The atoms of vision: Cartesian or polar?

The inherent structure of the encoding in early stages-of the visual system is investigated from a combined information-theoretical, psychophysical, a nd neurophysiological perspective. We argue that the classical modeling in terms of Linear spatial filters is equivalent to the assumption of a Cartes ian organization of the feature space of early vision. Wt, show that such a linear Cartesian feature space would be suboptimal for the exploitation of the statistical redundancies of natural images since these have a radially separable probability-density function. Therefore. a more efficient repres entation can be obtained by a nonlinear encoding that yields a feature spac e with polar organization. This prediction of the information-theoretical a pproach regarding the organization of the feature space of early vision is confirmed by our psychophysical measurements of basic discrimination capabi lities for elementary Gabor patches, and the necessary nonlinear operations are shown to be closely-related to cortical gain control and to the phase invariance of complex cells. Finally, we point out some striking similariti es between the polar representation in visual cortex and basic image-coding strategies pursued in shape-gain vector quantization schemes. (C) 1999 Opt ical Society of America [S0740-3232(99)03507-3].