ANALYTICAL CALIBRATION OF CLOSE—RANGE CAMERAS 
Dr Lilia Koleva 
TRANSROJECT CO. for Transport Designing, Sofia, Bulgaria 
Commission V 
ABSTRACT: 
A mathematical model based on the collinearity condition is suggested for calibration 
of  close-range cameras. This approach is realized by developing a computer program and 
tested by an experiment with Zeiss UMK 10/1318 cameras. The influence of number and 
distribution of the control points necessary on the accuracy of camera parameters is 
analyzed. The conclusion recomends the optimal number and distribution of these control 
points. 
KEY WORDS: Analytical, Calibration, Camera, Close-range, Terrestrial. 
INTRODUCTION for sophistication of the internal 
orientation (Livingston, 1980; Wester- 
A necessary prerequisite for the precise Ebinghaus, 1986; Preuss, 1975). 
solution of an analytical photogrammetric 
problem is the correspondence of the All this accounts for the interest in the 
photographs with the central projection theoretical and experimental investiga- 
and the high precision of their tion of the accuracy of the different 
parameters. The accuracy requirements for calibration methods; in the explanation 
the parameters are determined according of the influence of the distribution and 
to the accuracy requirements for the number of the: control points: in the 
final result and the specific object its recommendation of a proper distribution 
depth and the geometry of the photos of the points for each calibration method 
used. depending on the camera used. 
In the case of ciose-range photogrammetry TEST CALIBRATION 
the precision requirements are usually 
higher. Mainly  focusabie metric and it is done by single photos Or 
nonmetric cameras are used for which the stereopairs taken of a spatial (three 
optical laboratory methods of calibration dimensional) test object of control 
are not suitable (Livingston, 1980). points whicht is suitable for the 
Different analytical calibration methods calibration of metric cameras. The 
are used which can be divided into three internal orientation elements obtained 
principle groups: are used as known quantities in the 
solution of the photogrammetric problem. 
  
(i) camera calibration on a test object 
(pre-calibration); In order to obtain stable camera 
(ii) calibration simultaneous with the parameters a specific distribution of the 
solution of the photogrammetric points in the test object is required. 
problem(simultaneous calibration ); The accuracy of the determination of the 
(iii)self-calibration - calibration using internal orientation elements is 
the information from three or more influenced by the accuracy with which the 
convergent photographs without external orientation elements of the. 
control points. photographs are determined. In the 
simutaneous calibration the internal and 
Depending on the accuracy requirement for external orientation elements are 
the results various degrees of determined together in the process of the 
sophistication of the internal orienta- analytical solution. 
tion can be used - only the position of 
the internal perspective centre is Theoretical analysis 
determined or the radial or tangential 
lens distortion or film deformation are The analysis of the points distribution 
also taken into account. influence on the calibration accuracy is 
based on the collinearity condition, 
The authors, who investigated the simplified for the normal case of 
influence of the analytical calibration terrestrial stereophotogrammetry: 
on the accuracy of the results were 
convinced in its effectiveness although X-Xs … Z-Zs 2 
there is a difference in their opinion me, = É +, ZE 2" EF — (1) 
about the degree of the accuracy Y-Ys Y-Ys 
improvement (from 40% to 250%), about the 
number and location of the control points where p(x,=z) is an image point, P(X,Y,Z) 
for calibration and about the necessity is the respective point in the object