopograph, Photocartograph,
Aerocartograph, Stereophot, S t e r e o t o p and many ot h e r s were
inv e n t e d and c o n s t r u c t e d . A l l these instruments were based on
F i g . 1-4. P u l f r i c h ' s stereocomparator
- 10 -
the o p t i c a l or mechanical s o l u t i o n of the fundamental photo
grammetric problem of o b t a i n i n g r e l i a b l e measurements and
f i n a l l y maps from a e r i a l photographs. The problem was
s o l v e d by Otto von Gruber. He s o l v e d the problem, a t f i r s t ,
n u m e r i c a l l y u t i l i z i n g the method of l e a s t squares i n h i s famous
book "Doppelpunkt E i n s c h a l t u n g im Raum." He then suggested h i s
o p t i c a l - m e c h a n i c a l method. Under the c o n d i t i o n t h a t the i n t e r i o r
o r i e n t a t i o n of photographs i s known, the e x t e r i o r o r i e n t a t i o n
may be s o l v e d i n two p a r t s , f i r s t the e s t a b l i s h m e n t of r e l a t i v e
o r i e n t a t i o n and second, the e s t a b l i s h m e n t of a b s o l u t e o r i e n t a t i o n .
R e l a t i v e o r i e n t a t i o n y i e l d s the model of t e r r a i n on e l i m i n a t i n g
y - p a r a l l a x . A b s o l ute o r i e n t a t i o n w i l l o r i e n t the model i n
space w i t h r e s p e c t to the v e r t i c a l a f t e r s c a l e i s brought to a
d e s i r e d v a l u e .
Nontopographic photogrammetry a l s o e x p e r i e n c e d a sudden
development between the two World Wars. Meydenbauer 1s i d e a of
u t i l i z i n g photographic s u r v e y i n g i n a r c h i t e c t u r e was f u l l y
developed. The I n t e r n a t i o n a l A r c h i v e of Photogrammetry a l r e a d y
had a g r e a t c o l l e c t i o n of photographs of almost a l l important
European b u i l d i n g s and h i s t o r i c a l monuments. Even today t h i s
i s not a f o r g o t t e n branch of photogrammetry as i s obvious from
[20]. F i g . 1-5 r e p r e s e n t s the p l o t t i n g of contour l i n e s of
the i n t e r i o r of the Dome of Santa Maria d e l F i o r e i n F l o r e n c e .
The p l o t t i n g a l s o i n d i c a t e s the v a r i o u s f r a c t u r e s e x i s t i n g i n
the s t r u c t u r e and the e r o s i o n of f r e s c o s . The s i g n i f i c a n c e of
the work of the I n t e r n a t i o n a l A r c h i v e can be e a s i l y r e a l i z e d
- 11 -
from the f a c t t h a t a f t e r the Second World War the m a j o r i t y of
b u i l d i n g s destroyed d u r i n g the war were r e c o n s t r u c t e d by means
of photographs taken by the I n t e r n a t i o n a l A r c h i v e of Photogrammetry.
F i g . 1-5
A number of b u i l d i n g s were r e c o n s t r u c t e d from simple photographs
and post cards taken by amateurs and l a t e r e v a l u a t e d i n photo-
grammetric p l o t t e r s . In 1931 K. Schwidefsky, a w e l l known
- 12 -
photogrammetrist wrote a d i s s e r t a t i o n about the a p p l i c a t i o n of
stereophotogrammetry i n a r c h i t e c t u r e . (K. Schwidefsky: "Uber
d i e Awendung der Stereophotogrammetrie auf A r c h i t e c t u r v e r m e s s u n g " ) . *
He p a r t i c u l a r l y emphasized the a p p l i c a b i l i t y o f photogrammetry
to measurements of deformations and movements of b u i l d i n g s .
Archaeology i s a l s o a f i e l d where photogrammetry was used t o
a g r e a t e x t e n t . A r c h a e o l o g i s t s very soon r e a l i z e d t h a t some
o b j e c t s c o u l d become v i s i b l e on a i r photographs, although i t was
almost i m p o s s i b l e to d i s c o v e r them on the ground. During the
f i r s t World War Theodor Wiegand took many p i c t u r e s from an a i r
c r a f t over S y r i a and P a l e s t i n e f o r a r c h a e o l o g i c a l purposes.
A f t e r the war he e v a l u a t e d the p i c t u r e s and p u b l i s h e d them i n
1920.
For the m e t h o d i c a l o r g a n i z a t i o n of a r c h a e o l o g i c a l photogram
metry we are p a r t i c u l a r l y i ndebted to R.P. Poidebard (French)
and O.G.S. Crawford ( E n g l i s h ) . The former r e s e a r c h e d the
a r c h a e o l o g i c a l monuments of S y r i a (R.P. Poidebard: "Photographic 7
a e r i e n n e e t a r c h e o l o g i e . Recherches en Steppe s y r i e n n e - 192 5-
1931," B u l l e t i n de photogrammetrie P a r i s - 1932), and l a t t e r the
p r e h i s t o r i c monuments i n England. The Surveying I n s t i t u t e of
B e r l i n i n 1909 measured h i s t o r i c a l monuments of Greece. Dr. E.
D o l e z a l , the f i r s t p r e s i d e n t of the I n t e r n a t i o n a l S o c i e t y of
Photogrammetry r e p o r t e d about the whole procedure i n "Aufnahme
der Baudenkmaler Griechenlands durch d i e K o n i g l i c h e M e s s b i l d -
*"The a p p l i c a t i o n of stereophotogrammetry i n a r c h i t e c t u r a l s u r v e y i n g "
a n s t a l t i n B e r l i n , " * I n t e r n a t i o n a l A r c h i v e of Photogrammetry
I I 1909-1911.
In the i n v e s t i g a t i o n of c h a r a c t e r i s t i c s of waves and t h e i r
movements photogrammetry p l a y e d a v e r y s i g n i f i c a n t p a r t . W. Laas
i n d i c a t e d as e a r l y as 1906 i n h i s a r t i c l e "Die Messung von Meeres-
w e l l e n und i h r e Bedeutung f i i r den S c h i f f s b a u " * * the p o s s i b i l i t y
o f s e r i o u s a p p l i c a t i o n of photography to the purpose of wave
measurements. Russian s c i e n t i s t W. Dmitrevsky p u b l i s h e d i n
Leningrad i n 1927 a s m a l l book "Photogrammetric measurements of
sea waves." T h i s work was f o l l o w e d by German A. Schumacher, who
i n 1928 made known the r e s u l t s of photogrammetric e v a l u a t i o n of
waves d u r i n g the German e x p e d i t i o n under the t i t l e : "Die
sterephotogrammetrischen Wellen aufnahmen der deutschen a t l a n -
t i s c h e n E x p e d i t i o n . " * * *
*"Surveying of Greek h i s t o r i c a l monuments by the Royal Sur v e y i n g O f f i c e to B e r l i n "
**"Measurements of sea waves and t h e i r Importance f o r Ship C o n s t r u c t i o n "
***"Stereophotographs of Waves from the German A t l a n t i c E x p e d i t i o n "
- 1 4 -
Fig- 1-6
- 15 -
A t y p i c a l p l o t t i n g o f w a v e s i s shown i n F i g . 1 - 6 t a k e n
f r o m Lacmann's b o o k . * A n o t h e r s u r v e y o f waves t h a t i s h i s t o r i
c a l l y i m p o r t a n t was a c c o m p l i s h e d by F r e n c h m a n P h . J a r r e f r o m a
p i e r i n t h e h a r b o u r o f A l g i e r s i n 1 9 3 5 . * *
A v e r y i n t e r e s t i n g c o n t r i b u t i o n o f p h o t o g r a m m e t r y was a l s o
made i n m e t e o r o l o g y . I n 1891 t h e I n t e r n a t i o n a l M e t e o r o l o g i c a l
C o n g r e s s i n M u n i c h d e c i d e d t h a t t h e y e a r s 1896-97 w o u l d be t h e
I n t e r n a t i o n a l Y e a r s o f C l o u d s t o i n i t i a t e e x t e n s i v e • r e s e a r c h o f .
t h e a t m o s p h e r e . E v e n b e f o r e t h i s d e c i s i o n S t r a c h e y a n d W h i p p l e
made many p h o t o g r a m m e t r i c o b s e r v a t i o n s o f c l o u d s a t Kew o b s e r v a
t o r y , b u t l a t e r many p h o t o g r a m m e t r i s t s p a r t i c i p a t e d i n t h e
i n t e r n a t i o n a l r e s e a r c h . W o r l d famous p h o t o g r a m m e t r i s t C. Koppe
w r o t e a n a r t i c l e a b o u t t h e w h o l e w o r k u n d e r t h e t i t l e " P h o t o -
g r a m m e t r i e u n d i n t e r n a t i o n a l e W o l k e n m e s s u n g " - Z e i t s c h r i f t f u r
V e r m e s s u n g s Wesen, 1 8 9 8 . * * *
A b o u t 1930 R. F i n s t e r w a l d e r i n i t i a t e d t h e a p p l i c a t i o n o f
p h o t o g r a m m e t r y t o m e a s u r e m e n t s o f g l a c i e r movements i n t h e S w i s s
A l p s , a n d i n d o i n g s o he s o l v e d s e v e r a l v e r y i m p o r t a n t p r o b l e m s
i n g l a c i a l m e a s u r e m e n t s . F i r s t , d a n g e r a s a v e r y i m p o r t a n t
f a c t o r i n p h y s i c a l s u r v e y i n g o f g l a c i e r s was r e d u c e d t o a minimum.
I n t h e m a j o r i t y o f c a s e s y e a r - r o u n d o b s e r v a t i o n s d i d n o t c r e a t e
any d i f f i c u l t i e s a n d t h e r e f o r e s e a s o n a l c h a n g e s o f v e l o c i t y o f
g l a c i e r s c o u l d be d e t e r m i n e d . The m a i n a d v a n t a g e o f t h e p h o t o
g r a m m e t r i c m e t h o d was t h a t i t was n o t r e s t r i c t e d i n o b s e r v a t i o n s
t o a s i n g l e p o i n t , a s had b e e n t h e c a s e i n c l a s s i c a l m e a s u r e m e n t s
* [ 4 6 ] , **P h . J a r r e : " E t u d e p h o t o g r a m m e t r i q u e de l a h o u l e aux a b o r d s
de l a j e t e e de M u s t a p h a d a n s l a r a d e d ' A l g e r . " ( B u l l e t i n de P h o t o g r a n i m e t r i c 193 5]
* * * " P h o t o g r a m m e t r y and I n t e r n a t i o n a l M e a s u r e m e n t s o f C l o u d s . "
- 16 -
b u t t h a t o b s e r v a t i o n s o v e r a much l a r g e r a r e a g a v e more r e l i a b l e
a n d more o b j e c t i v e r e s u l t s .
E n g i n e e r i n g , i n g e n e r a l , o f f e r e d a g r e a t v a r i e t y o f p r o b l e m s
t h a t w e r e s o l v e d by p h o t o g r a m m e t r i c m e t h o d s . I t i s b e y o n d t h e s c o p e
o f t h i s t h e s i s t o go i n t o a d e t a i l e d d e s c r i p t i o n o f t h e s e m e t h o d s .
I t m i g h t be o f g e n e r a l i n t e r e s t t o s t a t e t h a t d e f o r m a t i o n s
o c c u p i e d t h e m i n d s o f many p h o t o g r a m m e t r i s t s . T h e y e v a l u a t e d
s l o w and f a s t d e f o r m a t i o n s , two a n d t h r e e - d i m e n s i o n a l d e f o r m a t i o n s ,
d e f o r m a t i o n s of- b u i l d i n g s , movements o f t o w e r s and dams, d e f o r m
a t i o n s o f b r i d g e s c a u s e d by s i d e w i n d s , l o a d s o f t r a f f i c , s i n k i n g
o f p i l l a r s and o t h e r f a c t o r s . I n t h e I n t e r n a t i o n a l A r c h i v e o f
P h o t o g r a m m e t r y , v o l u m e I V o f 1913-1914 J . P a n t o f l i c e k d e s c r i b e s
t h e s t e r e o p h o t o g r a p h i c m e a s u r e m e n t o f s m a l l movements i n h i s
a r t i c l e : " S t e r e o p h o t o g r a p h i s c h e s M e s s e n K l e i n e r Bewegungen."*
A t p r e s e n t t h e r e i s a m p l e e v i d e n c e t h a t p h o t o g r a m m e t r y i s b e i n g
u s e d f o r t h e d e t e r m i n a t i o n o f d e f o r m a t i o n s . * *
A s c a n be s e e n f r o m t h e a p p l i c a t i o n s o f n o n - t o p o g r a p h i c
p h o t o g r a m m e t r y a l r e a d y t o u c h e d u p o n , p h o t o g r a m m e t r y i s a
p a r t i c u l a r l y v a l u a b l e m e t h o d when n o r m a l c l a s s i c a l s u r v e y i n g
p r o c e d u r e s , w h i c h must be p e r f o r m e d on some o b j e c t s o r e v e n t s ,
a r e t o o d a n g e r o u s , t i m e c o n s u m i n g , d i f f i c u l t o r c o m p l i c a t e d .
N o n t o p o g r a p h i c p h o t o g r a m m e t r y h a s d e m o n s t r a t e d s p e c i a l v a l u e i n
s u r v e y i n g o f e x t r e m e l y s l o w o r e x t r e m e l y f a s t e v e n t s , a n d o f
o b j e c t s t h a t w o u l d be d e f o r m e d i f t h e y w e r e m e a s u r e d by t r a d i
t i o n a l means. F o r t h e s e r e a s o n s i t c o u l d be w i d e l y u s e d i n
* " S t e r e o p h o t o g r a p h i c m e a s u r e m e n t o f s m a l l movements" * * [ 5 6 ] and [69]
- 17 -
anthropology, ethnology and medicine. Many p h y s i o l o g i c a l
i n v e s t i g a t i o n s and measurements on humans can be made d i r e c t l y
on photographs. T h i s i s also, important i n ethnology, i n s t u d i e s
of c h a r a c t e r i s t i c s of races and to some e x t e n t i n zoology.
Although photogrammetry o f f e r s easy and simple s o l u t i o n s t o
many problems i n medicine i t has not y e t e s t a b l i s h e d a
p l a c e i n medicine which i t dese r v e s . However, there i s hope
t h a t w i t h s i m p l i f i c a t i o n s of photogrammetric procedures, medicine
w i l l r e a l i z e the p o t e n t i a l o f photogrammetry and w i l l adapt some
of the s o l u t i o n s . During the f i r s t World War Dr. W. Exner
suggested t h a t m u t i l a t e d limbs o f s o l d i e r s should be s t e r e o -
s c o p i c a l l y photographed and then p h o t o g r a m m e t r i c a l l y measured
f o r the c o n s t r u c t i o n o f the b e s t p r o s t h e s i s . In the war the
sug g e s t i o n has never been r e a l i z e d . One of the f i r s t a p p l i c a
t i o n s of stereophotogrammetry was the d e t e r m i n a t i o n of deforma
t i o n s of the sp i n e d u r i n g pregnancy. I t has been known f o r a
long time t h a t the spine deforms and a f t e r c h i l d b i r t h r e c o v e r s
a c e r t a i n amount but never to i t s i n i t i a l p o s i t i o n . By means
of s t e r e o s c o p i c p i c t u r e s the amount of permanent deformation
was a s c e r t a i n e d . Photogrammetry was a l s o used to e s t a b l i s h
the r a t i o and c o r r e l a t i o n between s p e c i f i c d i s e a s e s and the
s u r f a c e area i n v o l v e d by d e t e r m i n i n g the area, or volumes of
p a r t s of the body.
To nontopographic photogrammetry must be added micro-
photogrammetry and x-ray photogrammetry. Microphotogrammetry
i s not very s u i t a b l e f o r stereophotogrammetry s i n c e the images
- 18 -
o b t a i n e d by microscopes have i n s u f f i c i e n t depth of f i e l d . The•
problems of microphotogrammetry are d e s c r i b e d i n the a r t i c l e by
M. Z e l l e r : "Die Mikrophotogrammetrie" from the Photogrammetric
I n s t i t u t e of T.H. Z u r i c h i n 193 8.
X-ray photogrammetry i s even' today not used f o r p r e c i s e
measurement because of i t s poor r e s o l u t i o n , although i t has
been used f o r the d e t e r m i n a t i o n of l o c a t i o n s of some opaque
bod i e s . The main problem of x-ray photogrammetry i s the f a c t
t h a t shadow images are not the r e s u l t of a c e n t r a l p r o j e c t i o n .
X-ray photographs would be a r e p r e s e n t a t i o n of o b j e c t s i n
c e n t r a l p r o j e c t i o n o n l y i f the source of x-rays was p h y s i
c a l l y r e p r e s e n t e d by a p o i n t . Another problem i s the unsharp-
ness of the x-ray image. A measured o b j e c t must be of
hi g h c o n t r a s t i f a h i g h degree of accuracy i s r e q u i r e d .
Experiments are c o n s t a n t l y being conducted t o i n c r e a s e the
d e f i n i t i o n of x-ray photography and i f they succeed they w i l l ,
n a t u r a l l y , i n c r e a s e the a p p l i c a b i l i t y of x-ray photogrammetry
i n more a c c u r a t e measurements.
L a s t but not l e a s t i s the a p p l i c a t i o n of photogrammetry
to c r i m i n o l o g y f o r the r e g i s t r a t i o n of f a c t u a l f i n d i n g s . The
f e a s i b i l i t y of photogrammetry f o r those purposes was d i s c o v e r e d
very e a r l y , a f a c t which can be concluded from two a r t i c l e s by
F. E i c h b e r g . The f i r s t a r t i c l e was p u b l i s h e d i n 1911 under
the t i t l e "Die Photogrammetrie b e i k r i m i n a l i s t i s c h e n T a t b e s t -
andsaufnahmen"* and the second from 1913 was " E i n neuer Apparat
*"Photogrammetry i n c r i m i n a l i s t i c f a c t u a l f i n d i n g s "
- 19 -
f u r k r i m i n a l i s t i s c h e T a t b e s t a n d s a u f n a h m e n . " * * I n l a t e r y e a r s
many a r t i c l e s w e r e w r i t t e n a b o u t t h e a p p l i c a t i o n o f p h o t o g r a m
m e t r y t o p o l i c e s e r v i c e . One o f them b y C. S a n n i e a n d L. Amy
a p p e a r e d i n B u l l e t i n de P h o t o g r a m m e t r i e (1934) u n d e r t h e t i t l e
" L a p h o t o g r a p h i c m e t r i q u e s u r l e s . l i e u x . de c r i m e . " Some
c o m p a n i e s e v e n p r o d u c e d s p e c i a l s t e r e o s c o p i c c a m e r a s w i t h a
f i x e d b a s e w h i c h c o u l d be i n s t a n t l y u s e d , l i k e t h e D.K.-120 o f
Z e i s s - A e r o t o p o g r a p h . H o w e v e r , t h e f i r s t p h o t o g r a p h s f o r t h e
r e g i s t r a t i o n o f f a c t u a l f i n d i n g s w e r e t a k e n i n a s i n g l e c a m e r a
i n v e n t e d by E i c h b e r g . To e n a b l e m e a s u r e m e n t s i n t h r e e d i m e n s i o n s
t o be t a k e n he a d d e d t o t h e c a m e r a a s p e c i a l g r i d i n c e n t r a l
p r o j e c t i o n . The o p t i c a l a x i s o f t h e c a m e r a was a l w a y s h o r i z o n t a l
a n d t h e c a m e r a was a p p r o x i m a t e l y 1.5 m e t r e s a b o v e u s u a l l y
h o r i z o n t a l g r o u n d . S i n c e t h e f o c a l l e n g t h o f t h e o b j e c t i v e was
a known q u a n t i t y a n d s i n c e t h e g r i d , w h i c h a t f i r s t c o n s i s t e d
o f v e r y t h i n s t e e l w i r e s t h a t w e r e i n s t a l l e d i n t h e f o c a l p l a n e
a n d l a t e r o f a p l a n e - p a r a l l e l g l a s s p l a t e w i t h e n g r a v e d l i n e s ,
was a l w a y s r e p r e s e n t e d on a p h o t o g r a p h , r e l i a b l e m e a s u r e m e n t s
i n t h r e e d i m e n s i o n s c o u l d h a v e b e e n t a k e n d i r e c t l y f r o m t h e
p h o t o g r a p h .
