[Studies in Computational Intelligence 481] Artur Babiarz, Robert Bieda, Karol Jędrasiak, Aleksander Nawrat (auth.), Aleksander Nawrat, Zygmunt Kuś (eds.) - Vision Based Systemsfor UAV Applications (2013, Sprin

Vision System for Group of Mobile Robots 143
2.1 Camera Setup and Correcting Radial Distortion
of Camera’s Lens
The only requirement imposed on the camera setup by the vision algorithm is that it
should be possible to switch off all features like Auto Gain Control (AGC), Auto
White Balance (AWB), etc., in order to provide as constant colors as possible.
Is is also important to set the lens’s aperture properly, in order to avoid excessive
CCD blooming effect, which, in extreme cases, can distort shape of objects
being recognized, thus degrading algorithm’s precision. Every consumer-class
camera produces images with significant amount of radial distortion which degrades
the precision of measurements done on the basis of analysis of acquired
image, like estimation of the position and orientation of various objects on the
image. Many methods have been developed for the purpose of calibration the
camera, which take into account radial and tangential distortion introduced by
camera’s lenses. The most widely used method is described in [5]. This method
however requires precise measurements of coordinates of corresponding points in
real world and on image, which would take too much time. So the alternative
method is used here which is taken from [6]. It is very simple and quick, however
it requires user’s attention in choosing proper amount of compensation.
The method uses inverse mapping for finding the color of pixel in output image.
Each pair of integer pixel coordinates in output image is mapped to a pair of
coordinates in input image, which usually are real numbers rather than integers.
Color of the pixel in output image is then calculated either through bilinear, or
through nearest neighbour interpolation of the colors of pixels in the neighbourhood
of the mapped coordinates. Bilinear interpolation gives much better results
than nearest neighbour (NN) interpolation, however it is much slower.
The algorithm performing actual correction can be described as follows. Let
, be distorted input image and , be rectified output image of the
same size. Then, for any pair of pixel’s coordinates in the output image ,
the pair of corresponding coordinates in the input image , can be found
from the following formulas:
1 (1)
where
and
1 (2)
(3)
, (4)
and , are coordinates of the center of image. The parameter is to be chosen
by the user, useful value of it is in the range (0.001, 0.1), depending on the amount
of distortion introduced by the particular lens. The color of a pixel in the output