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are necessary, following again [6] . However, according to the ‘law of rotation axis'' of perspec- 
tive two coplanar geometric configurations situated in two planes B, and B, remain perspective 
to each other if B, is rotated around the trace s of B, /B,, and the center O of perspective is 
rotated around the vanishing point of B, on Bi. This means that a certain perspective of a plane 
configuration can be viewed independently of the standpoint and of the interior orientation, For 
methods of determination of interior orientation in which also the standpoint has to be determined 
by resection, this would mean that the determination becomes singular if the control points are 
situated in a plane. 
We arrive at the same result if we follow [9]. [ 7] . If we regard for a moment the photos 
as a strict perspective picture then object points and picture points are perspectively related to 
each other. We investigate now two cases : 
Assumption 1 : The field of control points is lying within a plane and has no extension into depth. 
Then, according to [9], photo and object are images of the same standpoint. Images of the same 
standpoint can be put into ool different positions, If we regard the object as image 1 and the photo 
as image 2 we then can say : To each arbitrary relative position of object (image 1) and standpoint 
belongs a unique respective position - described by the data of outer and inner orientation - of the 
photo (image 2), That means : for any arbitrarily chosen standpoint of the camera we can find a 
unique fictitious set of data of inner orientation, 
Assumption 2 : The field of control points is truly three-dimensional, Then object and photo have 
a unique relative position and a unique interior orientation, According to [9] and 1 7) the proof 
follows from the fact that three and more perspectives taken from the same standpoint have a 
unique relative position, Three-dimensional object and two-dimensional photo can always be in- 
terpreted as several images from the same standpoint : We imagine the control points to be grou- 
ped in different planes, Each of such planes represents one group of control points, All groups N i 
form the object. Each single plane is perspective to the photo, e q 
  
It seems that these basic facts, following from projective geometry, have not yet been 
regarded fully in methods proposed and also used in camera calibration : 
Since space resection is a fundamental concept of camera calibration [5] it can be expec- 
ted that in a setting of camera with near vertical axis the principal distance p and coordinate Z 
of the standpoint are highly correlated when calculated simultaneously in a calibration, This is 
shown in [4], [8] and in investigations carried out by the author's team, 
A possibility to improve this would be to determine also the coordinates of the standpoint. 
A proposal was made by Hallert, 
Another problem not yet answered in literature is the number of points necessary for a 
simultaneous determination of inner and outer orientation, Following S. Finsterwalder in [6] a 
minimum of six points is necessary, whereas an interpretation of the basic equations of perspec- 
tive mapping - vide [1], [5]. [7] - five points would suffice : Unknowns are the coordinates X,, 
Yo. Zo of the standpoint, three parameters o, K, 9 of rotation, the principal distance p, and the 
origin xg, yg of coordinates in the perspective, i, e, altogether [9] . Since each control point 
contributes two equations five points giving ten equations and thus already one overdetermination 
would suffice. 
Another important aspect is raised in (3] by Brown and concerns the question of the dis- 
tortion function, Not only is radial distortion a function of object distance, but it variates also 
throughout the photographic field, Except in [3] no practical investigations are known, 
A very interesting proposal for camera calibration has been made by Kólbl [13] . In the 
method adopted by him, three convergent photos with unchanged inner orientation taken by the 
same camera from three different standpoints of the same object are required, No object measu- 
rements are necessary, and experiments have shown the high accuracy of the method, 
Finally, camera calibration need not necessarily be a separate procedure but may be © 4 
combined with actual photography of the object, Then the unknown data of interior orientation : 
could be determined simultaneously with outer orientation. Such a procedure has been used in (3] : 
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