A f t e r t h e s e c o n d W o r l d War t h e d e v e l o p m e n t o f p h o t o g r a m m e t r y
was i n f l u e n c e d by t h e r a p i d d e v e l o p m e n t o f e l e c t r o n i c c o m p u t e r s . T h e y
o p e n e d t h e new f i e l d o f n u m e r i c a l a n d a n a l y t i c a l p h o t o g r a m m e t r y .
The p r o b l e m o f l o n g a n d t e d i o u s c o m p u t a t i o n was t h e m a i n h i n d r a n c e
t o t h e u t i l i z a t i o n o f n u m e r i c a l p h o t o g r a m m e t r y b e f o r e t h e a p p e a r -
**"A new a p p a r a t u s f o r c r i m i n a l i s t i c f a c t u a l f i n d i n g s "
- 20 -
ance of computers. Today t h i s ceases t o be a problem. F u r t h e r
instruments were improved and p a r t i c u l a r l y l a r g e improvement
i n n e g a t i v e m a t e r i a l has been a c h i e v e d . T h i s improvement g r e a t l y
i n f l u e n c e s the q u a l i t y of f i n a l r e s u l t s . New photographic
emulsions combine very h i g h s e n s i t i v i t y w i t h f a i r l y good r e s o l v i n g
power.
How f a r numerical photogrammetry w i l l e s t a b l i s h i t s e l f i n
the f i e l d of nontopographic photogrammetry remains to be
seen. There are a l r e a d y a few attempts i n t h a t d i r e c t i o n i n
a r c h i t e c t u r a l photogrammetry, where num e r i c a l methods have been
a p p l i e d i n the c r i t i c a l i n t e r p r e t a t i o n o f an a r c h i t e c t u r a l
monument by means of s t a t i s t i c a l a n a l y s i s .
At the end of t h i s h i s t o r i c a l i n t r o d u c t i o n o f nontopographic
photogrammetry i t i s important to emphasize t h a t the a n a l y t i c a l
development of the observed data from photographs p r e s e n t s few
l i m i t a t i o n s but t h e r e i s undeni a b l y a l i m i t of a b s o l u t e accuracy
which i s d e f i n e d by the q u a l i t i e s of the photographic images.
CHAPTER II
CLOSE-RANGE PHOTOGRAMMETRIC SYSTEMS
INTRODUCTION * ,
According to the name, close-range photogrammetry i s a
branch of nontopographic photogrammetry which involves r e l a t i v e l y
short object distances. The maximum object distance i s not
defined. Some photogrammetrists set the maximum range of close-
range photogrammetry at about 300 metres*, some others are li m i t e d
to much shorter distances. K. Schwidefsky thinks that the l i m i t s
of close range photogrammetry may be fixed at those distances
where the photographic range begins for the usual topographic
cameras which are focused to i n f i n i t y . * * The writer disagrees
with any r i g i d l i m i t s and thinks that the measuring f i e l d of
close-range photogrammetry should remain f l e x i b l e and open to
f a c i l i t a t e a l l kinds of solutions of problems that may occur
i n nontopographic photogrammetry. The terms "close-range photo
grammetry" and "nontopographic photogrammetry" are interchangeably
used and are associated with the application of photogrammetric
measurements to a l l other f i e l d s except to the f i e l d of topo
graphic mapping. There should be no difference between them.
The his t o r y of nontopographic photogrammetry displays a
wide spectrum of s c i e n t i f i c problems which can be solved by
photogrammetric methods. With the exception of the u t i l i z a t i o n
of photogrammetry i n architecture, criminology and inv e s t i g a t i o n
of t r a f f i c accidents, which has been a standard procedure i n
many European countries, a l l other applications have remained
i n the experimental stage. "Even though such experiments have
*[18] **[65]
- 22 -
proven the p o t e n t i a l i t y and u s e f u l n e s s o f photogrammetry as a
measuring t o o l i n these d i s c i p l i n e s , the widespread a p p l i c a t i o n
of t h i s technique i n most of these f i e l d s has not g a i n e d g e n e r a l
acceptance. The main reason f o r t h i s s i t u a t i o n seems t o be the
r a t h e r h i g h degree of h e t e r o g e n i t y i n c o n d i t i o n s and requirements /.
of the v a r i o u s a p p l i c a t i o n s . In g e n e r a l , each case i n c l o s e -!
range photogrammetry has to be c o n s i d e r e d a s p e c i a l case r e q u i r i n g
a d i f f e r e n t and perhaps unique a p p l i c a t i o n o f photogrammetric
techniques and i n s t r u m e n t a t i o n . " * The manufacturers of photogram
m e t r i c cameras cannot produce a s u f f i c i e n t l y l a r g e v a r i e t y of
m e t r i c cameras and r e s t i t u t i o n instruments a t a s u f f i c i e n t l y low
p r i c e t o cover r a t h e r d i f f e r e n t needs of nontopographic photo
grammetry.
There i s a l s o another e q u a l l y important reason t h a t c l o s e -
range photogrammetry has not obtained g e n e r a l acceptance. The
methods, instruments and ample p o t e n t i a l i t y of photogrammetry
are p r a c t i c a l l y unknown to s c i e n t i s t s . In the g r e a t m a j o r i t y
of c o u n t r i e s modern photogrammetry, as a s u b j e c t of academic
s t u d i e s , has remained the e x c l u s i v e p r o p e r t y of geodesy and
s u r v e y i n g . However, developments i n r e c e n t years are changing
the s i t u a t i o n s l i g h t l y . From an economical p o i n t of view,
•today, the c o s t of photogrammetric s u r v e y i n g , a l t h o u g h s t i l l
v e r y h i g h , i s v e r y o f t e n more ac c e p t a b l e than the c o s t s of
s u r v e y i n g by c o n v e n t i o n a l methods. P a r t i c u l a r l y when o p e r a t i n g
conveniences of photogrammetry i n some d i f f i c u l t cases are
compared to those o f c o n v e n t i o n a l survey the m e r i t s of the
former o f t e n become obvious.
*[18]
- 23 -
The great advances of a n a l y t i c a l photogrammetry have not
been used to a large extent i n nontopographic photogrammetry.
However, they w i l l become an inevitable t o o l when simple non-
metric cameras are introduced into precise photogrammetry.
DATA ACQUISITION SYSTEMS .
Cameras that are used i n nontopographic photogrammetry can
be c l a s s i f i e d i n t o two main categories: metric and non-metric
cameras.
Metric cameras are s p e c i a l l y developed for photogrammetric
purposes. The great majority of these cameras have elements
of " i n t e r i o r o r i e n t a t i o n " as fixed values that cannot be changed.
An object which i s photographed must be at such a distance from
the camera that the object i s " i n focus." Metric cameras include
phototheodolites and stereometric cameras.
The phototheodolites represent a combination of camera and
theodolite. They generally operate with glass plates and are
designed for a focus at i n f i n i t y , although some of them have
undergone subsequent modifications and can use either f i l m or
plate magazines. Every photogrammetric survey, regarding the
choice of camera i s influenced by two main factors: the object
size shown i n one photograph and i t s reduction to the photograph
scale. Given object distances are often controlled by circum
stances of s i t e and for economical reasons, or to avoid the
bridging of several models photogrammetrists are forced to use
a wide angle lens camera. In the l a s t ten years manufacturers
- 24 -
Fi g . 2.1. Modern Phototheodolite
have shown a tendency to use more and more wide angle lenses
with short f o c a l distances. Some new metric cameras can even
focus an object at close range by varying the p r i n c i p a l distance.
Those that have a f i x e d p r i n c i p l e distance are lim i t e d within
the depth of focus by the focal length and the aperture of the
lens.
Stereometric cameras are fix e d to base of a known length.
Therefore the minimum and maximum operational object distances,
within the required accuracy l i m i t s , are defined by the fix e d
geometry of the stereometric camera system. The f i r s t stereo
metric cameras appeared about 1907 when Thiele, i n Russia,
- 25 -
F i g . 2.2. Stereometric Camera
experimented with h i s stereopanoramograph. At about the same
time Ranza, i n I t a l y , and Boulade, i n France performed s i m i l a r
experiments. Between the two World Wars many types of these
cameras were offered by several manufacturers. Zeiss had the
DK 40 and the DK 120 (f = 55 mm), Wild the C4 and C12 (f = 90 mm)
which a f t e r the second World War were redesigned and appeared
as the C 120 and the C 40 cameras (f = 64 mm). Askania manu
factures the DMK 100/1318 which can be used either as a stereo
metric camera or as a phototheodolite, Galileo has the Bi-Camera
(f = 150 mm), Zeiss (Oberkochen) today offers the SMK 40 and
the SMK 120, and Sokkisha has also two stereometric cameras, the
SKB-45 and the SKB-100. These are, by no means, a l l of the
- 26 -
cameras, i n use. There a r e many o t h e r s . Some can change t h e
l e n g t h o f t h e base l i n e , some o t h e r s i n c o r p o r a t e ' a d d i t i o n a l
d egrees o f freedom by i n t r o d u c i n g convergence between t h e o p t i c a l
axes o f t h e two cameras o r t i l t o f t h e o p t i c a l a xes.
There i s no doubt t h a t m e t r i c cameras newly d e v e l o p e d by
such e s t a b l i s h e d f a c t o r i e s as Z e i s s , W i l d , t h e G a l i l e o a r e w e l l
s u i t e d t o many a p p l i c a t i o n s . However, t h e y have t h e i r d e m e r i t s
and t h e y c annot s o l v e many problems. S i n c e t h e g r e a t m a j o r i t y
o f m e t r i c cameras use g l a s s p l a t e s as an e m u l s i o n h o l d e r and
t h e r e f o r e have no g r e a t problems w i t h d i f f e r e n t i a l s h r i n k a g e ,
t h e y a r e v e r y heavy and b u l k y and cannot be used when p h o t o
graphs must be t a k e n i n v e r y s h o r t time i n t e r v a l s . They must
always have a v e r y s t a b l e p l a t f o r m and can h a r d l y be used f o r
exposures t a k e n v e r t i c a l l y downwards. A s p e c i a l d i s a d v a n t a g e
o f most m e t r i c cameras i s t h e i r i n a b i l i t y t o exchange l e n s e s .
A r a p i d i n c r e a s e o f i n t e r e s t i n t h e a p p l i c a t i o n o f p h o t o
grammetry i n v a r i o u s branches o f s c i e n c e cannot be s a t i a t e d w i t h
o n l y m e t r i c cameras. S t a n d a r d amateur and p r o f e s s i o n a l cameras,
t e l e v i s i o n s y s t e m s , h o l o g r a p h y , x - r a y s and many o t h e r "non-
c o n v e n t i o n a l " p h o t o g r a p h i c systems have been s e r v i n g as non-
m e t r i c d a t a a c q u i s i t i o n systems. Very c o n c e n t r a t e d i n v e s t i g a t i o n s
i n numerous photogrammetric c e n t r e s a l l o v e r t h e w o r l d a r e now
underway t o e v a l u a t e t h e q u a l i t y o f n o n - m e t r i c d a t a a c q u i s i t i o n
systems. The i d e a o f u s i n g r e l a t i v e l y cheap cameras f o r p h o t o
grammetric purposes i s , n a t u r a l l y , n o t new. S e v e r a l a t t e m p t s
have been made t o m o d i f y n o n - m e t r i c cameras by i n t r o d u c i n g
- 27 -
f i d u c i a l marks and s t a b i l i z i n g the i n t e r i o r o r i e n t a t i o n , but
these changes have proved to be very expensive, e s p e c i a l l y i f
the accuracy of metric cameras i s to be achieved. The r e s u l t s
of resent investigations show that there i s a d e f i n i t e place
i n photogrammetry f o r non-metric cameras, p a r t i c u l a r l y when the
requirements i n accuracy of measurements are not too high. The
main problem to be solved i s to devise a r e l i a b l e and simple
method of c a l i b r a t i n g of cameras. The standard laboratory
methods used for metric cameras are not very suitable for non-
metric because of t h e i r unstable parameters of i n t e r i o r o r i e n t a
t i o n . In general, the unknown parameters of the i n t e r i o r and
exterior o r i e n t a t i o n have to be determined for each i n d i v i d u a l
picture by the methods that w i l l be explained l a t e r .
The a p p l i c a t i o n of non-metric cameras for data a c q u i s i t i o n
systems i n photogrammetry may open the door of photogrammetry to
many engineers and s c i e n t i s t s i n a great variety of f i e l d s and
may enable them to make use of the technical and economical
advantages of photogrammetry." A l l indications are that non-
metric cameras w i l l play an important role i n future expansion
of close-range photogrammetry and i n i t s general acceptance as
a measuring t o o l i n a wide spectrum of d i s c i p l i n e s and f i e l d s .
Although experimental research has so far concentrated i n better
non-metric cameras (Hasselbland, R o l l e i f l e x SL, Robot, Linhof
Technika, etc.) and proven th e i r photogrammetric worthiness,
i t i s anticipated that less elaborate cameras can be used,
p a r t i c u l a r l y i n applications with medium and low accuracy
- 28 -
requirements."*
CALIBRATION OF CAMERAS
"Camera cal ibrat ion is a process whereby the individual
characterist ics of the mapping Or charting camera are determined.
These include the geometric constants known as the :inner, or
in ter ior , orientation elements and the image quality of the
cartographic lens . " * *
To obtain s i ze , form and dimensions of an object from a
photograph, the photograph must be correctly oriented. The
orientation is a geometrical condition determined by the or ien
tation elements. The orientation elements of a single photo
graph can be c lass i f i ed into two groups: elements of inter ior
and elements of exterior orientation.
The elements of interior orientation in turn, can be
referred to a camera or to a photograph. A bundle of l ight rays
from a point source which enters the entrance pupil of the
objective opt ical system leaves the exit pupil (centre of pro
jection) and forms an image in the plane of photographic emulsion.
This image is more or less blurred because of imperfections of
the opt ical system. After later development and f ixing,the
latent image is transformed to a negative image. It i s obvious
that the negative image w i l l also be blurred, but i t s shape and
density distr ibut ion w i l l d i f fer from those of the latent image.
The change depends upon "the characteristics of the photographic
*[44] ** [4]
- 29 -
m a t e r i a l , the s p e c t r a l composition o f the l i g h t , the c o n t r a s t
between source and background, and the p r o c e s s i n g method
a p p l i e d . " * From these c o n s i d e r a t i o n s , and knowing t h a t i n
r e s t i t u t i o n t h e o b s e r v e r decides where the "middle" of b l u r i s
f o r p l o t t i n g purposes and t h e r e f o r e i n t r o d u c e s a c e r t a i n p e r s o n a l
e r r o r , i t f o l l o w s t h a t the p o s i t i o n of the image i s r a t h e r an
undetermined concept. I t must be s u b s t i t u t e d by f i c t i t i o u s image
p o i n t s , i . e . the p o i n t s a t which the measuring mark i s p l a c e d
when e v a l u a t i n g the photograph.
The purpose o f i n t e r i o r o r i e n t a t i o n i s the r e c o n s t r u c t i o n
of the o b j e c t bundle. In d e a l i n g w i t h the o b j e c t bundle we
c o n s i d e r an i n f i n i t e number of o b j e c t rays which have the c e n t r e
o f the entrance p u p i l as t h e i r common p r o j e c t i o n c e n t r e . The
o b j e c t bundle must be d i s t i n g u i s h e d from the image bundle, which
has the c e n t r e o f e x i t p u p i l as i t s p r o j e c t i o n c e n t r e . The
c o n s i d e r e d o b j e c t and image rays correspond t o the p r i n c i p a l
r a y s and i n an i d e a l case the p e r s p e c t i v e c e n t r e s " are conjugate
a x i a l p o i n t s whose c h a r a c t e r i s t i c s are t h a t the p r i n c i p a l r a y s ,
p a s s i n g through the p e r s p e c t i v e c e n t r e i n the o b j e c t space,
emerge from the p e r s p e c t i v e centre i n the image space p a r a l l e l
t o t h e i r o r i g i n a l d i r e c t i o n . " * *
To o b t a i n the undeformed model from two o v e r l a p p i n g photo
graphs taken a t two d i f f e r e n t s t a t i o n s two o p e r a t i o n s must be
performed: (a) r e c o n s t r u c t i o n of o b j e c t bundles o f both
photographs and
*[57] **[4]
- 30 -
(b) r e c o n s t r u c t i o n o f t h e i r r e l a t i v e p o s i t i o n s
F o r the l a t t e r t h e o r i g i n a l d i s t a n c e between t h e p e r s p e c t i v e
c e n t r e s o f t h e o b j e c t b u n d l e s i s n a t u r a l l y r e d u c e d by a s c a l e
f a c t o r .
T h e r e f o r e i t can be c o n c l u d e d t h a t t h e i n t e r i o r o r i e n t a t i o n
r e c o n s t r u c t s t h e o b j e c t b u n d l e s and n o t n e c e s s a r i l y t h e image
b u n d l e s . O n l y i n t h e case o f P o r r o - K o p p e - p r i n c i p l e where t h e
g e o m e t r i c a l and o p t i c a l p r o p e r t i e s o f t h e camera and t h e
r e s t i t u t i o n p r o j e c t o r a r e i d e n t i c a l t h e i n t e r i o r o r i e n t a t i o n
i n c l u d e s a l s o t h e r e c o n s t r u c t i o n o f t h e image b u n d l e s . However,
t h e P o r r o - K o p p e - p r i n c i p l e / t o t h e w r i t e r ' s knowledge, has n o t
been used i n c l o s e - r a n g e photogrammetry.
The elements o f i n t e r i o r o r i e n t a t i o n a r e n o r m a l l y d e t e r m i n e d
by t h r e e t y p e s o f d e f i n i t i o n s : g e o m e t r i c a l , p h y s i c a l and f a c t u a l .
The g e o m e t r i c a l d e f i n i t i o n t r e a t s photography as a r e s u l t o f a
s i m p l e c e n t r a l p r o j e c t i o n d i s r e g a r d i n g a l l d e f o r m a t i o n s . The
p h y s i c a l d e f i n i t i o n i n c l u d e s a l l o p t i c a l d e f o r m a t i o n s o f t h e
camera assuming t h e r o t a t i o n a l symmetry o f d e f o r m a t i o n s around
t h e p r i n c i p a l p o i n t . The f a c t u a l d e f i n i t i o n c o m p r i s e s a g e n e r a l
c a s e . The p arameters o f t h e f a c t u a l i n t e r i o r o r i e n t a t i o n a r e
d e t e r m i n e d by t h e c a l i b r a t i o n p r o c e d u r e and a p p l i c a t i o n o f t h e
method o f l e a s t s q u a r e s f o r t h e e v a l u a t i o n o f o b t a i n e d r e s u l t s .
S i n c e t h e o b j e c t b u n d l e has a s p a c i a l c h a r a c t e r ( i t i s
d e t e r m i n e d i n t h r e e d i m e n s i o n a l space) and t h e c o r r e s p o n d i n g
images a r e r e c o r d e d on t h e t w o - d i m e n s i o n a l p h o t o g r a p h i c p l a n e ,
- 3 1 -
the reconstruction of object bundles from two-dimensional images
requires a perspective centre. According to the physical d e f i n i
tion the perspective centre i s the centre of the e x i t p u p i l . The
p r i n c i p a l point i s then defined as the foot of the perpendicular
from the perspective centre to the picture plane. This i s a
geometrical, d e f i n i t i o n because i t assumes a
lens. In the f a c t u a l d e f i n i t i o n object c i r c l e s are projected
as some d i s t o r t e d curved l i n e s and the calibrated p r i n c i p a l
point i s defined as a point with minimum asymmetry. W. Roos
uses a very simple d e f i n i t i o n of the p r i n c i p a l point which
corresponds to the applied c a l i b r a t i o n method. "The p r i n c i p l e
point i s the trace on the photograph of a ray of l i g h t through
the centre of the entrance p u p i l , which i s perpendicular i n the
object space to the picture plane."*
The camera Constant, C , i s a factor which connects
F i g . 2-3 *[58]
angular value x and the corresponding l i n e a r distance r 1 (see
Fi g . 2-3).
r 1 = C K F ( x ) (2.1)
Under the assumption of d i s t o r t i o n - f r e e o p t i c a l system and when
the photographed objects are at i n f i n i t y the camera constant
becomes the f o c a l length of the objective. According to the
geometrical definitionj.the camera constant i s the distance between
the perspective centre and the p r i n c i p l e point.
