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, and neurophysiological perspective. We argue that the classical modeling in terms of linear spatial filters is equivalent to the assumption of a Cartesian organization of the feature space of early vision. We 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 representation can be obtained by a nonlinear encoding that yields a feature space with polar organization. This prediction of the information-theoretical approach regarding the organization of the feature space of early vision is confirmed by our psychophysical measurements of basic discrimination capabilities 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 similarities between the polar representation in visual cortex and basic image-coding strategies pursued in shape-gain vector quantization schemes.