SIMPLE CALIBRATION TECHNIQUES FOR NON-METRIC CAMERAS 
George E. Karras, Dionyssia Mavrommati 
Department of Surveying, National Technical University of Athens 
GR-15780 Athens, Greece (e-mail: gkarras@central.ntua.gr) 
KEY WORDS. Non-metric Cameras, Interior Orientation, Lens Distortion, Camera Calibration, Bundle Adjustment, Rectification 
ABSTRACT 
Architectural documentation is carried out mostly with (analogue or digital) non-metric cameras or video-cameras. Unknown internal 
geometry is a main problem in this context, particularly for wide-angle lenses with their considerable amount of distortion. Self-cali 
brating bundle adjustment or jD test-field calibration may provide straightforward answers to this problem, yet on occasions such 
steps can prove too complicated or costly tor ordinary users. Hence, this paper discusses the use of simple pre-calibration approaches. 
Practical examples with wide-angle lenses are first given to illustrate that, in general, use of „nominal” values for the camera constant 
and the principal point causes no significant problem in most cases of low or moderate accuracy requirements. These same examples, 
however, reveal the marked effects of radial distortion. This is a main problem which needs to be controlled, even in the simple and 
most popular among users method of rectification (for which knowledge of the primary interior orientation parameters is irrelevant). 
Here, simple approaches for determining radial distortion are presented and assessed, ranging from the use of linear features on man- 
made objects to rectification of regular grids and its various alternatives. On the other hand, the easiest approach for full camera cali 
bration is probably by the common adjustment of images of targeted 2D objects taken under different viewing angles. In the results 
given the described methods for determining radial distortion have also been evaluated. In conclusion, both the merits and limitations 
of the discussed simple calibration techniques are outlined but also a gross distinction between analogue and digital camera is made. 
1. INTRODUCTION 
It is a common experience that most of today’s photogrammetric applications in architectural and archaeological documentation are 
carried out by means of non-metric cameras, either analogue or digital. This holds true not only regarding published projects but also 
encompasses those numerous unpublished cases in which non-metric images are applied on a routine basis by individual users, firms 
or public services in the course of everyday documentation tasks. Understandably enough, such a „metric” use of non-metric cameras 
(made possible by the analytical and digital photogrammetric as well as image processing tools) is very popular among non-expert 
users, namely architects, archaeologists, restorers, conservationists but also engineers. This possibility of using non-metric cameras is 
a decisive factor for what has been called the „démocratisation of photogrammetry”. 
But speaking of an ordinary amateur camera almost automatically raises the matter of its internal geometry' or its interior orientation. 
Indeed, many questions of non-experts revolve about this point. On the other hand, numerous camera types available on the market 
could be employed, and in fact are employed, for documentation and conservation purposes. To this one should add the fact that (per 
haps contrary to the wishes of some photogrammetrists...) a significant number of applications in archaeology or architecture pose 
moderate, or even low', accuracy requirements. In this context, the following (rhetorical) questions arise: 
• is every user expected to calibrate a camera? 
• and for all tasks? 
• and every camera? 
In the photogrammetric literature and practice there exist several alternatives regarding how to handle the problem of interior orienta 
tion. Here, the following approaches could be mentioned: 
Use of a projective approach. The use of projective equations, whenever possible, frees users from the need to know the interior 
orientation parameters of their camera. These are the cases of 2D-2D rectifications or of the 2D-3D direct linear transformation (DLT). 
The first technique, a very popular practical tool, is inherently limited to (nearly) planar objects, while the second generally requires 
geodetic control with sufficient extension in depth. And, of course, the problem ot lens distortion, which causes non-projective image 
deformations, remains. 
Test-field calibration. This is the conventional camera calibration approach, but it evidently implies that users have to construct 
(and maintain) an accurate targeted 3D test-field, designed for all cameras, lenses and focusing distances they will use. 
Bundle adjustment solutions. In principle, a geometrically sound bundle adjustment will produce good results for the particular 
application. However, unless performed in strictly controlled environments, different adjustments can yield strongly diverging values 
for the interior orientation elements. Thus, one cannot simply accept any solution as the definite values for the camera parameters. 
Other simpler techniques. Among such calibration alternatives, use ot image vanishing points is mentioned. Heie again, accept 
able results can be expected for the particular images used (for instance, historic photographs of destroyed buildings). Yet, the re 
peatability of such techniques is generally rather poor, and they could not be regarded as general-purpose calibration methods. 
Further to this, a fundamental question concerns the image coordinate system itself of analogue amateur cameras. Generally „fixed 
through the four corners of the negative, the image system is indeed very poorly defined. This clearly has a direct impact upon the re 
producibility of the image principal point. Thus, in most cases one may ask: is it meaningful to attempt and estimate a deviation from 
an „ideal” image centre if the location of this centre may be uncertain to an extent comparable to, or even larger than, the deviation it 
self? This consideration illuminates the following choice regarding interior orientation often adopted in practice. 
Proceedings 18 th International Symposium CIPA 2001 
Potsdam (Germany), September 18 - 21, 2001