If the object bundle i s sh i f t e d p a r a l l e l to i t s e l f from
the entrance p u p i l to the exit pupil as i t s projection centre
and the rays are produced to the intersection with the plane of
photograph, then these inter s e c t i o n points, in general, w i l l
not be i d e n t i c a l to the corresponding images on the photograph.
The p o s i t i o n of the perspective centre may be moved but normally
Fig. 2-4
- 33 -
i t i s impossible to f i n d a position of the perspective centre
such that the reconstructed object bundle from images of points
on the photograph i s i d e n t i c a l to the o r i g i n a l object bundle.
The difference i n location between the i n t e r s e c t i o n points and
the image points represents l i n e a r d i s t o r t i o n . I t i s obvious
that the d i s t o r t i o n has no absolute, or constant value for a l l
points but depends upon the position of a ray bundle with respect
to the photograph. Since r e s t i t u t i o n instruments use a central
projection to reconstruct the object bundle sp e c i a l measures
must be considered to eliminate or at l e a s t to minimize the
influence of the d i s t o r t i o n . Various methods that have been
applied and a l l use the s h i f t of the image points to positions
such that the d i s t o r t i o n i s neutralized. The s h i f t can be
performed o p t i c a l l y or mechanically. Optical methods use either
a special lens with the required amount of d i s t o r t i o n or a
d i s t o r t i o n compensating glassplate. The mechanical solu t i o n i s
achieved by varying the camera constant.
As a conclusion, i t can be said, that i n t e r i o r o r i e n t a t i o n
defines a p o s i t i o n of the photograph r e l a t i v e to the projection
centre and i s given by the position of the p r i n c i p a l point on
the photograph and the camera constant, according to the geo
metrical d e f i n i t i o n .
The determination of the position of the p r i n c i p a l point
can be made when two conditions are f u l f i l l e d . F i r s t , there
must be a s u f f i c i e n t number of image points i n the plane of the
photograph, and, second, the o r i g i n a l shape of the object bundles
- 34 -
must be known. The determination i s then reduced to a resection
problem with an additional condition: the remaining differences
i n l o cation between the image points and the points of i n t e r
section of the plane of photograph and the rays produced of the
object bundles must be symmetrical about the p r i n c i p a l point.
For p r a c t i c a l purposes one ray of the object bundles which
passes close to the centre of the photograph i s chosen as the
i n i t i a l ray. The ray intersects the photograph at r i g h t angle
i n i t s corresponding image point. If now some value for the
camera constant i s assumed (an approximate value of the f o c a l
length), then a prov i s i o n a l position of the object bundles i s
defined. Naturally other rays intersect the photograph i n
points that are not i d e n t i c a l t o - t h e i r corresponding images but
they are r e l a t i v e l y close. The differences i n positions between
image points and the corresponding intersection points measured
i n a rectangular coordinate system of the image plane represent
pr o v i s i o n a l d i s t o r t i o n s .
A'x = x - x' } (2.2)
A*y = y - y*,
where x 1 and y' are the coordinates of int e r s e c t i o n points.
Since the choice of the camera constant and the pro v i s i o n a l
p r i n c i p a l point i s r e l a t i v e l y good, only small, d i f f e r e n t i a l
changes i n po s i t i o n of the perspective centre must be determined
by the method of lea s t squares. These d i f f e r e n t i a l changes
consist of three s h i f t s dx, dy, dz, and three rotations da, dB
- 35 -
z
F i g . 2-5
and dy about x, y and z-axis respectively. Introducing these
changes the p r o v i s i o n a l distortions A'x and A'y w i l l create
new values denoting the new values by Ax and Ay, the approximate
value of the camera constant by h, and applying Otto von Gruber's
well known d i f f e r e n t i a l formulae,* two equations are obtained
Ax = A'x - dx - £ dz + 2 £ da - h ( l + d6 - ydy
2 } (2.3) Ay = A'y - dy - £ dz '+• h ( l + £r)da - d8 + xdy
*[28] , or [24]
- 36 -
R. Roelofs* r e s t r i c t s the whole computation to only two rows of
points along the x-axis and the y-axis assuming that the tangen
t i a l d i s t o r t i o n i s zero. Then equations (2.3) for points along
the x-axis become
Ax = A'x - dx - *- dz - h ( l + ~ ) dB } (2.4)
Ay = o,
and for points along the y-axis
Ax = o } ( 2 . 5 )
2 Ay = A'y - dy - ^ dz + h(1 + y)da
The coordinates of the p r i n c i p a l point with respect to the
changed p o s i t i o n of the perspective centre are dx and dy. I f
now the condition of symmetrical d i s t o r t i o n s i s to be s a t i s f i e d ,
pairs of points on the x-axis symmetrical with respect to the
p r i n c i p a l point are considered. For any pair of symmetrical
points x^ and x.. there are two equations i n accordance with
(2.4)
X • X • Ax. = A'x. - dx - ^ dz - h ( l + -i-5-)dB x l h h 2
and 2
X . X « Ax. = A'x. + dx - dz + h ( l + -£r) dB j j h h 2
I f now d i s t o r t i o n s Ax^ and Ax., are to be symmetrical, the
difference between them w i l l be zero.
[ 5 7 ]
A'x. - A'x. - 2dx - 2h(l •+ ^ r ) dB = o (2.6)
Since the approximate value of the camera constant i s d i r e c t l y
eliminated from further computations, i t has no influence on the
symmetry of d i s t o r t i o n . However i t does influence the amount
of d i s t o r t i o n . Therefore a camera constant must be determined
such that the d i s t o r t i o n i s d i s t r i b u t e d over the whole photo
graph. Then that camera constant i s c a l l e d : c a l i b r a t e d f o c a l
length.
The e x t e r i o r orientation, defines the p o s i t i o n of the camera
i n an object coordinate system. The perspective centre i s
determined by rectangular coordinates x , y , z . The a d d i t i o n a l J 3 o o o elements of the e x t e r i o r orientation are three r o t a t i o n angles
co, <J>, and K about x, y, and z-axes respectively. The purpose
of the exterior o r i e n t a t i o n i s to orient the reconstructed
object bundles with respect to the plotted o r i e n t a t i o n points
i n the same r e l a t i v e p o s i t i o n that the o r i g i n a l object bundles
occupied i n the respect to the o r i g i n a l ground points. In
t e r r e s t r i a l photogrammetry the elements of exterior o r i e n t a t i o n
are determined by some conventional survey procedures. In a"
r e a l photogrammetry they are i n d i r e c t l y obtained by absolute
orientation.
In close range photogrammetry the parameters of e x t e r i o r
o r i e n t a t i o n are sometimes determined i n the same way as i n
t e r r e s t r i a l photogrammetry. However in the great majority of
cases, p a r t i c u l a r l y when non-metric cameras are used, the
- 38 -
parameters of the exterior orientation are determined simultan
eously with the elements of i n t e r i o r orientation by a c a l i b r a t i o n
procedure.
Laboratory and f i e l d c a l i b r a t i o n procedures for a e r i a l
cameras are well established and known. These procedures are
not p a r t i c u l a r l y suitable for close-range cameras, since the
use of collimators, multi-collimators, goniometers, etc...
assumes camera focusing to i n f i n i t y . For the same reasons
s t e l l a r methods are also not applicable. In the great majority
of p r a c t i c a l cases cameras used i n close-range photogrammetry
are focussed to some f i n i t e distance or they have variable
focus.
The need for a standard method of c a l i b r a t i o n of close-
range cameras (metric as well as non-metric) led to the develop
ment of r e l a t i v e l y large number of procedures recommended by
various authors and i n s t i t u t i o n s . Almost a l l have one thing in
common: they are performed under normal working conditions and
therefore y i e l d r e a l i s t i c c a l i b r a t i o n r e s u l t s .
From these methods f i v e c h a r a c t e r i s t i c approaches used i n
close-range camera c a l i b r a t i o n have been selected and they w i l l
be described i n d e t a i l . -
HALLERT'S GRID METHOD*
Ha l l e r t ' s g r i d method i s used to determine the parameters
of i n t e r i o r o r i e n t a t i o n and the d i s t o r t i o n of cameras and
* [ 2 5 ]
- 39 -
projectors. The image of a very, accurate g r i d projected through
the lens of a photogrammetric instrument i n the normal p o s i t i o n
(<j> = or = K = o) i s evaluated. The coordinates of the projected
g r i d are measured i n the coordinate system of the object or
model space of the instrument. "The discrepancies between the
measured machine coordinates and the corresponding enlarged g r i d
coordinates are assumed to depend upon the errors i n the inner
and outer ori e n t a t i o n of the projector and the accidental errors
of the measurements."*
Fig. 2 - 6
If redundant observations are made, the adjustment of the
parameters of exterior orientation (dx Q, dy Q, d z Q , d<\>, dco, die)
* [ 2 5 ]
- 40 -
i s performed by the method of least squares.
The measured coordinates are compared with the g r i d
coordinates m u l t i p l i e d by scale factor h/f. Then the d i s
crepancies i n the measured coordinates are
dx = x - x'
dy = y -
i h
} (2.7)
f
Small changes of the parameters of exterior o r i e n t a t i o n
cause changes of the rectangular coordinates of projected points
and these changes are determined by well known d i f f e r e n t i a l
formulae derived by von Gruber:
2 d y = d y + £ dz + x d K + ^ t r d<f> + h (1 + £ s-)du), o h o h h 2
2 d x = dx + £ d z - y d K + h ( l +.£-)d<|> + ^ du. o h o - 1 h 2 T h
} (2.8)
If instead of machine coordinates the image coordinates h h
are applied (x = x' -; y = Y'f") t w o s i m i l a r equations are
obtained. dy = dy Q .+ ^- d z Q + x'j dx + h^f- d(J) + h ( l + ^-)dw
} (2.9)
dx = dx Q + d z Q - y'| d< + h ( l + j^-)d<j> + S l Z l hdw
From these equations the observation equations r e s u l t .
v y = dy Q + ^-.4z Q + x * j die + h ^ ^ - dcj> + h ( l + ^4)dw - dy, } (2.10)
v = dx + ^- dz - y*£ d< + h.(l + ^W) + h ^ i l ~ du - dx. X O f 0 J f X f 2 ' ^ f 2
- 41 -
The same f i n a l equations are obtained i f instead of the
projector, a camera i s calibrated. The photograph of the g r i d
i s taken from a point v e r t i c a l l y above the centre point of the
g r i d and with the negative plane accurately p a r a l l e l to the
object plane. A two dimensional test f i e l d contains a great
number of g r i d points or targets arranged i n a concentric
c i r c u l a r pattern. The adjustment i s performed independently
y
/'
8' 2'
4 /
7' ! ( <
fa _^ a
c
3 2
6' 4'
V
F i g . 2-7
for points on a single c i r c l e . The number of points on each
c i r c l e can vary. H a l l e r t suggested two combinations of f i v e
and nine-point adjustments. The five-point adjustment includes
the centre of the g r i d (C) and four stations on a c i r c l e . The
nine-point adjustment includes eight points on a c i r c l e and the
- 42 -
centre. I t i s obvious that the nine-point adjustment i s con
siderably stronger than the corresponding fi v e - p o i n t combination.
Therefore the nine-point combination may be applied for larger
c i r c l e s , and the fi v e - p o i n t adjustment w i l l s u f f i c e for smaller
r a d i i .
If the corrections to the elements of orientation are to
be determined equations (2.10) must be changed to the form
vy = - d y Q - ^ - d z Q - x'j d K - h P- dcj) - h(l + ^-) do) - d y } (2.11)
x' .12 v = - dx - V dz + y'§- d< - h ( l + ^ - ) dcj> - h ^ | — du> - dx x o f o J f f 2 ' T f 2
Taking, for example, a c i r c l e of radius R containing four
stations 1, 2, 3, 4 and the centre (C) for the f i v e - p o i n t
adjustment (see F i g . 2-7), the c o e f f i c i e n t s of the normal
equations are obtained from the observation equations knowing
the rectangular coordinates of the f i v e stations.
Stations: C 1 2 3 4
Latitude (Y'): o a -a . -a a
Departure (X 1): o a a -a -a
a = R cos 45°
R s i n 45°
- 43 -
COEFFICIENTS OF OBSERVATION EQUATIONS AND THE NORMALIZATION
0
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- 44 -
[dl] - a (dy i+dy 2 - d y 3 - d y i f - d x i + d x 2+dx3 - d x i t) = a N 5 2
a 2 a 2
[el] = [dx] + ^"(dy i-dy2+dy 3-dyi f+dxi+dx2+dx3+dxi l) = [dx] + -^2 N 5 3
2 2 [ f l ] = [dy] + j 2 -(dyi+dy2+dy 3 +dy l t +dxi-dx2+dx3-dx l t ) = [dy] + -prUs*
The normal equations w i l l then be:
5 dx + h(5 + ^-)dc|> + [dx] = o o E
5 d y Q . •+ h(5 + dcu + [dy] = o
2
8 ^_ d z Q + a N 5 i = o
8 ^ d< + a N 5 2 = o
( 5 + i | i ) d x Q + h(5 + + ^fr)d* [dx] + N53 = o { 5 + i | l ) d W + h(5 + S|£.)dw + [dy] + fj- N 5* = o
Since many terms of the normal equations are zero standard
solutions of the normal equations such as Gauss-Dolittle, Cholesky,
Gerasimov, Banakiewicz and some others are not the shortest
methods. In t h i s case, probably, the best method i s to solve the
li n e a r equations d i r e c t l y . From the f i r s t and f i f t h normal
equations unknowns dx Q and dcf> are obtained by the elimination
method. The f i r s t normal equation i s m u l t i p l i e d by the factor
i ( 5 5 1 0 f 2 ' 1 4a 2
- -n-(5 + —ET) and I S added to the f i f t h equation.
- 45 -
- (5 + ^ - ) d x o - |(25 + 40 p- + 16 f )dcf> - |(5 + [dx] = o
(5 + ^-)<ix o + h(5 + + ^-)dc}> + [dx] + |J- N 5 3 = o
h(5 + l | i •+ 8|1 _ 5 _ S a l ' . ^ . |l ) d ({> = 1 ( 5 + [dx]-[dx ] - | J - N 5 3
9/1-a A-, 2 -.2
d(j).h ±11^ = [dx] ( l + l ^ - l ) - N 5 -3
- 5 £ * /4[dx] - 5 -N53, a 2
- d < t ) " 24iAh ( — 5 > fT
_ f 2 , [dx] _ 5 N 5 3 v a < f > " a 2h V 6 24 V (2.12)
The unknown dx Q i s obtained when the l a s t equation for dcj>
i s substituted into the f i r s t normal equation.
4a 2, f 2_ , [dx] _ 5 N53_N 5 dx = - [dx] - h(5 .+. ^ r ) f 2'a2"h v 6 24 '
5 axQ - - .dx, - [d x ] f f i - 1 [fcc, 2 | 0 ^ + 2 P _ | ^
And from here
AV - r ^ v i 2a 2 + f 2 . „ 5 f 2 + 4a 2 n dx Q - - [dx] + N 5 3 24a 2 ( 2 ' 1 3 )
In the same manner, taking the second and s i x t h normal
equations the next two unknowns dy Q and dco are determined.
a a ) i ^ h ( 6 ~2A—} (2.14)
- 46 -
,q„ _ 2a 2 + f 2 , „ 5 f 2 + 4a 2 / 0 1 C , dy o - - [dy] _ - + N s i t 2 4 a 2 (2.15)
The l a s t two unknowns d z Q and d< are derived d i r e c t l y from
the t h i r d and fourth normal equations respectively.
d z o = " s l N 5 1 ( 2 ' 1 6 )
d K = " 8ah N s 2 . (2.17)
" I f the points are chosen so that they within each combination
have the same distances from the centre,point, the r a d i a l d i s
t o r t i o n w i l l r e s u l t i n changes of d z Q between the d i f f e r e n t
combinations."* Naturally, the whole adjustment procedure i s
based on the assumption that the approximate values of the elements
of o r i e n t a t i o n are close to the r e a l values. In the case i n
which the corrections to the approximations are large quantities,
d i f f e r e n t i a l equations (2.10) are no longer s t r i c t l y v a l i d , since
i n t h e i r derivation by Taylor's series a l l terms of second or
higher order were disregarded as being p r a c t i c a l l y i n s i g n i f i c a n t .
In a s i m i l a r way the formulae for the nine-point adjustment
combination may be derived. The f i n a l expressions for the
corrections to the elements of orientation, the standard deviation
of unit weight and weight and c o r r e l a t i o n numbers may be found as
i n [26].
H a l l e r t ' s procedure has been applied to a great number of
p r a c t i c a l adjustments i n a l l kinds of perspective imaging. The
applications to x-rays apparatus, microscopes, t e l e v i s i o n s and
*[25]
- 47 - .
a va r i e t y of metric and non-metric cameras are described i n
many of his papers published i n in t e r n a t i o n a l surveying and
photogrammetric p e r i o d i c a l s . *
JACOBI'S METHOD FOR NON-METRIC CAMERAS
Jacobi's method can be used for metric but i s p a r t i c u l a r l y
suitable for non-metric cameras. The mechanical system of a
non-metric camera needs no modifications and can be l e f t untouched
since the elements of i n t e r i o r and exterior orientations are
simultaneously determined for every single photograph. This i s
possible only i f a c a l i b r a t i o n system of known points i s photo
graphed together with the measured object. The great majority
of non-metric cameras have variable focus objectives and some
of them also have exchangeable lenses. "To overcome these
s t a b i l i z a t i o n problems, the o p t i c a l axis of the lens i s i n t r o
duced. The exterior orientation i s defined from the or i e n t a t i o n
of the o p t i c a l axis. The r a d i a l lens d i s t o r t i o n i s defined from
the same o p t i c a l axis. The picture plane may not be perpendi
cular to the o p t i c a l axis but the introduction of 2 angles, a
and 8 w i l l describe the difference i n d i r e c t i o n between the
o p t i c a l axis and the picture normal so that the camera geometry
of a f l e x i b l e camera can be s u f f i c i e n t l y described a n a l y t i c a l l y . " * *
(See F i g . 2-8)
The lens d i s t o r t i o n i s a n a l y t i c a l l y defined by means of a
series and the number of terms defines degree of s o p h i s t i c a t i o n .
*[26], [25], [29], [27] **[39]
- 48 -
F i g . 2-8
Jacobi i n his work used only the r a d i a l d i s t o r t i o n expressed by
the well-known polynomial
dr = a 3 r 3 + a 5 r 5 + a 7 r 7
naturally, t h i s simple formula cannot t h e o r e t i c a l l y s a t i s f y a l l
lenses but the d i s t o r t i o n of most q u a l i t y lenses can be expressed
by t h i s equation. The parameters of the lens d i s t o r t i o n ( a 3 , as,
a 7 , a g , a i i •••) are to a great extent correlated, but as long
a s only the f i r s t three terms are used the c o r r e l a t i o n i s at a
minimum and can be tolerated. The number of control points i n
a c a l i b r a t i o n system i s another important factor of c o r r e l a t i o n .
