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PROCEDURES OF CORRECTION OF THE GEOMETRY DISTORSIONS 
FOR DIGITAL IMAGES 
A. Guamieri, A. Vettore 
Dip. Territorio TESAF - Università’ di Padova - Italy 
AGRIPOLIS - Statale Romea 16 
35020 Legnaro (Padova) 
Phone +39-049-8275580, fax +39-049-8372713 
e-mail: vettoan@ux 1 .unipd.it 
Commission VI, Working Group 3 
ABSTRACT 
Since a few years digital fotocameras have widely spread on the market, principally because of their price, quality 
image improvement and easy of use. In order to extract from these digital images reliable 3D informations regarding 
objects position and dimension, both the exact knowledge about perspective and dimensional relations between image 
and scene, and the knowledge about the geometric distortions parameters are needed. 
Therefore, the aim of this work was to develope, in the ambit of the Photogrammetry course, an alternative calibration 
method and to implement it as teaching software, by which the parameters of the major forms of geometric distortions, 
i.e. radial, decentering and thin-prism, can be estimated. Basically, the proposed method was realized putting together 
the Tsai-Lenz and Weng-Cohen-Hemiou calibration algorithms and applying the Levenberg-Marquardt algorithm as 
non linear optimization procedure. The software was developed in Matlab programming language, because its code can 
be to structured in text-like scripts, allowing therefore to share and to understand a program in easier way compared to 
software written, fo instance, in Fortran or C. 
The method has been implemented in such a way to allow a full camera calibration or a computation of the exterior 
orientation parameters only, using inner orientation and distortion parameters determined from previous full calibration. 
This approach can be useful if only an estimate of new targets positions is required, in which the inner and distortion 
parameters are already given. 
1. INTRODUCTION 
The camera calibration, typical issue in computer 
vision, is becoming today very important also in digital 
photogrammetry applications, where dimensional mea 
surements are required. The main aspect of camera ca 
libration is concerned with the estimate of internal 
parameters of the camera, that define the perspective 
and dimensional relations between 3D points in the 
scene and corresponding image coordinates. Another 
important aspect of calibration regards the determi 
nation of geometrical relations between camera and 
scene through estimate of external parameters, and the 
correction of geometrical lens distortions. 
On the other hand, digital non-metric fotocameras are 
widely spreading on the market since a few years, 
principally because of their price, quality image impro 
vement and easy of use. At the present the image 
quality of amateur digital cameras is surely not at the 
same level of film cameras in terms of resolution (300 
dpi vs 2500 dpi with a 35mm film), image dimension 
(640 x 480 pixels), colours spectrum (24 bits, rather 
than continous) and limited dynamic range of the CCD, 
in lights and shadows capturing. As rule of thumb, 
increasing the dimension and the number of CCD cells 
the image quality is improved, but the final price is 
augmented as well. Despite the exposed drawbacks, the 
easy and quickly download of images on a computer 
and the perspective of improvements in image quality 
lead to a reasonable scenario in next future, where digi 
tal cameras will substitute the film ones in the most 
common applications. 
On the ground of these considerations, we have deve 
loped an alternative calibration method of digital non 
metric camera, in order to employ this kind of relative 
expensive device in digital photogrammetry applica 
tions. 
Following the classification presented in [4], we can 
identify three main groups for the existing camera cali 
bration techniques: 
1) Direct Nonlinear Minimization: in this category 
the parameters estimation involves using an itera 
tive algorithm, which tries to minimize residual 
errors of some equations. The adopted camera 
model can be very general, to cover many kind of 
distortions, but it requires a good initial guess of 
the parameters because the procedure is iterative. 
Furthermore including the estimate of lens distor 
tions, the procedure may be unstable, the correla 
tion between external and distortions parameters 
can lead to divergence or false solutions.