CIP A 2003 XIX th International Symposium, 30 September - 04 October, 2003, Antalya, Turkey 
In this paper we want to focus on three aspects concerning this 
question: 
1. How do we manage with the high degree of geometric 
distortions (particularly the radial symmetric distortion) 
when we apply direct image resampling techniques such as 
rectification? 
2. How will we set up internal camera parameters including 
those related to lens distortions when we make use of 
different programs? And being more specific, how will we 
manage all the different mathematic schemes that are 
involved in the description of the same phenomenon? 
3. In case of being the distortion well-known, what is the most 
efficient way of working? Should be a good practice to 
eliminate it as a first stage by image re-sampling prior to 
any further process such as re-projection or restitution? Or 
would it be better to have it mathematically modelled doing 
the re-sampling as a unique stage that maps for instance 
distortion and rectification at the same. 
It is obvious that, nowadays, we are more focused on a certain 
type of cameras, those that have been leading the reconciliation 
of non-skilled people and Photogrammetry. In a general sense, 
the boom of this science as a powerful instrument for heritage 
recording has been made possible thanks to the irruption of 
digital cameras on the scene. 
2. INTRODUCING “LDS” 
Lens Distortion Simulator is a computer application that will 
bring some light to some points that are often found obscure by 
many users, and particularly by students when they face this 
question. The following lines will act as a review of some key 
points. We will just focus on the radial symmetric distortion and 
not so much on the tangential and asymmetric due to the higher 
dimensional magnitude and conceptual importance of the first 
one as it affects the principal distance concept. For this reason, 
only radial distortion simulation is being implemented with the 
main purpose of simulating its consequences on images; this is 
something that we consider very didactic. On the other hand, it 
will allow to know which range applies to those parameters and 
at what levels they have noticeable effects. 
Figure 1. The simple fact. 
In the classic Optics language, as shows the figure 1, the 
distortion is defined as the inconstancy of lateral magnification. 
But even if the classic definition is easy to learn, as it explains 
the differences in terms of point image-coordinates between 
real and theoretical locations (those resulting from the 
perspective laws compliance), the complexity comes from the 
diverse ways of expression of this difference sometimes as an 
error and sometimes as a correction. (It depends on authoring). 
These displacements, that can be easily understood, become 
hard, dense and opaque when the user finds that different 
programs use different nomenclature and parameterisation. As a 
result sometimes the user finds expressions of error while in 
others terms of corrections. But all definitions are in fact the 
same; all models define the displacement of points from their 
bundle perspective rules compliant positions, but using different 
notation to this same fact. 
3. THE CONCEPT OF RADIAL SYMMETRIC 
DISTORTION. 
It is important to take into consideration that the concept of 
radial distortion itself does not offer a clear panorama at all, at 
least from a didactic point of view 
Many authors such as Bonneval, Ghosh, Moffit, or Mikhail, 
define radial distortion as the deviation of light rays during lens 
crossing. 
It seems that such definition comes from the didactic need of 
making the model fit into a perfect projective scheme where the 
projection centre can be exactly located in a certain point (like 
pinhole camera), or instead of this, it could also be considering 
the nodal image point being equally well-located and 
determinable. 
In this way, the lense’s radial distortion is measured as a 
distance or separation (along radial directions contained in the 
image plane) between the actual positions and their ideal 
corresponding ones. So that an ideal ray trajectory and its 
resulting image spot are exactly determined by the value of the 
principal distance (f) and the incidence angle (a). 
Image Plane 
Figure 2. Scheme of ray deviation. 
Under such assumptions, the radial distortion is expressed in 
terms of residuals or errors: actual position - theoretical 
position. 
dr = r - r' = r - f*tana HI 
This expression of “error” gives us the sign criterion: It will be 
considered positive the outgoing way and negative the opposite 
one. We can see its results in the following figure: The red 
figure corresponds to a positive distorted image (“pincushion”) 
of a perfect square shape, while the blue one results from a 
negative distortion (“barrel”).