"Especially i n applying a c a l i b r a t i o n system containing only
the minimum number of control points, i t might happen that the
i t e r a t i v e optimization procedure does not converge."*
In the actual c a l i b r a t i o n procedure a l l parameters are
* [ 5 ]
- 4 9 -
seldom determined for every photograph since some of them are
not altered from photograph to photograph. The most convenient
way i s to determine these parameters once and for a l l i n a
laboratory test f i e l d , and then the normal c a l i b r a t i o n procedure
w i l l determine only the unstable parameters for every single
photograph. One of the stable parameters i s the r a d i a l d i s t o r t i o n
of the lens. In some cameras the housing and fo c a l plane are so
r i g i d and stable that the angles a and 8 can be given the fi x e d
value of zero.
In general the c a l i b r a t i o n provides the six elements of
exterior o r i e n t a t i o n (X , Y , Z , u), <j>, K) , the f i v e elements o o o
of i n t e r i o r o r i e n t a t i o n (X 1, Y ', c, a, 8 ) , and the three
parameters of the r a d i a l d i s t o r t i o n ( a 3 , a 5 , a 7 ) . To f i n d a
unique solution of the fourteen unknowns at least 5 well d i s
tributed control points and t h e i r measured images must be
known. In a p r a c t i c a l case of c a l i b r a t i o n a larger number of
control points i s taken and then by the u t i l i z a t i o n of the
method of l e a s t squares the most probable values of the unknown
parameters are determined. The number of unknowns i s reduced
when the parameters of the r a d i a l d i s t o r t i o n are determined
beforehand using a three-dimensional laboratory t e s t f i e l d . In
t h i s case they are referred to the o p t i c a l axis of the lens and
not as usual to the p r i n c i p a l point of the photograph. With the
exception of the lens d i s t o r t i o n , a l l parameters of i n t e r i o r as
well as of exterior o r i e n t a t i o n are determined a n a l y t i c a l l y for
each photograph. Jacobi's solution i s b a s i c a l l y very simple
- 50 -
and involves four consecutive coordinate transformations. Figure
2-9, 2-10, and 2-11 display the a n a l y t i c a l r e l a t i o n s between an
object and i t s photographed image graphically. The diagrams
may help to understand and explain the elements involved i n the
coordinate transformations.
Fig . 2-9
The f i r s t transformation i s a general s p a t i a l transformation
of a point from the geodetic or c a l i b r a t i o n coordinate system
(Xp, Yp, Zp) to the camera coordinate system (x c/ y z c) where
the z-axis of the camera coordinate system i s i d e n t i c a l with the
o p t i c a l axis of the lens. The transformation i s normally expressed
i n matrix notation by the following formula
- 51
X c
Yc —
z c
a i i ai2 a i 3
3-2 1 a2 2 a2 3 a 3 1 ^32 ^3 3
X_, - X P o Y_ - Y
P O Z n - Z P o
( 2 . 1 8 )
where the a-matrix i s a known f u n c t i o n of to, cf> and
A =
-costf)cosK+sin(J)sinwsinK -coswsinK sin<f>cosK+coscf>sinu)sinK:
-cos<f>sinK-sincj>sintocosK COSUCOSK sincf>sinK-coscJ>sin(jdcosK
sin<f>cosu) sinw cos<J>cosw
( 2 . 1 9 )
The second tr a n s f o r m a t i o n "performs a p e r s p e c t i v e p r o j e c t i o n from a camera-located system upon a plane i n the d i s t a n c e c from the p e r s p e c t i v e c e n t r e . " * * This plane i s normal to the o p t i c a l a x i s . The o r i g i n f o r both coordinate systems i s the p e r s p e c t i v e c e n t r e , 0 .
poinf
F i g . 2-10
* [ 4 ] * * [ 3 9 ]
- 52
= c —
Y* = c (2.20)
= c
The r e s u l t i n g coordinates x' and y* are referred to a coordinate c c
system with o r i g i n at the p r i n c i p a l point.
The t h i r d transformation transforms the l a s t coordinates
upon a plane perpendicular to the prolongation of the o p t i c a l
axis. P h y s i c a l l y t h i s i s non-existing plane. The uncorrected
photograph plane
perspective centre
•oo c°r, 'Oo
F i g . 2 -11
- 5 3 -
image coordinates i n t h i s plane are denoted by x' d and y ' d and
the corrected coordinates by x' and y* where 3. ct
x' a=x' d{a 3 [ ( x « d ) 2 + ( y ,d ) 2 ] + a 5 [ ( x ' d ) 2 + ( y ' d ) 2 ] 2 + a 7 [ ( x ' d ) 2 + ( y ,
d ) 2 ] 3+l} (2.21
y ,a = y ,
d { a 3 [ ( x ' d ) 2 + ( y ,d ) 2 ] + a 5 [ ( x ' d ) 2 + ( y « d ) 2 ] 2 + a 7 [ ( x ,
d ) 2 + ( y ,d ) 2 ] 3+l}
2* = C, a d
The f i r s t two transformations t r e a t the whole problem as a
purely geometrical central projection with the d i s t o r t i o n - f r e e
camera lens while the t h i r d transformation determines the r a d i a l
d i s t o r t i o n i n the a u x i l i a r y plane by the application of the
appropriate polynomials.
The fourth and l a s t transformation brings the corrected
intermediate coordinates into the adopted image coordinate
system by rotations a and 3 around the perspective centre.
The transformations from the comparator coordinate system
(x 1, y') into a two dimensional geodetic system are well described
i n [ 1 . 5 ] . The transformations are made i n f i v e steps and are
given by the f i n a l formula i n matrix notation
. Z C, P = D 2
r ^ E =9- (K - H) - P . (2.22) . u d <~ O
where symbols P, D 2t , E, K, H, and P Q are abbreviations of the
following matrices:
- 54 -
P = (2.23)
D 2t =
coscj)COSK sinusin ( j )COS<-siniccosu c o s c j s i n c j J C O S K + s i n t a s i n K
cos<J)sinK sintosin<t>sinK+cosd)cosK coswcoscJisinK-sinaicosK
-sincj) sinucoscj) coscocost})
E =
e o o P o e o P
o o
(2.24)
(2.25)
where e p = l - a 3 [ ( x ' d ) 2 + ( y 1f l ) 2 ] - a 5 [ ( x * f l ) 2 + ( y • & ) 2 ] 2 - a 7 [ ( x ' d ) 2 + ( y ' d ) 2 ] 3 (2.26
K =
x'
y 1
c
^ coordinates i n the comparative system (2.27)
- camera constant
H =
x
o coordinates of the p r i n c i p a l point of (2.2 8) symmetry
x.
- coordinates i n the camera system (2.29)
If the elements of i n t e r i o r and exterior o r i e n t a t i o n are
known, any point i n the c a l i b r a t i o n net can be transformed into
- 55 -
the image plane by means of these matrices. Orientation elements,
however, are known only to t h e i r approximations and the mathe
matical transformations are made at f i r s t using these approximate
values. Use of the l a t t e r w i l l naturally lead to a ce r t a i n
amount of error between computed and measured image coordinates.
Under the assumption that there are more observations than
unknowns (n > u) the most probable values of the o r i e n t a t i o n
elements are determined by the method of le a s t squares.
v v = min (2.30)
The above condition of le a s t squares i s s a t i s f i e d when
3 (vfcv) 3 X j
= O, (2.31)
where x.. represents the unknowns. The derivation y i e l d s the
c o e f f i c i e n t s of observation equations
3 F . 9V. _ l _ i
L i j SXj axj '
(2.32)
where i s a functional r e l a t i o n between unknowns and observations,
The corresponding matrix of the c o e f f i c i e n t s of observation
equation w i l l then be
a i b i '' C; U l
A =
a 2 b 2 c 2 ... u: (2.33)
n n n u n
- 56 -
The normalization of the observation equations i s performed
by the following procedure
(2.34)
[aa][ab][ac] .... [au]
N = I [ab] [bb] [be] [bu]
[au][bu][cu] .... [uu]
Differences between computed and measured values are usually
denoted by 1^, and then the matrix of absolute terms i s equal to
l i
1 2
1 = I 1 3 I (2.35)
n L
and r
[al]
[bl] = A f c l (2.37)
[ul]
The system of normal equations given by the expression Nx + n = o
whose number i s equal to the number of unknowns i s solved and
y i e l d s the corrections for the approximations of the or i e n t a t i o n
elements.
n =
x. = -N _ 1n (2.38)
- 5 7 -
X. = x. + x . , ( 2 1 3 9 )
3 3° 3
where X_. q i s an approximation and x.. i s i t s correction.
Although the t h e o r e t i c a l adjustment of a c a l i b r a t i o n i s
r e l a t i v e l y simple, the p r a c t i c a l procedure faces a very serious
problem, namely the c o r r e l a t i o n between the unknowns and the
approximation of the orientation parameters. Some approximation,
p a r t i c u l a r l y those of the i n t e r i o r orientation are very close
to the r e a l values, while the elements of exterior o r i e n t a t i o n
can be very f a r from the actual values of the unknowns. The
c o r r e l a t i o n and the inaccuracy of the exterior o r i e n t a t i o n
elements w i l l not allow i t e r a t i v e adjustments to converge.
Jacobi suggested a method which, according to his a r t i c l e s [38]
and [39], has shown quite s a t i s f a c t o r y r e s u l t s . In his words
i n [39] " t h i s i n s u f f i c i e n c y of the adjustment can be overcome
by l e t t i n g a l l the orien t a t i o n elements that have good approxi
mate values appear as constants, while at f i r s t the o r i e n t a t i o n
elements with poor approximated values appear as unknowns."
Under the assumption that the p r i n c i p a l point i s i n the middle
of the photograph and the lens i s d i s t o r t i o n free, the camera
constant i s taken from the distance s e t t i n g of the lens and
the elements of ex t e r i o r o r i e n t a t i o n are adjusted. The adjust
ment i s usually performed by three or four i t e r a t i v e adjustments
which normally y i e l d r e l a t i v e l y good r e s u l t s of the parameters
of exterior o r i e n t a t i o n . "In the next step, the ex t e r i o r orien
t a t i o n c, x Q' and y * are a l l incorporated as unknowns, the
d i s t o r t i o n parameters as well as the angles a and 8 are given
constant values of zero. In t h i s way the approximated values
of a l l the unknowns are encumbered with the same error, and the
c o r r e l a t i o n between <D and y ' , $ and x ' w i l l not disturb the J o o
adjustment."* The f i n a l step i s the introduction of the r a d i a l
d i s t o r t i o n parameters as unknowns i n the adjustment. Since a l l
other elements have very good approximations from previous
adjustments, only one or two i t e r a t i o n s usually s u f f i c e and
normally that ends up the adjustment. Very seldom i s the fourth
step used to determine angles a and 8 since that adjustment makes
no s i g n i f i c a n t change i n the already adjusted elements of
or i e n t a t i o n .
Although Jacobi's method has received an i n t e r n a t i o n a l
acceptance and has been applied by various i n s t i t u t i o n s a l l over
the world there are s t i l l some questions l e f t unanswered by t h i s
theory and p r a c t i c e : to what degree of accuracy the approximations
of parameters of exterior orientations must r e a l l y be known,
what i s the influence of c o r r e l a t i o n of the unknowns, and f i n a l l y ,
what i s the optimum number and d i s t r i b u t i o n of c a l i b r a t i o n control
points? When these questions receive d e f i n i t e answers the method
w i l l come close to the perfect solution of the c a l i b r a t i o n problem.
BROWN'S ANALYTICAL PLUMB LINE METHOD
This method, unlike other previously described methods, i s
concerned only with the determination of r a d i a l and decentering
lens d i s t o r t i o n s , while the remaining elements of i n t e r i o r
*[39]
- 59 -
o r i e n t a t i o n must be predetermined by some other method. Brown
used the well known f a c t that r a d i a l d i s t o r t i o n i s a function
of object distance, and therefore for any f o c a l s e t t i n g , the
corresponding d i s t o r t i o n correction must t h e o r e t i c a l l y be
determined by a camera c a l i b r a t i o n procedure. However, i n
p r a c t i c a l photogrammetry i t i s s u f f i c i e n t to know r a d i a l and
decentering lens d i s t o r t i o n s for only two d i s t i n c t f o c a l settings
The d i s t o r t i o n for any other setting can be mathematically
computed applying Magill's formula
d r
s
= d r _ c o - m
s
d r c o ' (2.40)
where d r g i s d i s t o r t i o n for focus on object plane at distance s
from the camera, dr^ i s the d i s t o r t i o n of lens focusing at i n f i n i
dr i s the d i s t o r t i o n of lens for inverted i n f i n i t e focus, and — CO '
m i s the magnification of the lens for the object plane at
distance s. The magnification mg i s obtained from the formula
ms = ^4- (2.41)
From the o r i g i n a l Magill's formula, which i s for close
range photogrammetry of rather small p r a c t i c a l value Brown
developed a more convenient formula. If d i s t o r t i o n dr and S i
dr for two object planes at distances S i and s 2 from the S 2
camera are known and i f they are substituted into equation
(2.40) two expressions w i l l r e s u l t with new unknowns dr_ O T and
dr thus 00
- 60 -
dr = dr — d r S 1 -°° S i - f oo
dr = dr — d r s 2 -°° s 2 - f 0 0
(2.41)
The solution of the two equations y i e l d s the values of the
unknown quantities.
dr = ( d r s ! ' d " s 2 ) ( s 2 - f ) ( S l - f) <=° f (S i - s 2)
/dr - dr . , dr = dr + 1—^ S 2 ) ( S 2 " £ ) (2.43)
S 1 S i - s 2
If the l a s t two equations are now substituted into Magill's
o r i g i n a l formula (2.40) the d i s t o r t i o n for an a r b i t r a r y object
distance s i s obtained.
d r = dr + ( d r s i " d r s 2 ) ( s 2 - f) _ _ f _ ( d rS l ~ d r s 2 ) ( s 2 - f ) ( S l - f )
S S i S i - s 2 s-f f ( S i - s)
j j j j s 2 - f , ( s 2 - f ) ( S i - f ) , s 2 - f , dr = dr + dr — - dr -.— c s , — f- - dr — + s S i S i S i ~ S 2 s i (s-f) ( s i - s 2 ) s 2 S i ~ S 2
d r ( s 2 - f ) ( S l - f ) s 2 (s-f) ( S i - S 2 )
d r = dr [1 + (1 - A] - dr (1 -S Si S i ~ S 2 S-f S 2 S i ~ S 2 s-f
dr = dr [1 + ( S 2 " £ ) ( s - g i ) ] - dr <s 2-f) ( s - S l ) a r s S i 1 1 ( s i - s 2 ) ( s - f ) J s 2 ( s i - s 2 ) (s-f)
The f i n a l formula can be written i n the following form:
d r s = (1 + a s ) d r s i - o ^ d r ^ (2.44)
where
Therefore, when d i s t o r t i o n s for two d i s t i n c t i v e object
planes are known one can compute the d i s t o r t i o n for any object
plane at distance s from the camera. The known r a d i a l d i s t o r t i o n s
can be expressed by previously known polynomial for the r a d i a l
component of the t o t a l d i s t o r t i o n
dr = a. r 3 + a- r 5 + a„ r 7
S i 3si 5si 7s i
and
dr = a_ r 3 + a c r 5 + a_ r 7 , s 2 3s 2 5s 2 7s 2
or for the general case
d r s = a 3 s r 3 + a 5 s r S + a 7 s r ? (2.46)
The unknown c o e f f i c i e n t s , a, , a-,, a i n the l a s t equation can j S O S / s
be obtained by the application of equation (2.44).
a3s = ( 1 + a s ) a 3 s i " a s a 3 s 2
a5s = ( 1 + a s ) a 5 s i ' a s a 5 s 2 ( 2 ' 4 7 )
a_ = (1 + a j a . - a a,, 7s s' 7si s 7s 2
The d i s t o r t i o n function dr of a normal lens i s usually
a function of only the f i r s t term of the polynomial. Other terms
can be disregarded as p r a c t i c a l l y i n s i g n i f i c a n t . They become
- 62 -
important i n the case of lenses for a e r i a l photogrammetry which
are made with a very small d i s t o r t i o n over the usable f i e l d .
"When higher order terms are i n s i g n i f i c a n t for a given lens,
equation (2.44) has a consequence of spe c i a l importance to some
applications, i t implies the existence of an object plane
distance for which d i s t o r t i o n i s zero."*
Knowing the r a d i a l d i s t o r t i o n s at two distances sx = 2f
and s 2 = 0 0 one can compute the distance s for which the d i s t o r t i o n
defined only by the f i r s t term of the polynomial w i l l be zero
throughout the usable f i e l d . Equation (2.44) w i l l then be
(1 + a ) d r o j r - a dr =0, s 2f s °°
or from which
d r 2 f a s = dr -dr ( 2 ' 4 8 )
b U J -oo i 2 f
Equation (2.45) which defines a can be also written i n s
the following form
(1 - | ) (s - S l ) a = J 2 , (2.49)
s (1 - f i ) (s - f)
which a f t e r the introduction of the corresponding values for S i
and s 2 becomes
s - 2f ' *
V - f ^ T <2'50>
Equating expressions (2.48) and (2.50) and then rearranging *[10]
- 63 -
the equation for the distance s at which the d i s t o r t i o n i s zero
i s determined as follows:
d r s - 2f a r 2 f f - s dr^ - d r 2 f
d r 2 f d r 2 f s ( l + -= ^-5 ) = f (2 + -g ) dr - dr ' dr - dr„ r oo 2f 0 0 2f
dr 2dr - dr„,-s °° = f 2f
d r ~ " d r2 f d rco - d r
2 f
d r 2 f s = f (2 - (2.51)
When an object i s i n a plane at distance s from the camera
i t s image w i l l be d i s t o r t i o n free. This naturally implies only
that points are i n the object plane. A l l other image points
that are outside the plane are s t i l l sharp due to the depth of
the f i e l d as a function of the fo c a l length, and the aperture
w i l l be affected by d i s t o r t i o n s . For a l l p r a c t i c a l purposes i n
the case of spa c i a l objects Magill's formula i n i t s o r i g i n a l
form cannot s a t i s f y the requirements.. "What i s needed, then,
i s a further extension of Magill's formula to account f o r the
v a r i a t i o n of d i s t o r t i o n for points d i s t r i b u t e d throughout the
photographic f i e l d . " * To solve the problem Brown used simple
geometrical r a t i o s from F i g . 2-12, the polynomials of the r a d i a l
d i s t o r t i o n and the Gaussian form of the thin-lens equation.
*[10]
- 64 -
F i g . 2-12
Points 0, P and Q are i n the image plane for a lens focussed
on an object plane at distance s from the camera. Points 0', P 1,
and Q' are i n an image plane for a lens focussed on an object
plane at distance s*.
From s i m i l a r t r i a n g l e s COP and CO'P* we obtain
or
r' = ^ - r (2.52)
The r a d i a l d i s t o r t i o n dr , i s computed by the previously
known polynomial
- 65 -
d r . = a ' 3 ( r ' ) 3 + a'sU1)5 + a'yU')7
When the value of r 1 from equation (2.52) i s substituted
i n the l a s t expression we have
C , . dr , = a ' 3 ( ^ - ) J r 3 + a ' s ( ^ - ) ' r s + a ' 7 ( ^ - ) r 7 (2.53)
s s s
or
From F i g . 2-12 i t i s obvious that
C s d r s s ' = C - , d r s " s 1
dr . = a ' 3 ( ^ - ) 2 r 3 + a'5( -Vr5 + a'7( Vr7
(2.54) ss' 3 VC ' 3 XC ' ' VC s s s
The Gaussian equations of the thin lens applied to the two
image planes give
s C f s
and
-. + 1 s' C ' f
s
Rearranged, the l a s t two equations y i e l d i n turn
1 = s' - f C ' f s ' ' s
and
1_' • s - f C s fs
- 66 -
Now d i v i d i n g the second equation by the f i r s t , the .required C s '
r a t i o n ^ — for equation (2.54) i s obtained, s
2*1 = (s - f ) s ' , . C s (s' - f ) s
When d i s t o r t i o n functions (6r ) are determined by the s
c a l i b r a t i o n process then the correction, according to Brown i n
[10], i s performed i n four steps.
