THE COMPARISON OF CAMERA CALIBRATION PROCEDURES - 
A PROJECT UPDATE 
Hartmut Ziemann 
Photogrammetric Research 
National Research Council 
Ottawa, Ontario KIA OR6 
Canada 
ABSTRACT 
a 
t 
The report summarizes with reference to more extensive referenced reports work carried/and reported 
in the past, work accomplished recently, problems still to be solved and work awaiting execution. 
INTRODUCTION 
The camera calibration project of the former Working Group on Image Geometry has been reviewed in 
[Ziemann 1976/ very briefly, with an emphasis on image quality data and on results derived in a 
doctorial thesis in /Ziemann 1978/, and extensively in view of the logisties of the project in /Ziemann 
and Merchant 1980/. Since than emphasis has been placed on the development of a mathematical model 
able to accomodate all the different procedures. This update is a summary of that work. A longer 
report had been prepared for the German Research Foundation /Ziemann 1981/. This report is being 
extended at present and will be submitted within the next few weeks to the German Research Foundation, 
who funded the authors one-year stay at the Institute for Photogrammetry at Bonn University. 
INPUT DATA 
Table 1 on the following page summarizes the input data in their characteristics and availability. 
It can be noted that not all photographic records taken for the project were made available to the 
National Research Council (NRC) for measurement, nor were all records available at NRC measured or all 
measurements carried out by project participants made available to NRC either all or in machine- 
readable form. As a result, four of the nineteen procedures cannot yet be processed at NRC. 
THE MATHEMATICAL MODEL 
  
The present status of the mathematical model which is based on that reported in /Slama 1972/ has 
been given in /Ziemann 1982a/. This paper clarifies the selection of a reference plane, of the 
reference points for image coordinates, of standard lens distortion curves (see also /Ziemann and El- 
Hakim 1982a/) and of the same image coordinate system for all different contributed data, and overcomes 
the problems associated with the use of the equivalent focal length in stellar calibration versus the 
use of the calibrated focal length in other calibration procedures by means of the standard lens 
distortion curves. The model implies the point of best symmetry as reference point for both the 
radially symmetrical distortion and the decentering distortion. An investigation has been started to 
determine whether this choice is optimal for the decentering distortion which may possibly-be better 
referenced to the -principal- point of-autocollimation. This investigation uses data from procedure 
no. 9 which is based on a multibank collimator array with collimators thus positioned that a full- 
format image is obtained under well-controlled laboratory conditions. 
FORMATION AND REDUCTION OF NORMAL EQUATIONS 
  
A program system has been developed for the stepwise formation and reduction of normal equations 
under the assumption that image-point locations are. not correlated-with each other. -While possibly not 
generally valid, the assumption-is justified for this project because of image-point locations were 
corrected for image deformation by means of réseau points located in the vicinity of the image points, 
whenever the réseau was also imaged. The latter was not the case for procedures nos. 3,—5-and 7 which 
are the standard equivalents of procedures nos. 4, 6 and 8, and for procedures nos. 9 and 14. 
For uncorrelated image-point locations, the normal equation contributions expressing the 
correlation between image-point location and object-space location, exterior orientation of the 
respective photograph and interior orientation of the respective lens/camera system are all formed for 
that particular image point only; hence, the normal equation subsums computed for an image point can be 
reduced prior to the summation of the overall normal equations. This makes it possible to handle a 
very large number of unknown image points. During the formation of the observation equations 
information is collected about the occurance of a certain point in different photographs. This 
information is used in a next program to summarize all subsums requiring summation for a certain 
object-space point, and the resulting sums are then reduced. This procedure again makes it possible to 
handle a very large number of unknown object-space points assumming that not so many of those are 
fisaíficantly correlated; also, it does not place a limit on the number of photographs in which a point 
S imaged. 
After the elimination of all unknown image-point and object-space-point locations, the partially 
reduced subsums are added up as required for each photograph and reduced column after column. 
The final reduction phase eliminates all unknown parameters of the geometric-optical performance of 
the lens/camera system(s). The program system will eventually be usable as a photo-variant reduction 
process. For the time being, the reduction for unknown object-space locations and exterior and 
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