CALIBRATION OF CLOSE-RANGE PHOTOGRAMMETRIC SYSTEMS 1481 
well documented, and again I would like to refer to the literature e.g., 28121421 The basic 
resection approach fails for telelenses with cone angles of 2? or less. Merrit?? has over- 
come this problem applying the Hartman method. 
"ON THE JOB" CALIBRATION 
When performing a calibration utilizing object photography, the object space has to be 
controlled to meet the requirements stated above, e.g., at least one full control point for 
every two unknown parameters. 
In close-range photogrammetry often photo scales of 1:10 or larger are encountered, 
which means that 10 um in photo scale represents 0.1 mm in the object. To achieve and 
maintain this accuracy for control by conventional surveying procedures is time consum- 
ing and often difficult even when maintaining a laboratory testfield. Often, however, ac- 
curacy requirements permit the construction of a special control frame*5? which main- 
tains its geometric configuration sufficiently well to be used for control purposes. 
The mathematical formulation is usually the same as for the laboratory calibration. Al- 
though it is not explicitly a calibration method, I would like to mention the “Direct 
Linear Transformation” approach, developed at the University of Illinois! in this con- 
text. It has been modified recently to incorporate radial symmetric and asymmetric lens 
distortions!?. These require five parameters in addition to the original eleven, which 
means a minimum requirement of eight object space control points. Over-determination 
is, of course, highly desired. As pointed out by Abdel-Aziz and Karara?, the method is 
highly economical as far as computer costs are concerned, and provides accuracies simi- 
lar to the more conventional space resection type approach. 
SELF CALIBRATION 
This approach differs significantly from the previous ones in that it does not require 
object space control as such for the calibration. According to Kólbl!5 three convergent 
photographs are taken of the same object with the same camera and unchanged interior 
orientation. Utilizing the coplanarity condition and well identified object points, the 
basic parameters of interior orientation are computed. Recently this approach has been 
extended to include radial symmetric, asymmetric, and tangential lens distortions. These 
are modelled somewhat differently to what has been the general practice!$. Brown$ 
also has been applying self calibration in close-range photogrammetry using multiple 
station arrangements. 
As mentioned before, these self calibration approaches do not require object space 
control, except for the actual object evaluation, which like any other photogrammetric 
evaluation requires two horizontal and three vertical control points. It has to be noted 
here that for these methods the interior orientation is considered as unchanged between 
photographs, which might not always be the case for non-metric photography, where the 
interior stability of the camera can be rather weak. 
At the Department of Surveying Engineering at the University of New Brunswick a 
self calibration method was devised by the author and his collaborators?!! which per- 
mits the determination of the interior orientation parameters for each photograph while 
using the coplanarity condition and minimum object space control. 
THE UNB SELF CALIBRATION APPROACH 
Based on the coplanarity condition, the method requires at least one overlapping 
stereomodel, but is however more general and can be applied to multiple stereo models 
as well as photogrammetric blocks. Due to expected changes in interior orientation the 
working unit is always the individual photograph. 
According to Figure 1 the base vector between two camera stations C' and C" is 
D. Xc" = Xc 
B-|B,l-2|yYc-Yc (1) 
B, Ze — Zc 
while the vector U' from C' to an object point P(X,Y,Z) is expressed as