COSC 4393/6397
Digital Image Processing
Department of Computer Science
University of Houston
Assignment #2
Due: 10/03/07
1. Many artificial vision systems have been motivated by the image sensing
capabilities of biological vision systems. One such mechanism is scene sampling,
motivated by the inherent in the structure of the retina. Photoreceptors in the
retina are distributed to provide high resolution on the central part of the retina
(fovea) with decreasing resolution towards the periphery. This has motivated the
log-polar image geometry.
When compared to the usual cartesian images, the log-polar images allow faster
sampling rates on artificial vision systems without reducing the size of the field of
view. The log-polar transformation is a conformal mapping from the points on the
cartesian plane (x,y) to points in the log-polar plane ():
The mapping is described by:
=log x2+y2
θ=atan y
x
⎛
⎝
⎜⎞
⎠
⎟
Write a program to map an input image to the log-polar space. For visualization,
should be a discrete variable. You can achieve this by equating =radius and
ignoring the log operation. sampling should be a free parameter. Test your
code with =64. This should result in a polar image of size 128x64 for an input
image of size 256x256.
2. In recent years, there has been research that supports the hypothesis that there is
further magnification of the foveal region from retina to cortex. Several
researches have measured the cortical magnification factor as a function of retinal
eccentricity. One such measurement is the complex map, C = log(Z + a), that