(a) Distance s 1 i s f i r s t computed from the approximate
coordinates x, y, z of the photographed point applying
photogrammetric intersection.
(b) Using (2.49) and l a t e r (2.47) c o e f f i c i e n t s a, ,, a ,
and a 0 , are determined. 3s C ,
(c) The r a t i o ^ — i s then computed by (2.55). This r a t i o c s
i n conjunction with the c o e f f i c i e n t s of polynomials
y i e l d s the r a d i a l d i s t o r t i o n at the observed r a d i a l
distance r. ' . ' " •
(d) With known values of the r a d i a l d i s t o r t i o n s the
observed image coordinates (x, y) are corrected by
the following amounts.
6x = — 5r , r ss'
and <Sy = - <Sr , -* r ss *
- 67 -
I t i s advisable to use an i t e r a t i v e computation process
u n t i l the required degree of accuracy of the f i n a l r e s u l t s i s
obtained.
The determination of r a d i a l d i s t o r t i o n s for two d i f f e r e n t
settings of focussed lens i s performed by the plumb l i n e method.
For the use of Magill's formula two values of r a d i a l d i s t o r t i o n s
must be known, na t u r a l l y , for two d i f f e r e n t distances. " I t
requires that d i s t o r t i o n c o e f f i c i e n t s be precalibrated for one
object plane s 2 (usually, s 2 •= 00) and regards as unknown the
d i s t o r t i o n c o e f f i c i e n t s for the p a r t i c u l a r object plane on which
the camera i s focussed."* The numerical reduction needs no
absolute control points but i f there are some known distances
in object space and the geometry of photographs i s highly con
vergent, Brown's method can determine the coordinates of the
p r i n c i p a l point and the p r i n c i p a l distance. When distances are
not given, a pre-established value of the p r i n c i p a l distance
i s used i n computations.
For projects i n which two d i f f e r e n t cameras are used for
moving objects, the d i s t o r t i o n c o e f f i c i e n t s of each s t a t i o n w i l l
have to be determined by the plumb-line method. "This method
involves photographing a set of plumb lines arrayed i n the
desired object plane and exploits the fact that, i n the absence
of d i s t o r t i o n , the central projection of a s t r a i g h t l i n e i s
i t s e l f a s t r a i g h t l i n e . Systematic deviations of the images of
plumb l i n e s from s t r a i g h t l i n e s thus provide a measure of
* [10]
- 68 -
d i s t o r t i o n i f properly reduced."*
The non-distorted image of a plumb l i n e i n the coordinate
system of the photograph can be expressed i n the following form:
where p i s the perpendicular distance of the l i n e from the o r i g i n
and 9 i s the bearing of the distance (See F i g . 2-13). Since the
applied lenses are not d i s t o r t i o n - f r e e plumb l i n e s w i l l be
represented by some curved l i n e s , when corrected for r a d i a l and
decentering d i s t o r t i o n w i l l represent points of a s t r a i g h t l i n e .
This f a c t can be mathematically expressed by the following two
equations
x' s i n 0 + y* cos 9 = p, (2.57)
x + x ( a 3 r 2 + asr1* + a 7 r 6 ) +
+ [ b i ( r 2 + 2x 2) + 2b 2xy][1 + b 3 r 2 + ...] (2.58)
y' y + y ( a 3 r 2 + a 5 r " + a 7 r 6 ) +
+ [2bixy + b 2 ( r 2 + 2y 2)][1 + b 3 r 2 + . . . ] ,
where
x = x - x. "P
y = y - (2.59)
r = / (x - x p ) 2 + (y - y p)
Factors a 3 , as and a? are the c o e f f i c i e n t s of the r a d i a l
* [10]
- 69 -
d i s t o r t i o n and b i , b 2 and b 3 are the c o e f f i c i e n t s of the
decentering d i s t o r t i o n .
1 F i g . 2-13
When the image coordinates x' and y' of the j - t h point on
the i - t h l i n e are substituted into (2.58), from thence into
(2.59) and f i n a l l y into (2.57), the following type of observation
equations i s obtained.
f ( x i j ' Y i j ? XP' YP' a 3 ' a s ' a ? ' b l ' h z ' b 3 ; 8 i ' p i * = 0 < 2- 6°)
The number of observation equations i s equal to the number
of measured points. The number of normal equations i s equal to
the number of unknowns, which i n case of the m used l i n e s i s
8 + 2 m (eight unknowns of i n t e r i o r orientation x p, y p , a 3 , a 5 ,
a 7 , b i , b 3 / b 5 and a pair of unknowns 8., p. for each of the
- 70 -
l i n e s ) . I f the number of o b s e r v a t i o n s exceeds the number o f
unknowns a l e a s t squares adjustment which y i e l d s the most pro b a b l e
v a l u e s of the unknown parameters can be performed. As i n the
m a j o r i t y of cases i n adjustments by i n d i r e c t o b s e r v a t i o n s ,
approximations of the r e q u i r e d q u a n t i t i e s are determined f i r s t
and then the adjustment p r o v i d e s s m a l l c o r r e c t i o n s t o the
approximations.
x. . = x. . 0 + v x} 13 x. . 1 3 (2.61)
y. . = y. . 0 + v ID ID Y ± j f
where x.. 0 and y . . 0 are measured c o o r d i n a t e s and v and v ID 1D x.. y. ID u ID
are the c o r r e s p o n d i n g r e s i d u a l s .
x p = x p ° + 6 x p
y p = y p ° + 6y p
a3 = a.%0 + Sa 3
a 5 = a 5 0 + 6a 5
a 7 = a 7 ° + 6a 7 (2.62)
0 b i = b i u + 5b
b 2 = b2° + 5b2
b 3 = b 3 ° + 6b 3
e i = e i ° + 6 0 j L
- 71 -
where (°) values are approximations and 6's are corrections
obtained by the adjustment.
Substituting expressions (2.61) and (2.62) into the o r i g i n a l
observation equations and expanding the r e s u l t by Taylor's s e r i e s ,
the f i n a l form of the observation equations i n matrix notation
i s obtained:
v = Ax + I, (2.63)
where
A =
9f
v =
3 f 9 f \ 3 x . . j I 3 y . . I
3 f
' 3 f A / 3 f . j I 3 y .
n
v X. . I D
I D
v
V,
3 f 3 f
3 f 3 f
3 f 3YT
3 f 3YT
n n
3 f
^ P A V 8 ypA v 3 A » A
3 f
, 9 xP y 2 v9 yp/2 v 3 a 3/ 2
3f 3a3
n
. 3 9 i A
3 f 39
1/2
3 f 39 ,
n
(2.64)
3 f 3p
3 f 3p 1' 2
3 f _ 3 p ,
n
(2.65)
- 72 -
and
x =
fix. . ID fiy. .
J i D 5x„
59
fip.
Hi
l2
n
(2.66)
(2.67)
Quantities are the values of the function (2.60), for
approximations (2.61) and (2.62).
Further procedure i s i d e n t i c a l with the already described
method of normalizing of the observation equations and solving
of normal equation i n Jacobi's method of c a l i b r a t i o n .
N = A A
n = AtZ
x = - N _ 1n
(2.68)
As Brown states "the re c o v e r a b i l i t y of x p and y p i n the
plumb-line c a l i b r a t i o n method depends d i r e c t l y on the magnitude
- 73 -
of the r a d i a l d i s t o r t i o n ; the greater the d i s t o r t i o n , the better
the recovery of x p, y p."*
Although Brown c a l l s his method the plumb-line c a l i b r a t i o n
method the author cannot completely accept i t as a c a l i b r a t i o n
method since i t does not determine the camera constant. Compared
to Jacobi's method i t has one d e f i n i t e advantage. Brown's
method needs no spe c i a l surveying methods to determine the
coordinates of targets i n the object space. I t requires only
n number of plumb l i n e s . The method i s a t t r a c t i v e i n i t s
observational s i m p l i c i t y . The disadvantage compared to Jacobi's
method i s that i t does not determine the elements of ex t e r i o r
orient a t i o n .
Recent research by Youssef Abdel-Aziz at the University
of I l l i n o i s * * a l s o showed that Brown's extension of Magill's
formula gives good res u l t s for symmetrical lens d i s t o r t i o n only
for those points which are inside the range of the two known
p r i n c i p a l distances. The results obtained for points outside
the range are not good. Abdel-Aziz developed a new version of
the extended Magill's formula and apparently achieved a much
higher accuracy than that obtained by D.C. Brown.
ABDEL-AZIZ'S CALIBRATION METHOD
In a way s i m i l a r to Brown's Abdel-Aziz investigates the
geometrical c h a r a c t e r i s t i c s of p a r a l l e l l i n e s i n a ce n t r a l
*[10] **[1]
- 74 -
projection to determine the p r i n c i p a l point, the p r i n c i p a l
distance and the r a d i a l d i s t o r t i o n s of a photograph. However
he does not use plumb-lines as te s t objects but uses a set of
p a r a l l e l l i n e s which int e r s e c t at r i g h t angles i n a plane and
four thin wires (pins) perpendicular to the plane.
Two oblique photographs are taken of the te s t f i e l d with
a change i n t i l t of approximately 90 degrees.
F i g . 2-14
Neither of the o p t i c a l axes should be c o l l i n e a r with or
p a r a l l e l to the di r e c t i o n s of l i n e s i n the plane of the t e s t
object.
The po s i t i o n of the p r i n c i p a l point i s determined as the
i n t e r s e c t i o n of two l o c i of the p r i n c i p a l point. These l o c i
- 75 -
are the l i n e s perpendicular to the vanishing l i n e s (vv) and
passing through the nadir points. The nadir point i s obtained
using the r a d i a l displacements of the t h i n pins which are
perpendicular to the plane of the t e s t object. One locus of
the p r i n c i p a l point i s determined using each oblique photograph
and then the i n t e r s e c t i o n of the two l o c i i s the p r i n c i p a l
point. This procedure i s obvious from diagrams 2-15, 2-16
and 2-17.
V vanishing line
F i g . 2-15
- 76 -
F i g . 2-16. Construction of the nadir point
0
\
principal point )tQ> / / y N / /
Fig. 2-17 ^
From diagram 2-17 i t i s obvious that the p r i n c i p a l distance
can be computed by the following formula:
C = /ab (2.69)
- 77, -
Although Abdel-Aziz's method i s very simple the author
cannot see that i t has any p a r t i c u l a r p r a c t i c a l value. Compared
to other methods already described i t s s i m p l i c i t y i s i t s only
merit.
ABDEL-AZIZ-KARARA CALIBRATION METHOD
This method of c a l i b r a t i o n was recently developed at the
University of I l l i n o i s . The method has a very i n t e r e s t i n g and
s i g n i f i c a n t c h a r a c t e r i s t i c , since for data reduction the c l a s s i c a l
elements of i n t e r i o r o r i e n t a t i o n (principal point and camera
constant) are not used. "The proposed method involves a d i r e c t
l i n e a r transformation from comparator coordinates into object
space coordinates. In a sense, i t i s a simultaneous solution
for two transformations. Since the image coordinate system i s
not involved i n the approach, f i d u c i a l marks are not needed.
Furthermore, the method i s a d i r e c t solution and does not involve
i n i t i a l approximations for the unknown parameters, of inner and
outer o r i e n t a t i o n of the camera.*
The two mentioned transformations are:
(1) transformation from comparator coordinates into image
coordinates, and
(2) transformation from image coordinates into object-
space coordinates.
Since the method does not involve f i d u c i a l marks i t i s
p a r t i c u l a r l y s u i t a b l e for reduction of data obtained by non-metric
*[2]
- 78 -
cameras, which r a r e l y have f i d u c i a l marks.
The f i r s t transformation from comparator coordinates into
image coordinates i n a n a l y t i c a l photogrammetry i s done by the
following formulae
x = ai + azx + a 3y
y = a 4 + a 5x + a 6y, (2.70)
where x, y are image coordinates and x, y are comparator
coordinates. The second transformation i s performed by the
formula
X ai i a i 2 ai 3 X - X o
y = A a 2 I 3 - 2 2 a 2 3 Y - Y o
(2.71)
-c a 3 I a 3 2 a 3 3 Z - z o _
where X, Y, Z are object space coordinates, X Q , Y Q / Z q are object
space coordinates of the exposure sta t i o n , A i s a scale factor
and a.. are c o e f f i c i e n t s of spacial transformation.
Equation (2.71) i n matrix form can be also expressed i n
form of two equations
a n ( X - X ) + a i 2 (Y-Y ) + a i 3 (Z-Z ) , \J \J \J • /-\
X " T " C ~Z / T r - . j . V , /TT t r \ i / r-i r-r \ v a 3 1(X-X Q) + a 3 2 ( Y - Y Q ) + a 3 3 (.Z-ZQ)
a 2 i ( X - X 0 ) + a 2 2 ( Y - Y Q ) + a 2 3 (Z-Z Q) 7 + C a 3i(X-X Q) + a 3 2 ( Y - Y Q ) + a 3 3 (Z-Z Q) = 0
(2.72)
The expressions for image coordinates (x, y) from equations
(2.70) are now substituted into equation (2.72).
- 79 -
a n ( X - X Q ) + a 1 2 ( Y - Y Q ) + a i 3 ( Z - Z ) a i + a 2 x + a 3 y + c a, ? ( X-x o) + a 3 2 ( Y - Y o ) + a 3 3 ( Z - Z o ) = 0
( 2 . 7 3 ) a 2 i ( X - X ) + a 2 2 ( Y - Y Q ) + a 2 3 ( Z - Z Q )
ai* + asx + asy + c .„ „ . — • ... . . . — r — • j-=—-—r = 0 J a 3 i ( X - X ) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z Q )
To e l i m i n a t e y from the l a s t two equations the f i r s t
e q u a t i o n i s m u l t i p l i e d by a 6 / the second by - a 3 and the two
are added.
( a i a 6 - a 3ai,) + ( a 2 a 6 - a 3 a 5 ) x +
( a G a i i - a 3 a 2 i ) (X-X ) + ( a 6 a i 2 - a 3 a 2 2 ) (Y-Y Q) + ( a 6 a i 3 - a 3 a 2 3 ) (Z-Z Q) + c a 3 1 ( X - X Q ) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z Q ) =
In the same manner x can be e l i m i n a t e d i f the f i r s t
e q u a tion of (2.73) i s m u l t i p l i e d by a 5 and the second by - a 2
and the two are added.
( a i a 5 - a 2 a 4 ) + ( a 3 a 5 - a 2 a 6 ) y +
( a 5 a i i - a 2 a 2 1 ) ( X - X q ) + ( a 5 a x 2 - a 2 a 2 2 ) ( Y - Y Q ) + ( a 5 a i 3 - a 2 a 2 3 ) ( Z - Z Q ) + C a 3 1 ( X - X Q ) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z o )
The l a s t two equations o b t a i n e d by the e l i m i n a t i o n of y
and x r e s p e c t i v e l y can be s i m p l i f i e d by i n t r o d u c t i o n of new
symbols to the f o l l o w i n g form
d + d x + b i X + b 2 Y + b 3Z + b„ , _ d l + d 2 X + b 9 X + b 1 0 Y + b u Z + b 1 2 " 0
( 2 . 7 4 ) d 3 + d,y + bsX + b 6 Y + b 7Z + b 8 _
3 4 y b 9X + b 1 0 Y + b n Z + b i 2 '
where
- 80 -
di a i a 6 - a 3 a i ,
d 2 = a 2 a 6 -
d 3 = a i a 5 - a 2 a it
d. = a 3as - a 2 a 6
bi = c ( a 6 a i 1 - a 3 a 2 1)
b 2 = c ( a 6 a i 2 - a 3 a 2 2 )
b 3 = c ( a 6 a i 3 ~ a 3 a 2 3)
b- = - ( b i X Q + b 2 Y Q + b 3
b 5 a5 a11 - a 2 a 2 1
b 6 = a 5a 1 2 — a 2 a 2 2
b 7 = asai 3 — a 2 a 2 3
b 8 = - ( b 5 x o + b s Y Q + b 7 V
b 9 = a 31
bi 0 = a 3 2
bi 1 = a 3 3
bi 2 = - (a 31 X + a 3 2Y + 0 0 a 3
(2.75)
When terms di and d3 i n equations (2.74) are put over the
denominator of the t h i r d terms the equations become
-,' , (bi+b 9d 1)X+(b 2+bi 0d 1)Y+(b 3+bi id x) Z+(b^+bt 2d t) U 2 X b 9X+bioY+biiZ+bi 2
u
, (b 5+b 9d 3)X+(b6+biod 3)Y+(b 7+bi id 3) Z+(b 8+bi 2d 3) -h Y b 9X+bioY+biiZ+b i 2
u
or applying new abbreviated notation
bi*X + b 2*Y + b 3*Z + bk* x + b 9X + bi 0Y + b u Z + bi 2
b5*X + b 6*Y + b 7*Z + b 8* b 9X + b i 0 Y + b i i Z + b i 2
= 0
= 0,
(2.76)
- 81 -
where
b i * = | (bj + b 9 d i )
b 2 * = i - (b 2 + b i o d i ) O-Z
b 3 * = i (b 3 + b u d : ) a 3
bh* = i (b„ + b i 2 d i ) ; (2.77) 4
b 5 * = i (b 5 + b 9 d 3 )
b 6 * = i (b 6 + b i 0 d 3 )
b 7 * = J ( b 7 + b n d 3 )
b 8 * = i (be + b i 2 d 3 ) CU
I f the numerators and denominators i n equations (2.76)
are d i v i d e d by b 1 2 we o b t a i n
x + b i * b i 2 X + b 2 *
b i 2 Y b 3 * b i 2 Z + b 4 *
b i 2 _ b 9
b i 2 X + bio b i 2
Y + b n b i 2 Z + 1
y +
or w i t h new symbols
b 5 * b i 2
X + b 6 * b i 2
Y + b 7 * b i 2
Z + b 8 * b i 2
b 9
b i 2 X + bio b i 2
Y + b n b i 2
Z + 1
v + £ l X + l 2 Y + £ 3 Z + &i» _ £ 9 X + £i 0Y + £ u Z + 1 U
v + l s X + £ 6 Y + i7Z + le =
1 Z9X + £i 0Y + i i i Z + 1
(2.78)
- 82 -
The l a s t equations are the fundamental equations for
Abdel Aziz-Karara method. They can be s l i g h t l y s i m p l i f i e d
by s e l e c t i n g the image coordinate system i n such a way that
the coordinate axes are p a r a l l e l to the axes of the comparator's
coordinate system and so that i t s o r i g i n i s i n the p r i n c i p a l
point. In t h i s case the c o e f f i c i e n t a 5 i n the second of
equations (2.70) becomes zero.
x = ai + a 2x + a 3y
y = a >t + a 6y
This w i l l n aturally also simplify equations (2.73)
ai i ( X - X Q ) + a 1 2 ( Y - Y Q ) + a 1 3 ( Z - Z o ) ax + a 2x + a 3y - c a 3 l ( X _ X O ) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z o ) = 0
a, + a 6y - c a 2 1(X-X Q) + a 2 2 ( Y - Y P ) + a 2 3 ( Z - Z Q ) a 3i(X-X Q) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z Q )
Equations (2.80) have 12 unknowns which are l i n e a r l y
dependent. The number of unknowns can be reduced to 11 by
substituting c , c c = — and c = — x a 2 y a 6
Then equations (2.80) become
a n (X-X Q)+a 1 2 ( Y - Y Q ) + a i 3 (Z-Z Q) ai + x + a 2y - c x a 3 2 ( X - X Q ) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z Q ) = 0
(2.79)
(2.80)
a 2 i(X-X )+a 2 2(Y-Y )+a 2 3(Z-Z ) (2.81) a, + v - c : : ° ° ° = 0
3 y y a 3 i ( X - X Q ) + a 3 2 ( Y - Y Q ) + a 3 3 ( Z - Z Q ) U
- 83 -
These equations are the o r i g i n a l observation equations
but they cannot be applied i n least square adjustment because
they are not l i n e a r . However, they can be made l i n e a r by
expanding them i n Taylor's series and neglecting terms of
second or higher order as s u f f i c i e n t l y small and p r a c t i c a l l y
i n s i g n i f i c a n t . The proposed method of Abdel Aziz-Karara does
not use the conventional c o l l i n e a r i t y approach because i t
requires the approximations of unknowns. Abdel Aziz and Karara
expand equations (2.78) i n the Taylor's series and obtain
V + XSLx + Yi2 + Z£ 3 + lk + + xX£g + x Y £ 1 0 + xZJlii + x = 0
v y + + XSL5 + Y£ 6 + Zl7 + SLS + yX&g + yY£i 0 + yZ&n + y = 0
Compared with conventional methods the proposed method
has two clear advantages. I t does not contain errors due to
i t e r a t i o n c r i t e r i a and i s not influenced by neglecting of
second and higher order terms i n l i n e a r i z a t i o n of the observation
equations.
