Design considerations for a space-variant visual sensor with complex-logarithmic geometry

A space-variant sensor design based on the conformal mapping of the half disk, w=log (z+a), with real a >0, which characterizes the anatomical structure of the primate and human visual systems is discussed. There are three relevant parameters: the circumferential index κ which is defined as the number of pixels around the periphery of the sensor, the visual field radius R (of the half-disk to be mapped), and the map parameter a, which displaces the logarithm´s singularity at the origin out of the domain of the mapping. It is shown that the log sensor requires O (κ²log (R/a)) pixels. An analysis is presented which makes it possible to compare directly the space complexity of different sensor designs in the complex logarithmic family. In particular, rough estimates can be obtained of the parameters necessary to duplicate the field width/resolution performance of the human visual system