The method i s p a r t i c u l a r l y suitable for non-metric cameras
without f i d u c i a l marks. Since there are altogether eleven
unknowns, s i x well d i s t r i b u t e d points w i l l give a unique solution.
Redundant measurements make the adjustment of required quantities
possible and lead to the most probable values according to the
theory of l e a s t squares.
- 84 -
CONCLUSION ON CALIBRATION OF CLOSE-RANGE CAMERAS
Close-range photogrammetry as a r e l a t i v e l y new branch of
the s c i e n c e of photogrammetry has to meet the requirements of a
g r e a t v a r i e t y of s p e c i a l a p p l i c a t i o n s . T h i s need i s p a r t i c u l a r l y
obvious w i t h r e s p e c t t o the used cameras. S i n c e a v a i l a b l e
commercial m e t r i c cameras cannot completely s a t i s f y the needs,
non-metric cameras are used t o enlarge the f i e l d of a p p l i c a t i o n
of c l o s e - r a n g e photogrammetry. The c a l i b r a t i o n of non-metric
cameras must a l s o i n c l u d e some checks of c o n d i t i o n s t h a t are
normally assumed to be f u l f i l l e d i n commercial cameras. These
c o n d i t i o n s are the s t a b i l i t y o f the i n t e r i o r o r i e n t a t i o n under
d i f f e r e n t exposure set-ups, s t a b i l i t y of r a d i a l and d e c e n t e r i n g
d i s t o r t i o n , the p e r p e n d i c u l a r i t y of the o p t i c a l a x i s and the
image plane, and f l a t n e s s of f i l m . To a v o i d the i n s t a b i l i t y
of camera c a l i b r a t i o n parameters, some r e c e n t approaches combine
the p r ocesses of data a c q u i s i t i o n and c a l i b r a t i o n u s i n g the
same exposure.
In i t s fundamental concept the c a l i b r a t i o n of camera i s a
space r e s e c t i o n problem. Since a g r e a t m a j o r i t y of c a l i b r a t i o n
methods a p p l i e d to cameras w i t h almost p e r f e c t l y v e r t i c a l o p t i c a l A .
a x i s , t h e r e must, i n the author's o p i n i o n , be good c o r r e l a t i o n
between the camera co n s t a n t and the Z c o o r d i n a t e of the camera o
s t a t i o n when they are s i m u l t a n e o u s l y determined by c a l i b r a t i o n .
T h i s problem was touched upon by some German photogrammetrists*
but needs more i n v e s t i g a t i o n . *Dohler, Gelhaus, L i n k w i t z
- 85 -
A n o t h e r e x t r e m e l y i m p o r t a n t q u e s t i o n i s t h e number and
d i s t r i b u t i o n o f c o n t r o l p o i n t s i n t h e t e s t f i e l d w h i c h w i l l l e a d
t o t h e most e c o n o m i c a l and b e s t s o l u t i o n o f c a l i b r a t i o n p a r a m e t e r s .
DATA REDUCTION SYSTEMS
Data r e d u c t i o n i n s t r u m e n t s can g e n e r a l l y be c l a s s i f i e d i n t o
two main c a t e g o r i e s :
(1) Analogue p l o t t e r s
(2) A n a l y t i c a l p l o t t e r s
ANALOGUE PLOTTERS
The t a s k o f an analogue p l o t t e r i s t o c o n v e r t two c o n j u g a t e
c e n t r a l p r o j e c t i o n s i n t o a s i n g l e o r t h o g o n a l p r o j e c t i o n . They
c o n s i s t o f t h r e e b a s i c p a r t s :
(a) p r o j e c t i o n system,
(b) system w h i c h d e t e r m i n e s t h e space i n t e r s e c t i o n o f
t h e c o r r e s p o n d i n g r a y s , and
(c) v i e w i n g system
P r o j e c t i o n systems can be: o p t i c a l , m e c h a n i c a l , o r o p t i c a l -
m e c h a n i c a l .
R e s t i t u t i o n i n s t r u m e n t s w i t h o p t i c a l p r o j e c t i o n systems
c o n s i s t o f two o r more p r o j e c t o r s w h i c h p r o j e c t t h e c o r r e s p o n d i n g
c o n j u g a t e b u n d l e o f r a y s and t h e i n t e r s e c t i o n o f r a y s c r e a t e s
a space model.- T h i s p r i n c i p l e was a l r e a d y s u g g e s t e d by Scheimp-
- 86 -
flug and the f i r s t instrument of that type was b u i l d by Gasser
using dichromatic anaglyphic (red-green) projection as well as
the alternate b l i n k i n g system to determine the i n t e r s e c t i o n
points of the corresponding rays. Although these instruments
are t e c h n i c a l l y very simple, from economical reasons very
f e a s i b l e , and are used i n photogrammetric compilation more than
any other type of instruments, the author does not think that
they can be applied to a greater extent i n close-range photo
grammetry. Their main l i m i t a t i o n i s a very narrow range of
p r i n c i p a l distance. In addition they take no care of d i s t o r t i o n
and assume that photography i s made by d i s t o r t i o n - f r e e lenses.
The exceptions are instruments with Porro-Koppe p r i n c i p l e .
F i g . 2-18. P r i n c i p l e of o p t i c a l projection system
- 87 -
In the case of mechanical projection systems the i n t e r
section of conjugate rays i s r e a l i z e d as the mechanical i n t e r
section of two space rods. The d i s t o r t i o n , p a r t i c u l a r l y with
wide angle lenses, can be p r a c t i c a l l y compensated by mechanical
or o p t i c a l means. Typical examples of these r e s t i t u t i o n
instruments are Santoni's Stereocartograph and Wild's Autographs
A5, A6, A7 and A8.
F i g . 2-19. P r i n c i p l e of mechanical projection system
In instruments with optical-mechanical projection systems
a combination of o p t i c a l and mechanical systems i s used. Thus
the main requirements of o p t i c a l and mechanical systems are
- 88 -
avoided. An example i s Hugershoff's Aerocartograph.
P 1
F i g . 2 - 2 0 . P r i n c i p l e of optical-mechanical projection systems
I t i s beyond the scope of t h i s thesis to describe i n d e t a i l
r e s t i t u t i o n instruments for close-range photogrammetry. There
are a c t u a l l y no sp e c i a l instruments and the data compilation i s
performed with e x i s t i n g instruments of t e r r e s t r i a l and a e r i a l
photogrammetry which are well described i n most text books of
photogrammetry. When metric cameras are used these instruments
have no great problems i n the evaluation of photographs. However
the photographs obtained by non-metric cameras are larg e l y
influenced by rather s i g n i f i c a n t and i r r e g u l a r r a d i a l and de-
centering- d i s t o r t i o n . Standard mechanical and o p t i c a l systems
- 89 -
cannot completely compensate f o r the i n f l u e n c e o f d i s t o r t i o n s
and f o r h i g h e r requirements of accuracy o n l y a n a l y t i c a l
p l o t t e r s p r o v i d e s a t i s f a c t o r y r e s u l t s . I t i s a l s o important t o
note t h a t standard p l o t t i n g instruments b a s i c a l l y do not have
s u f f i c i e n t range o f p r i n c i p a l d i s t a n c e to e v a l u a t e photography
taken w i t h s t e r o m e t r i c o r non-metric cameras. P l o t t i n g i n such
cases must be performed i n an a f f i n e model w i t h an exaggerated
p r i n c i p a l d i s t a n c e and v e r t i c a l s c a l e . G e n e r a l l y t h i s technique
i s not w e l l known to photogrammetrists. A l s o s i n c e t h i s i s the
on l y method by analogue approach f o r r e d u c i n g o f photographs
taken by m e t r i c and non-metric cameras w i t h s h o r t e r f o c a l l e n s e s
i t i s worthwhile d e s c r i b i n g the method i n d e t a i l , p a r t i c u l a r l y
s i n c e the author c o u l d f i n d very l i t t l e about the method i n
E n g l i s h language.
A l l c o n v e n t i o n a l analogue s t e r e o r e s t i t u t i o n instruments
have changed v e r y l i t t l e i n t h e i r c o n c e p t i o n from the be g i n n i n g
u n t i l today. They were a l l based on the i d e a of Scheimpflug
t h a t the r e s t i t u t i o n can o n l y be c o r r e c t l y performed i f the
o b j e c t bundles are r e c o n s t r u c t e d . Although t h i s w i d e l y adapted
i d e a r e s t r i c t e d the development of photogrammetry i n o t h e r
d i r e c t i o n s i t brought the f i r s t p r a c t i c a l successes i n a e r i a l
photogrammetry. A g r e a t m a j o r i t y of "todays" r e s t i t u t i o n
instruments were designed when a e r i a l cameras had an angle o f
view of 60 degrees. The mechanical and o p t i c a l c o n s t r u c t i o n of
these instruments were made a c c o r d i n g to the used f o c a l l e n g t h s
of used cameras and a c c o r d i n g to a c c e p t a b l e a c c u r a c i e s . When
- 90 -
i n the mid 1930's, R. Richter i n Jena constructed a camera
objective of 80 degrees a new era started. The o l d instruments
could not accommodate wide angle photography and only a f t e r the
Second World War various companies started the production of
stereo instruments for shorter focal lengths. A l l these i n s t r u
ments were, na t u r a l l y , b u i l t according to the idea of Scheimpflug
with the reconstruction of object bundles. However, i t was
r e a l i z e d that conventional instruments with normal concept could
not be further developed. A l i m i t was set at a lens of about
110 degrees. Even for these super wide lenses r e s t i t u t i o n
instruments have to be s p e c i a l l y redesigned. When p r i n c i p a l
distances of cameras used for a e r i a l mapping become shorter than
the p r i n c i p a l distances of p l o t t i n g instruments the need for
a f f i n e r e s t i t u t i o n a r i s e s . In these cases the r e s t i t u t i o n can
be accomplished by d i f f e r e n t p r i n c i p a l distances, giving improper
inner orie n t a t i o n .
The idea was conceived i n Russia. At f i r s t Russian photo
grammetrists t r i e d to solve the problem by conventional r e s t i t u t i o n
instruments applying special working methods. This solu t i o n
could not f u l f i l l the requirements i n accuracy and another
solution had to be found. For some strange reasons the t h e o r e t i c a l
ideas and conceptions i n Russia were not as r i g i d as i n Western
Europe and America. That fact gave Russian photogrammetrists a
certa i n advantage which proved to be very f r u i t f u l and resulted
i n quite a number of universal p l o t t i n g instruments. Under the
term "universal p l o t t i n g instrument" they r e f e r to the a p p l i c a t i o n
- 91 -
o f photography made u s i n g cameras o f v a r i o u s f o c a l l e n g t h s .
Some o f t h e s e i n s t r u m e n t s , f o r example, t h e S t e r e o g r a p h SD o f
Drobyshev and t h e S t e r e o p r o j e c t o r SPR-2 o f Romanovski a r e w e l l
d e s c r i b e d i n two p u b l i c a t i o n s w h i c h appeared o u t s i d e R u s s i a . *
The p r i n c i p a l d i s t a n c e o f an a f f i n e r e s t i t u t i o n i n s t r u m e n t (C a)
i s l a r g e r t h a n t h e camera c o n s t a n t ( C k ) , when photography i s
made w i t h s m a l l e r f o c a l l e n g t h , and t h e r e f o r e t h e r e s t i t u t i o n
b u n d l e o f r a y s becomes n a r r o w e r and c r e a t e s a v e r y d e s i r a b l e
e f f e c t . The a n g l e between t h e space r o d s i n p l o t t e r s w i t h
m e c h a n i c a l p r o j e c t i o n system can be k e p t w i t h i n r e a s o n a b l e
l i m i t s . N a t u r a l l y , i t s h o u l d n o t be f o r g o t t e n t h a t t h e s c a l e
i n t h e z - d i r e c t i o n i s deformed and t h e amount o f d e f o r m a t i o n i s
a f u n c t i o n o f t h e r a t i o o f t h e camera c o n s t a n t and t h e p r i n c i p a l
d i s t a n c e o f t h e r e s t i t u t i o n i n s t r u m e n t .
The a f f i n e r e s t i t u t i o n can be a l s o p e r f o r m e d w i t h used
s t a n d a r d u n i v e r s a l p l o t t i n g i n s t r u m e n t s . An example w i t h t h e
St e r e o m e t r o g r a p h - Z e i s s , Jena w i l l h e l p t o u n d e r s t a n d t h e g e n e r a l
p r o c e d u r e . The b a s i s o f t h e t h e o r y i s p r e s e n t e d i n F i g u r e 2-21.
A wide a n g l e l e n s was used f o r photography and t h e r e f o r e t h e
p r i n c i p a l d i s t a n c e o f t h e r e s t i t u t i o n i n s t r u m e n t i s l a r g e r t h a n
t h e camera c o n s t a n t . The r e s u l t i n g t i l t o f t h e a f f i n e model t
a l s o becomes l a r g e r than" t h e t i l t t o f t h e o r i g i n a l p h o t o g r a p h .
T h i s f a c t i s o b v i o u s from t h e . d i a g r a m . B^ and r e p r e s e n t
p l a n e s o f t h e o r i g i n a l p h o t o g r a p h s , where and B ^ a r e t h e
e l e v a t e d p o s i t i o n s o f photographs used. The c o r r e s p o n d i n g
p r o j e c t i o n c e n t r e s o f t h e o r i g i n a l and a f f i n e model a r e 0,., 0^
* [ 4 ] , [66]
- 92 -
and 0 I # 01X respectively. The o r i g i n a l photographs are elevated
i n such a way that the rays coming from the a f f i n e model coincide
with the o r i g i n a l positions i n a horizontal plane.
F i g . 2-21. Elevated a f f i n e model
The derivation of basic geometrical r e l a t i o n s can be
obtained from Figure 2-22.
F i g . 2-22
The t i l t of the elevated photograph depends upon the t i l t
of the o r i g i n a l photograph and an a f f i n e factor k.
tan t = k tan t (2.83)
The a f f i n e factor i s defined as the r a t i o of the v e r t i c a l
scale m, to the planimetric scale m,. h c 1 m,
k = ^ (2.84)
From the l a s t diagram i t can be seen that (ON) = k(ON) = C k
k c q s . The p r i n c i p a l distance of the a f f i n e photograph w i l l
then be
- 94 -
C = (ON) cos t = k C, C O S ^, (2.85) a k cos t
where i s the camera constant. From the l a s t expression i t i s
obvious that the value of C & depends upon the a f f i n e factor and
the t i l t . From the diagram i t i s also obvious that the p r i n c i p a l
point H of the o r i g i n a l photograph i s displaced for distance d
from the p r i n c i p a l point i n the image plane B. ]
d = (MN) - (HN) (2.86)
(MN) = C tan t (2.87) ci
(HN) cos t = (HN) cos t ,
or
<™) = ™ S-T = c k tan * IH (2-88)
Substituting expressions (2.88) and (2.87) into equation - cos t (2.86) and bearing i n mind that tan t = k tan t and C = k C. r -^ a k cos t
the f i n a l formula for distance d i s obtained
j o J. J. n 2 COS t COS t. or,. d = C k tan t (k - 35^) , - (2.89)
which can be further s i m p l i f i e d for the case when the angle of
t i l t i s a very small quantity.
C, • d = j t a n t (k 2 - 1) (2.90)
This decentering of the photograph i s i n the Stereometrograph
automatically accomplished. To simplify the procedure the t i l t
i s divided into two components o) and w. At f i r s t <j> i s introduced
- 95 -
for the decentering d of the image holder d :
d = J % ( k 2 - 1 ) , x b k p '
( 2 . 9 1 )
where the meaning of quantities a and b is obvious from Figure
2 - 2 3 .
F ig . 2 - 2 3
Ih — +4 — + 3 — +2 — + /
O
2 — - 3
4
Wheel
Sliding mechanism A can be shifted along the image holder
and along a scale which is subdivided in units of C.
The pract ical procedure consists of the determination of C
the affine factor k = approximately, which is followed by c k
- 96 -
the decentering of the image holder according to equation (2.91).
The decentering i s performed manually and by i t e r a t i o n s . No
considerations are given to the introduced errors of the a f f i n e
model which r e s u l t from the difference between equations (2.91)
and (2.89), and from a non-linear scale enlargement along the
image holder.
This method does not give perfect r e s u l t s . Nobody can
expect that from an a f f i n e r e s t i t u t i o n , although the method
could be further elaborated. The necessity of the close-range
photogrammetry systems may i n i t i a t e further elaboration. As
long as the general accuracy of the output i s greater than the
errors of the a f f i n e r e s t i t u t i o n the geometrical and mathematical
approximations can be considered to be v a l i d .
ANALYTICAL PLOTTERS
A n a l y t i c a l p l o t t e r s use ;instead of o p t i c a l , mechanical or
optical-mechanical projection systems^a mathematical projection
system, which describes the relationship between points and l i n e s
i n various coordinate systems. There are b a s i c a l l y two coordinate
systems which are employed i n a n a l y t i c a l photogrammetry. They
are: the image coordinate system and the object space coordinate
system. The mathematical formulae which connect the two systems
have already been given and explained i n conjunction with the
c a l i b r a t i o n of cameras (see Jacobi's method).
The need f o r a n a l y t i c a l photogrammetry i n close-range
- 97 -
photogrammetry systems a r i s e s when the accuracy r e q u i r e d i s too
h i g h to be s a t i s f i e d by an analogue r e s t i t u t i o n instrument.
V a r i o u s sources o f s y s t e m a t i c e r r o r s cannot be e l i m i n a t e d by a
c o n v e n t i o n a l r e s t i t u t i o n instrument. The Manual o f Photogram
metry* s t a t e s t h a t "the j u s t i f i c a t i o n f o r a n a l y t i c a l photo
grammetry i s found i n those a p p l i c a t i o n s i n which the concept
of a simple c e n t r a l - p e r s p e c t i v e p r o j e c t i o n i s no l o n g e r adequate
t o d e s c r i b e the p h y s i c a l c h a r a c t e r i s t i c s o f the r e c o r d . "
A n a l y t i c a l photogrammetry has a g e n e r a l meaning and the same
formulae are v a l i d f o r t e r r e s t r i a l , a e r i a l , b a l l i s t i c and non
topo g r a p h i c photogrammetry.
A n a l y t i c a l p l o t t e r s fundamentally c o n s i s t o f two p a r t s :
a d i g i t a l computer and a comparator. The f i r s t p a r t i s respon
s i b l e f o r the numerical e l a b o r a t i o n of "the simultaneous
r e s t i t u t i o n of the o r i e n t a t i o n of any number o f photographic
r e c o r d s and the r e c o n s t r u c t i o n of the t h r e e - d i m e n s i o n a l space
by the i n t e r s e c t i o n of corresponding r a y s . " * The comparator
serves t o o b t a i n the c o o r d i n a t e s of photograph images. Comparators
can be mono or s t e r e o comparators. Monocomparators measure
the image c o o r d i n a t e s o f p o i n t s i d e n t i f i e d on a s i n g l e photo
graph. Stereocomparators permit simultaneous measurements o f
i d e n t i f i e d p o i n t s on both photographs, but each photograph has
an independent and separate c o o r d i n a t e system.
There are q u i t e a number of comparators on the market and
t h e i r d e t a i l e d d e s c r i p t i o n can be o b t a i n e d from t e x t books i n
*[4]
- 98 -
photogrammetry or d i r e c t l y from manufacturers. There i s no
need t o r e p e a t these d e s c r i p t i o n s i n t h i s t h e s i s .
As f a r as non-topographic photogrammetry i s concerned i t
i s important to emphasize t h a t a n a l y t i c a l p l o t t e r s b a s i c a l l y
have no l i m i t a t i o n s as to the type and o r i e n t a t i o n of a camera,
as long as the bundle of rays can be expressed as a mathematical
model which c h a r a c t e r i z e s the geometric and dynamic p r o p e r t i e s
of the p a r t i c u l a r data a q u i s i t i o n system.
The a n a l y t i c a l approach i s e s p e c i a l l y advantageous i n the
most g e n e r a l case of c l o s e - r a n g e photogrammetry where the
elements of i n t e r i o r and e x t e r i o r o r i e n t a t i o n as w e l l as the
c a l i b r a t i o n parameters of the cameras are s i m u l t a n e o u s l y
determined w i t h the o b j e c t space c o o r d i n a t e s . The g e n e r a l
t r e n d i n c l o s e - r a n g e photogrammetry i s toward i n c r e a s e d a p p l i
c a t i o n of a n a l y t i c a l r e s t i t u t i o n methods. S o l v i n g v e r y s o p h i s
t i c a t e d mathematical models these methods reached extremely
h i g h a c c u r a c i e s . I t can o n l y be hoped t h a t instrument manu
f a c t u r e r s i n coming years w i l l be able to produce a s m a l l and
i n e x p e n s i v e stereocomparator w i t h automatic c o o r d i n a t e r e g i s t r a t i o n
which w i l l y i e l d s u f f i c i e n t accuracy to s a t i s f y the v e r y h i g h
requirements of c l o s e - r a n g e photogrammetry.
CHAPTER I I I
APPLICATION OF PHOTOGRAMMETRY IN OPHTHALMOLOGY
INTRODUCTION
The a p p l i c a t i o n of close-range photogrammetry i n o p h t h a l -
mology as i n a l l o t h e r non-topographic f i e l d s has gained (a' v e r y
l i t t l e acceptance. There have been, however, q u i t e a number o f
attempts to i n t r o d u c e the conveniences o f photogrammetry f o r
measuring of i n s i d e or o u t s i d e p a r t s of the eye. In the g r e a t
m a j o r i t y o f cases these attempts remained i n the experimental
stage. Many s c i e n t i s t s r e c o g n i z e d a c o n s i d e r a b l e p o t e n t i a l f o r
growth of the a p p l i c a t i o n of photogrammetry i n ophthalmology,
but u n t i l now photogrammetry has not developed e f f e c t i v e means
of r e a c h i n g and communicating w i t h the l a r g e number of p o t e n t i a l
u s e r s . Another problem not l e s s s i g n i f i c a n t i s the ignorance
o f people i n the m e d i c a l p r o f e s s i o n of photogrammetry as a
measuring t o o l f o r t h e i r d i s c i p l i n e s . However, i n r e c e n t years
t h e r e have been s u f f i c i e n t i n d i c a t i o n s t h a t the s i t u a t i o n i s
undergoing s i g n i f i c a n t changes. On the one hand i t may be
hoped t h a t v e r y soon photogrammetrists w i l l modify methods and
instruments to accommodate the p o t e n t i a l u s e r s . On the o t h e r
hand i t i s hoped t h a t these p o t e n t i a l u s ers w i l l o b t a i n an
e f f e c t i v e e d u c a t i o n i n photogrammetry such t h a t they w i l l be
a b l e to use r a t h e r unique photogrammetric techniques and
instruments.
Some o p h t h a l m o l o g i c a l i n s t i t u t i o n s i n the w o r l d have a s
v e r y advanced r e s e a r c h c e n t r e s where photogrammetry has became
a normal t o o l . Probably the best example i s the Helmholtz
- 100 -
Moscow Research I n s t i t u t e f o r Eye Diseases. Under the s u p e r v i s i o n
of Dr. L.S. Urmakher t h i s I n s t i t u t e had developed by the e a r l y ,
f i f t i e s a number o f measuring techniques which are now s t a n d a r d
i n R u s s i a . They even developed a s p e c i a l p l o t t e r f o r v i s u a l
b i o m i c r o s c o p i c measurements o f the eye.
The Department of Experimental Ophthalmology a t the U n i v e r s i t y
Eye C l i n i c i n Lund, Sweden, i n c o n j u n c t i o n w i t h the D i v i s i o n of
Photogrammetry a t the Royal I n s t i t u t e o f Technology i n Stockholm
developed s e v e r a l photogrammetric methods f o r exophthalmometry,
f o r the d e t e r m i n a t i o n of the p u p i l l a r y aqueous flow i n the l i v i n g
human eye and f o r measurements of the apparent s i z e o f s t r u c t u r e s
i n the a n t e r i o r chamber.
The Ophthalmic Research I n s t i t u t e of A u s t r a l i a w i t h the
a s s i s t a n c e o f the Department of Lands and Survey of the V i c t o r i a
S t a t e Government produced the f i r s t stereophotogrammetric a n a l y s i s
of the human fundus o c u l i i n 1969.
L a s t but not l e a s t i s the r e s e a r c h a t the Department of
Ophthalmology a t the U n i v e r s i t y of B r i t i s h Columbia i n e v a l u a t i o n
of the cup of the o p t i c nervehead f o r a study i n c h r o n i c simple
glaucoma. v
The eye as an o b j e c t of r e s e a r c h has v e r y s p e c i f i c p r o p e r t i e s
which make almost any measurement by c o n v e n t i o n a l methods extremely
d i f f i c u l t . The fundamental problem of measurements i s the
m o b i l i t y of the l i v i n g eye which makes d i r e c t measurements
- 101 -
p r a c t i c a l l y i m p o s s i b l e r e g a r d l e s s o f in s t r u m e n t s , apparatus and
methods t h a t a r e a p p l i e d . The a d d i t i o n a l problem i s the h e t e r o -
g e n i t y o f requirements w i t h r e s p e c t t o every i n d i v i d u a l element
of t h e eye and i t s p a t h o l o g i c a l changes.
B a s i c a l l y t he problems can be c l a s s i f i e d i n t o t h r e e major
groups depending on the p a r t o f the eye t h a t i s measured:
(a) measurements o f the f r o n t of the eye
(b) measurements o f the o p t i c a l system, and
(c) measurement of the r e t i n a
A. complete photogrammetric procedure i s seldom performed.
Very often, p l o t t i n g i s unnecessary s i n c e s u f f i c i e n t i n f o r m a t i o n
can be o b t a i n e d d i r e c t l y by s t e r e o s c o p i c i n v e s t i g a t i o n o r by
spot measurements sometimes r e l a t i v e comparison o f two photo
graphs w i l l s u f f i c e and absolute measurements are unnecessary.
The a b s o l u t e measurements to a very h i g h degree of accuracy
i n s i d e the eye a r e i m p o s s i b l e by photogrammetric methods.
Although t h e l a s t f a c t o r l a r g e l y reduces the a p p l i c a b i l i t y
o f photogrammetry t h e r e are s t i l l enough problems which can be
e a s i l y s o l v e d by a p p l y i n g the proper photogrammetric approach.
MEASUREMENTS OF THE FRONT OF THE EYE
In t h i s group.of problems the author i n c l u d e s s t e r e o p h o t o -
grammetric exophthalmometry, d e t e r m i n a t i o n o f the diameter o f
the cornea, measurements of tumourous growths upon the eye,
i n v e s t i g a t i o n and d i f f e r e n t i a l d i a g n o s t i c s o f i n t e r n a l neoplasms
- 102 -
and measurements of the radius of curvature of the s c l e r a
(see F i g . 3-1).
(a) Stereophotogrammetric exophthalmomentry
Determination of the position of the ocular bulbs i s
divided into the determination of the position of a single eye
or both eyes with respect to the o r b i t s by means of exophthal-
mometry, and the determination of the position of the eyes
r e l a t i v e to each other (pupillar distance).
sclera
choroid
F i g . 3-1. Schematic representation of the normal eye
The f i r s t problem i n c l i n i c a l praxis normally i s solved
by means of exophthalmometer, an instrument whose o r i g i n a l
construction was made over a hundred years ago by Cohn i n Breslau.
- 103 -
a new
At present the most commonly used type i s Hertel's mirror
exophthalmometer, although there are some improved versions,
l i k e Davanger's exophthalmometer.
In 1968 Dr. E.O. Backlund from the Department of Neurosurgery, Karolinska Sjukhuset i n Stockholm suggested stereophotogrammetric exophthalmometry.
The stereophotography of the object was made with a p a i r
of Nikon cameras with frames 24 x 36 mm. They were mounted
on a r i g i d metal base and connected with a steroprism.
Exposed stereophotographs were r e s t i t u t e d by various
methods depending on the degree of accuracy required. For an
extremely high accuracy a stereocomparator was used and by
means of a n a l y t i c a l solution the systematic errors due to the
inaccuracy of c a l i b r a t i o n parameters were eliminated. For
les s e r accuracy an analogue approach was applied disregarding
the systematic errors of c a l i b r a t i o n . The cross-section before
and a f t e r a decompression operation were recorded numerically
or g r a p h i c a l l y with a standard deviation of about 0.5 mm for
differences between the sections. According to E.O. Backlund
the p r e c i s i o n of Hertel's exophthalmometer cannot be compared
to that of stereophotogrammetry.
dx
k F i g . 3-2* the cross-section and the aescription are taken from [7]
- 1 0 4 -
"The section shows the c i r c u l a r shape of the eyes, the
nose etc. One section (dotted line) i s recorded before and
the other a f t e r a right-sided decompression operation for
exophthalmos. The new position of the eyeball and a s l i g h t
postoperative edema over the nose can be seen."*
The conclusion about the method can be taken d i r e c t l y
from [ 6 8 ] : "The advantages of a stereophotogrammetric exoph-
thalmometry are the photographic documentation, the accuracy,
the i r r e s p e c t i v e of the examiner and the comfort to the
patients compared to Hertel's method. The drawbacks of the
method are the tedious procedures of evaluation and the complex
instrumentation required for the same procedures."
(b) Measurements of the radius of curvature of the s c l e r a
There are two photogrammetric methods, as far as the author
knows, which are at present used to determine the radius of
curvature of the s c l e r a of a l i v i n g eye. The f i r s t method of
Dencks-Rzymkowski** was developed i n Bown, Germany by 19 4 0 .
The photographs were taken i n a stereocamera with a format
of 6 x 13 cm and a f o c a l length of 9 cm. The necessary base
of photography was 6 . 5 cm. To allow the absolute measurements
on the r e s t i t u t e d model a small millimeter scale i s photographed
together with the s c l e r a . The stereophotogrammetric evaluations
are performed d i r e c t l y on negatives by means of a mirror stereo
scope and graphical measurements of parallax difference. Any
*the cross-section and the description are taken from [7] * * [ 6 0 ]
- 105 -
d e v i a t i o n from a r e g u l a r p a t t e r n of contour l i n e s can be e a s i l y
d e t e c t e d d i r e c t l y on the p l o t t e d model.
outside
inside
F i g . 3 - 3 * * The h o r i z o n t a l and v e r t i c a l c r o s s - s e c t i o n of the s c l e r a
The second method was developed a t the Helmholtz Moscow
Research I n s t i t u t e f o r Eye Diseases. The r a d i u s o f c u r v a t u r e
of the s c l e r a was determined by means of a s t e r e o p h e r i c n e t.
Si m u l t a n e o u s l y comparing a s t e r e o p a i r o f the eye and a s t e r e o
net o f s i m i l a r r a d i u s the d i f f e r e n c e s between the two s u r f a c e s
can be e a s i l y d e t e c t e d . From the d i f f e r e n c e s i n e l e v a t i o n the
r a d i i o f c u r v a t u r e a r e computed. To s i m p l i f y the computation
they prepared/a s p e c i a l s e t of t a b l e s from which the r a d i i
- 106 -
can be d i r e c t l y o b t a i n e d from the d i f f e r e n c e s i n e l e v a t i o n .
Other problems i n the a p p l i c a t i o n of photogrammetry f o r
measurements o f the f r o n t of the eye are v e r y s i m i l a r from a
t e c h n i c a l p o i n t of view. From a s t e r e o p a i r taken by s t e r e o
cameras measurements are made on a r e s t i t u t i o n instrument.
There are sometimes some s p e c i f i c m o d i f i c a t i o n s i n the
approach because of the s p e c i a l c h a r a c t e r of the problem
i n v o l v e d or by the r e q u i r e d accuracy. For example, to study
a tumourous growth upon the eye the photographs are taken
p e r i o d i c a l l y and photogrammetric measurements determine
i n d i r e c t l y the r a t e o f change to an accuracy of ±0.02 mm.
To achieve t h i s h i g h accuracy i n a b s o l u t e u n i t s "... a s m a l l
b r a s s o b j e c t c o n s i s t i n g of s i x s t e p s , each of 0.4 mm depth,
was photographed s t e r e o s c o p i c a l l y and the p l o t t e d measurements
were compared w i t h those o b t a i n e d by p h y s i c a l measurement."*
Another s p e c i f i c problem was the photogrammetric d e t e r m i n a t i o n
of the p u p i l l a r y aqueous flow i n the l i v i n g eye.** The
r e c o r d i n g camera c o n s i s t e d of a c o r n e a l microscope w i t h a
m u l t i - s l i t p r o j e c t o r and a movie camera mounted a t f i x e d a n g l e s .
A very d e t a i l e d d e s c r i p t i o n of the method and the r e s u l t s
o b t a i n e d can be found i n [37]. From a photogrammetric p o i n t
of view i t i s of no p a r t i c u l a r v a l u e .
* [53] **[37]
- 107 -
MEASUREMENTS OF THE OPTICAL SYSTEM
Under the o p t i c a l system the author c o n s i d e r s the a n t e r i o r
chamber and the l e n s of the eye. I t i s i m p o s s i b l e to make any
d i r e c t measurements on the o p t i c a l system of the l i v i n g eye and
photogrammetry p r a c t i c a l l y remains as the o n l y method which w i l l
p r o v i d e reasonably good r e s u l t s .
To o b t a i n the elements o f the eye's o p t i c a l system f o r
d i a g n o s t i c purposes of v a r i o u s forms of glaucoma, the depth of
the a n t e r i o r chamber must be known. Photographic r e c o r d i n g i s
normally performed by a s t e r e o s l i t camera. From the s t e r e o p a i r s
the measurements are then obtained by some r e s t i t u t i o n instrument.
The r e q u i r e d q u a n t i t y i s the d i s t a n c e between the v e r t e x o f the
cornea and the v e r t e x of the f r o n t s u r f a c e of the c r y s t a l l i n e
l e n s .
A l l a b s o l u t e measurements i n s i d e the eye are i n f l u e n c e d by
the curved s u r f a c e o f cornea. To i n v e s t i g a t e the amount of '2
s y s t e m a t i c e r r o r . The Swedish team of S. Henriksson, 0 . Holm
and C.E.T. Krakau* used an o p t i c a l model which c l o s e l y s i m u l a t e d
the r e a l s i t u a t i o n . The model was s p h e r i c a l l i k e the o u t e r
c o r n e a l s u r f a c e and i t s r e f r a c t i v e index was the same (n = 4/3)
as t h a t o f the cornea and the a n t e r i o r chamber.
To f o l l o w a r e f r a c t e d l i g h t ray a r e c t a n g u l a r c a r t e s i a n
c o o r d i n a t e system w i t h the o r i g i n i n the c e n t r e of the sphere
was used. The o r i e n t a t i o n of the c o o r d i n a t e axes was such t h a t
*[33]
- 108 -
the y-axis was p a r a l l e l to the ray outside the sphere.
F i g . 3-4
Point P on the outside surface of the cornea where the ray
path i s refracted i s known from i t s coordinates. Instead of
using pure rectangular or polar coordinates the authors* used
a mixture such that point P was defined by 9, r and y, where r
i s the perpendicular distance of point P from the y-axis of
the coordinate system. The refracted ray intersects the xy
coordinate plane i n point P 1 defined by coordinates 9, £ , 0.
A well known formula for r e f r a c t i o n determines a r a t i o
between angles of incidence ( a ) , r e f r a c t i o n (8) and r e f r a c t i v e
index (n).
n = sin a s i n 6
(3.1)
[33],
- 109 -
s i n a = ^ (3.2)
r - £ . tan (a - g) = . — - 2 — ' (3.3)
(R - r 2 ) /
Combining equations (3.2) and (3.1) we o b t a i n
s i n 3 = ^ | ^ (3.4)
The unknown q u a n t i t y i s value £ To compute t h i s value as a f u n c t i o n of r , R, and n l e t us w r i t e equation (3.3) i n the f o l l o w i n g form
C Q = r - (R 2 - r 2 ) 1 / 2 tan (a - g) (3.5)
Since
s i n a _ s i n g . , _fi. _ tan a - tan g- _ cos a cos g _ s i n a cos g -tan(a &) 1 + fcan a t a n ^ ^ s i n a s i n g cos a cos g +
cos a cos g
- s i n g cos a s i n a / l - s i n 2 g - s i n g / l - s i n 2 a + s i n a s i n g y ( 1 - s i n 2 B ) ( 1 _ s i n 2 a ) + s i n a s i n 3 . '
and s u b s t i t u t i n g i n the l a s t expression the values f o r s i n a and s i n g from equations (3.2) and (3.4) we o b t a i n
r / r 2 r / r 2
tan(a-g) = R / 1 " ri^W " nR / 1 " R^ = r/n 2R 2 - r 2 - r/R 2 - r 2
/ { 1 " n ^ } ( 1 ~ WY + / ( n 2 R 2 - r 2 ) (R 2 - r 2 ) +
When the l a s t expression f o r tan (a - g) i s s u b s t i t u t e d
- 110 -
i n t o e q u a t i o n (3.5) and r i s put over the denominator o f (3.6)
we o b t a i n
5 = r / ( n 2 R 2 - r 2 ) (R 2 - r2~) + r 3 - r / ( n 2 R 2 - r 2)(R 2 - r 2 ) + r ( R 2 - r 2 ) ° / ( n 2 R 2 - r 2 ) ( R 2 - r 2 ) + r 2
or f i n a l l y
E = (3.7) ° / ( n 2 R 2 - r 2 ) ( R 2 - r 2 ) + r 2
I n s t e a d of t a k i n g a s i n g l e ray l e t us now c o n s i d e r a bundle
of p a r a l l e l r a y s o u t s i d e the eye which are p a r a l l e l t o the y - a x i s
o f the c o o r d i n a t e system. These rays w i l l i n t e r s e c t the sphere
a t v a r i o u s d i s t a n c e s d from the yz-plane, where
d = r cos 8 (3.8)
A f t e r r e f r a c t i o n the same rays w i l l be a t decreased d i s t a n c e s
from the yz plane a t y = o by the amount of t;, where
% = (r - 5 Q ) cos 8 (3.9)
Planes which c o n t a i n l i g h t rays a t d i s t a n c e s d l f d 2 , d 3 ...
from the yz-plane- are p a r a l l e l o u t s i d e the. sphere but because o f
the r e f r a c t i o n are not p a r a l l e l i n s i d e the sphere. T h e r e f o r e
the rays which emerge from the a n t e r i o r chamber to the cornea
and l a t e r t o the camera w i l l d i v e r g e - by an amount t h a t cannot
be n e g l e c t e d . Compared w i t h the d i s t a n c e to the nodal p o i n t of
the s l i t camera the s i z e of the a n t e r i o r chamber i s s m a l l and
t h e r e f o r e the l i g h t r a y s a t the nodal p o i n t can be c o n s i d e r e d
- I l l -
F i g . 3-5. P r o j e c t i o n o f a r e f r a c t e d r a y i n the xy-plane
as being p a r a l l e l . Denoting the ort h o g o n a l p r o j e c t i o n s o f r
and £ on the xy-plane as r 1 and £' we o b t a i n
r ' = r cos 8
V = ? cos 6 (3.10)
a - • 6 = Y /
or (r - £ ) cos 9 . , ^o tan y' = — /R2 - r 2
An o p t i c a l s e c t i o n through the a n t e r i o r chamber i s i n t r o
duced by the XY plane where the Y a x i s makes an angle v w i t h the
y - a x i s of the c o o r d i n a t e system of the l i g h t rays and the z and
Z-axes c o i n c i d e .
- 112 -
From F i g u r e 3-5 i t i s obvious t h a t
PR _ PA _ PC QR AB CD '
or cos y'
/ R 2 - r 2 _ / R 2 - r 2 - g' xcot v _ / R 2 - r 2 - g ^ c o t v - d sin ( v-y') ,, r' - VQ : r' - Vi ~~ r' - V i 1
To determine the s c a l e r a t i o a t a p o i n t on the sphere and
i n the plane of the o p t i c a l s e c t i o n the q u o t i e n t of the areas i s
computed. A d i f f e r e n t i a l p a r t of the s u r f a c e area of the sphere
i s g i v e n by the e x p r e s s i o n
dA = r d r d0, (3.13)
and of the c o r r e s p o n d i n g p a r t of the o p t i c a l s e c t i o n by
dA' = 5 a dg 2 d8 , ... ^ cos(90° - V)
Thus, the s c a l e r a t i o becomes
The a u t h o r s * t a b u l a t e d values f o r the s c a l e r a t i o e x p r e s s i n g
i t as a f u n c t i o n of r o n l y where r i s d i r e c t l y measured on photo
graphs. The second v a r i a b l e 8 was v a r i e d i n steps of 5 degrees
from o° to 25°, where r i s given f o r every 0.5 mm and d f o r -2 mm,
0, and +2 mm. "When e s t i m a t i n g the e f f e c t on Q a t a displacement
along the x - a x i s ( i . e . p a r a l l e l to the i r i s plane) we have to
take the simultaneous change of r i n t o c o n s i d e r a t i o n . " *
* [ 3 3 ]
- 113 -
The whole discussion was concerned with displacements of
objects inside the anterior chamber. Just how r e a l i s t i c the
r e s u l t s obtained are i s d i f f i c u l t to say. A l l derived formulae
were based on the assumption that the cornea i s a sphere. The
author could not f i n d i n l i t e r a t u r e what kind of deviations the
cornea can have from the i d e a l i z e d spherical surface nor what
the range of the r e f r a c t i v e index i n the cornea and the anterior
chamber i s . These questions must be answered before we can re f e r
to measurements inside the l i v i n g eye as the absolute measure
ments.
MEASUREMENTS OF THE RETINA
The observations and photography of the r e t i n a are made
through the p u p i l . The whole process of observations of parts
of the r e t i n a i s r e l a t i v e l y new. In year 1850 the famous German
ophthalmologist and p h y s i c i s t Hermann von Helmholtz concluded
that, according to the p r i n c i p l e of the r e v e r s i b i l i t y of the
l i g h t path, l i g h t w i l l traverse the same route through an o p t i c a l
instrument (the eye can be considered as an o p t i c a l instrument)
from one end to the other. Therefore the l i g h t which comes from
a luminous body through the pupil to the r e t i n a w i l l return i n
exactly the same way back to the luminous body. If an observer
could i n s e r t his eye between the source of l i g h t and the i l l u m i n
ated r e t i n a he would be able to get some of the r e f l e c t e d l i g h t .
Naturally, t h i s cannot be done without some a u x i l i a r y apparatus
which w i l l prevent the illuminating l i g h t from being intercepted.
- 114 -
Helmholtz s o l v e d the problem by i n s e r t i n g t h r e e p l a n e - p a r a l l e l
g l a s s p l a t e s i n the d i r e c t i o n of o b s e r v a t i o n under an angle
which enabled the l i g h t of a luminous body to be r e f l e c t e d
i n s i d e the l i v i n g eye. The p r i n c i p l e i s obvious from F i g u r e
3 - 6 .
F i g . 3 -6
- 1 1 5 -
Helmholtz also solved the second problem by obtaining a
sharp image of r e t i n a . The r e f l e c t e d l i g h t from the r e t i n a i s
refracted by the eye lens, anterior chamber and cornea and has
various ray paths. When the focal point of the d i o p t r i c system
i s i n the cornea (as with emmetropic individuals) the l i g h t rays
leave the eye as p a r a l l e l rays. When the fo c a l point i s farther
back (myopic persons) the ex i t rays converge, and i n the case of
hyperopic i n d i v i d u a l s the rays diverge. To eliminate these
e f f e c t s Helmholtz introduced a very weak concave lens which could
be moved along the o p t i c a l axis and therefore was able to bring
" i n focus" the image of the retina for any l i v i n g eye. The whole
apparatus was c a l l e d ophthalmoscope.
The discovery of Helmholtz was further developed. Many
s c i e n t i s t s contributed to various improved designs of ophthalmo
scopes. In 1861 Girand-Jeulon succeeded i n constructing the
f i r s t stereoscopic ophthalmoscope. I t has since been changed
several times and the l a t e s t design i s the Shepens-Binocularo-
phthalmoscope. Its p r i n c i p l e can be obtained from Figure 3-7.
Photography combined with an el e c t r o n i c f l a s h u n i t made i t
possible to obtain measurements of the r e t i n a . Cameras e s p e c i a l l y
designed for these purposes are c a l l e d fundus cameras. Such
cameras are mostly used for routine fundus photography i n
hospitals, ophthalmological practice and research centres, but
are supplemented by a u x i l i a r y accessories and can be used for many
other research, projects. Among these accessories a stereo-
- 116 -
F i g . 3-7 r
s e p a r a t o r f o r s u c c e s s i v e stereophotography of the o c u l a r fundus
i s o f p a r t i c u l a r i n t e r e s t . A g r e a t m a j o r i t y o f o p h t h a l m o l o g i c a l
i n s t i t u t i o n s i n the Western World use the Zeis s - f u n d u s camera
w i t h v a r i o u s k i n d s of s t e r e o s e p a r a t o r s . These instruments are
a l l w e l l d e s c r i b e d i n the o p h t h a l m o l o g i c a l l i t e r a t u r e . The
author found a very i n t e r e s t i n g v e r s i o n o f the fundus camera
designed by the Helmholtz Moscow Research I n s t i t u t e (see F i g .
3-8).
L i g h t r a y s coming from the observed eye (1) are r e f l e c t e d ,
by two m i r r o r s (2) which make two separate images. The two
i n d i v i d u a l bundles o f rays then pass through a p l a n e - p a r a l l e l
p l a t e (3) which c o r r e c t s e v e n t u a l d i s t o r t i o n s o f the l e n s (4).
The bundles of rays are then r e f l e c t e d by two symmetrical
- 117 -
! l -—i
y i
a I r v , I —y i i i
Observed Eye-
F i g . 3-8
mirrors (5) onto f i l m holders (6). The sharp images of the
object are obtained by an additional o p t i c a l system (view-range-
finder) which i s not shown on the diagram.
Unfortunately fundus photographs i n r e s t i t u t i o n instruments
cannot be evaluated i n absolute units to a very high degree of
accuracy. The magnification of the focussed image i n the f i l m
plane i s due to two factors which depend on the eye o p t i c a l system
and the camera o p t i c a l system. The magnification i s usually
expressed by the following formula f
e (3.16)
where f i s the f o c a l length of the camera and fQ i s t h e f o c a l
length If the observed eye. The second factor Is generally known
- 118 -
only approximately." As long as i t i s impossible to determine
the f o c a l length of the eye with s u f f i c i e n t accuracy, no magni
f i c a t i o n can be given for measuring purposes, and we have to
content ourselves with indicating the angle which a c e r t a i n
object subtends on the fundus. Thus 1° i n the eye i s roughly
equivalent to 0.75 mm on the f i l m , or 1 mm on the f i l m to 1°20'
i n the eye. This rel a t i o n s h i p i s a function of the r e f r a c t i v e
and a x i a l ametropia of the patient's eye."*
The stereophotogrammetric measurements of the fundus were
i n i t i a t e d at the Ophthalmic Research I n s t i t u t e of A u s t r a l i a i n
1968 to obtain two dimensional or three dimensional quantative
measurements of structures and to time events i n the fundus.
The f i r s t part of the research project was done using c l a s s i c a l
r e s t i t u t i o n instruments (A-5 and A-8 from Wild) and the output
was i n small contour-line representations of the fundus. From
the contour-lines p r o f i l e s were graphically constructed. The
second section of the project was e n t i r e l y evaluated on an
a n a l y t i c a l p l o t t e r . For t h i s purpose they used Nistri-Bendix
a n a l y t i c a l p l o t t e r based on the concepts of Helava of the
National Research Council of Canada. Dr. G. Crock described
i n d e t a i l the whole operation. "The operator placed the stereo-
p a i r s on the f i l m carriage plates and f i r s t found the o p t i c a l
centre of the f i l m by measuring the diameter of the fundus image
on the negative. He then entered the photo base measurement
into the a n a l y t i c a l p l o t t e r which would automatically compute
the perspective centres. A l l r e l i e f displacements were then
M 5 1 ]
- 119 -
r a d i a l from t h a t p o i n t . Other data such as the camera f o c a l
l e n g t h , the o b j e c t d i s t a n c e , the camera base and m a g n i f i c a t i o n
were then entered. Next he chose s i x p o i n t s near v e s s e l
c r o s s i n g s , w e l l o u t s i d e the c e n t r e of i n t e r e s t . These p o i n t s
were coded and g i v e n X.Y.Z. c o o r d i n a t e s f o r model l e v e l l i n g and
a b s o l u t e o r i e n t a t i o n subsequently by the I.B.M. 7044 computer."*
The author f i n d s t h i s d e s c r i p t i o n somewhat c o n f u s i n g and
ambiguous. In the f i r s t i n s t a n c e G. Crock e x p l a i n s n o t h i n g
about the accuracy of data entered i n t o the a n a l y t i c a l p l o t t e r .
The u n c e r t a i n t y of the m a g n i f i c a t i o n i s not even mentioned a t
a l l . Secondly, he t a l k s about X, Y, Z c o o r d i n a t e s of the p o i n t s
near v e s s e l c r o s s i n g s which are used f o r the a b s o l u t e o r i e n t a t i o n .
T h e r e f o r e these c o o r d i n a t e s are not model c o o r d i n a t e s but
c o o r d i n a t e s i n some a b s o l u t e c o o r d i n a t e system. There i s not a
s i n g l e word about how these c o o r d i n a t e s can be determined to a
h i g h e r degree of accuracy. The author c o n s u l t e d s e v e r a l ophtha
l m o l o g i s t s but not a s i n g l e one c o u l d t e l l him what the l i m i t s
of d e v i a t i o n s from the standard eye are. There are , however,
s e v e r a l dimensions t h a t are r e l a t i v e l y s t a n d a r d i z e d but they
c e r t a i n l y cannot i n s u r e a very p r e c i s e a b s o l u t e o r i e n t a t i o n , or
a l l measurements o b t a i n e d by photogrammetric methods of the
fundus are much l e s s r e l i a b l e than can normally be expected from
photogrammetry.
The Department of Ophthalmology at the U n i v e r s i t y of B r i t i s h
Columbia i n i t i a t e d a s i m i l a r p r o j e c t to the above A u s t r a l i a n
*[12]
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research. The main task was to determine whether photogrammetry
can be applied to obtain r e l i a b l e quantitative measurements of
the cup of. the o p t i c nerve and by evaluation of measurements to
determine the r a t e of progression of glaucomatous damage. A
Zeiss fundus camera was used for stereophotography on 35 mm KX
135 Kodachrome f i l m . The camera had f i d u c i a l marks attached
additionally.. The f i r s t stereophotographs were taken using the
A l l e n stereoseparator with a base of 2.25 mm. To avoid movements
of the fundus as a photographed object, instantaneous stereo-
photographs, were taken by a special twin prism mounted i n front
of the objective so as to insure a constant base separation.
The r e s t i t u t i o i a of photographs was performed on the Wild A8
p l o t t e r at. the B r i t i s h Columbia Institute of Technology by an
experienced photogrammetrist. A detailed description of the
method and r e s u l t s can be found i n [61]. Again, as i n the a r t i c l e
by G. Crock. I t can be found that "absolute o r i e n t a t i o n was
achieved by marking and recording 3 points at r e t i n a l b i f u r c a t i o n
or arteriovenous crossing on the photographs which could subse
quently be: used as reference points."* The "absolute orientation"
must have some other meaning i n t h i s context, because according
to "Manual of Photogrammetry," t h i r d e d i t i o n , volume II page
614, the following d e f i n i t i o n can be found. "The stereoscopic
model formed by the completion of r e l a t i v e o r i e n t a t i o n has an
undetermined r e l a t i o n s h i p to the horizontal and v e r t i c a l datums.
The adjustment of the r e l a t i v e l y oriented model, to make i t
conform i n scale and i n horizontal and v e r t i c a l p o s i t i o n with
the datums of the map sheet, i s c a l l e d absolute o r i e n t a t i o n ,
* [ 6 1 I
- 121 -
and g e n e r a l l y f o l l o w s r e l a t i v e o r i e n t a t i o n . "
From the s t e r e o s c o p i c model i n the W i l d A8, contour l i n e s
of the o p t i c nervehead and then f o u r c r o s s - s e c t i o n s d i r e c t l y
from the contour l i n e s were drawn. The areas o f c r o s s - s e c t i o n s
were determined by the method of g r a p h i c a l i n t e g r a t i o n ( p l a n i -
meter).
Saheb, Drance and Nelson i n [61] f i n i s h e d w i t h the s t a t i s t i c a l
a n a l y s i s o f a c h i e v e d r e s u l t s . As f a c t o r s which i n f l u e n c e the
accuracy o f the f i n a l r e s u l t s they took photography, photogram
m e t r i c p l o t t i n g and the c o n s t r u c t i o n of the p r o f i l e and i t s
pl a n i m e t r y . Using the same model the c o n t o u r - l i n e p l o t t i n g was
repeated s e v e r a l times. In the same manner c r o s s - s e c t i o n s were
p l o t t e d and areas were determined r e p e a t e d l y . N a t u r a l l y , the
a c t u a l accuracy of the method remained unknown s i n c e a l l r e p e t i
t i o n s were performed w i t h the same instruments and under the
same c o n d i t i o n s . E v e n t u a l s y s t e m a t i c e r r o r s i n f l u e n c e a l l
r e s u l t s e q u a l l y and t h e r e f o r e the standard d e v i a t i o n s o b t a i n e d
c h a r a c t e r i z e p r e c i s i o n and not accuracy of the method. The
e x p l a n a t i o n f o r the standard d e v i a t i o n of photography i s not
presented but the author assumes t h a t the v a l u e was d i r e c t l y
o b t a i n e d from the manufacturer of the f i l m used. T h i s v a l u e i s ,
n a t u r a l l y , i n f l u e n c e d by the g r a i n of the f i l m , s t a b i l i t y o f
emulsion h o l d e r and the image-side r e s o l v i n g power o f the fundus
camera.
The r e s e a r c h a t the U n i v e r s i t y o f B r i t i s h Columbia has
- 122 -
F i g . 3-9 Stereogram and p l o t t i n g of the fundus
- 123 -
shown t h a t "stereophotogrammetry may now be an a d d i t i o n a l
t o o l i n e v a l u a t i n g and f o l l o w i n g glaucoma p a t i e n t s and might be
p a r t i c u l a r l y v a l u a b l e i n f o l l o w i n g the progress of o c u l a r hyper
t e n s i v e s , p a t i e n t s u n r e l i a b l e on v i s u a l f i e l d t e s t i n g , and the
c o n g e n i t a l glaucomas."*
SUMMARY AND CONCLUSION
A l l the d e s c r i b e d problems i n q u a n t i t a t i v e ophthalmology
show t h a t t h e r e i s undoubtedly a p l a c e f o r photogrammetry as a
measuring t o o l . . U n f o r t u n a t e l y , they a l s o show t h a t the a p p l i c a
t i o n o f c l o s e - r a n g e photogrammetry i s almost a t the v e r y b e g i n
n i n g as a r e c o g n i z e d measuring d e v i c e i n ophthalmology. The
attempts which have been made to s o l v e p a r t i c u l a r problems were
always concerned o n l y about p a r t i c u l a r problems d i s r e g a r d i n g
a u n i v e r s a l s o l u t i o n t o a l l q u e s t i o n s . Each p a r t i c u l a r camera,
p l o t t i n g i nstrument and method a p p l i e d was s i m p l i f i e d to the
very maximum so as t o serve the problem t a c k l e d . They might
have found the b e s t and e a s i e s t s o l u t i o n but t h i s s o l u t i o n o n l y
proved t h a t photogrammetry can be h e l p f u l and can be used. In
the g r e a t m a j o r i t y of cases the a p p l i c a t i o n of photogrammetry .
remained on i n the experimental stage. Without the combined
e f f o r t s o f m e d i c a l p r o f e s s i o n and photogrammetrists no success
can be a c h i e v e d . P o t e n t i a l users i n medicine must be persuaded
by photogrammetrists t h a t many of t h e i r problems can be s o l v e d
much f a s t e r , more e a s i l y and more a c c u r a t e l y . I t should be
demonstrated t o them t h a t photogrammetry i n c l u d e s a v e r y - f a s t
* [61]
- 124 -
procedure of r e g i s t e r i n g f a c t s by photography, t h a t photogram
metry can a l s o measure and evaluate v e r y f a s t changing events,
t h a t photogrammetry o f f e r s a means to measure an o b j e c t w i t h o u t
having t o touch i t p h y s i c a l l y , t h a t n o n - v i s i b l e l i g h t r a y s can
be employed to achieve s p e c i a l e f f e c t s , and t h a t photogrammetry
can measure o b j e c t s under the microscope. I t should not be
f o r g o t t e n t h a t photogrammetric measurements u s u a l l y r e q u i r e v e r y
c o m p l i c a t e d and expansive instruments f o r photography and r e s t i
t u t i o n , t h a t to operate economically a p r o j e c t must be of a
c e r t a i n minimum s i z e , and t h a t measurements cannot be d i r e c t l y
o b t a i n e d as i n c l a s s i c a l procedures.
In o r d e r t o make f u l l use of photogrammetry, the author
suggests t h a t some c e n t r a l photogrammetric s t a t i o n s hould be
e s t a b l i s h e d . T h i s c e n t r a l s t a t i o n can then serve many h o s p i t a l s
and m e d i c a l i n s t i t u t i o n s . Only i n t h i s manner can the e x p e n d i t u r e
of s u f f i c i e n t funds f o r photogrammetric instruments be j u s t i f i e d .
A t the same time such a c e n t r a l s t a t i o n c o u l d c a r r y on e x t e n s i v e
r e s e a r c h i n t o i n i t i a t i n g the p r o d u c t i o n of i n e x p e n s i v e cameras
and p l o t t e r s which can be a p p l i e d g e n e r a l l y and not j u s t f o r a
p a r t i c u l a r problem. As long as there i s o n l y a l i m i t e d number
of problems i n c l i n i c a l p r a c t i c e which are s o l v e d by photogram
metry todays expensive u n i v e r s a l p l o t t e r i s h a r d l y j u s t i f i a b l e .
Another problem not l e s s important i s the e d u c a t i o n of the
m e d i c a l p r o f e s s i o n i n photogrammetry. There i s q u i t e a number
o f p o t e n t i a l u s e r s who have never heard of photogrammetry, a t a l l .
- 125 -
T h i s f a c t might be the major hindrance f o r a q u i c k e r s u c c e s s .
Let us hope t h a t the c o n s i d e r a b l e f l e x i b i l i t y o f c l o s e - r a n g e
photogrammetric systems w i l l be r e c o g n i z e d by p o t e n t i a l u s e r s
as w e l l as by photogrammetrists.
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- 1 2 8 -
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