Six formal properties of two-dimensional anisotropie visual filters: Structural principles and frequency/orientation selectivity

Abstract

Six formal properties of anisotropic linear two-dimensional filters are noted which are relevant for modeling the mechanisms of spatial visual information extraction. These properties concern the relationship between the organizational principle of a two-dimensional anisotropic spatial filter or neural receptive field (such as elongation, or concatenation of subunits, or differential operators mediated by lateral inhibition in neural laminae) and the resulting general consequences for spatial frequency and orientation selectivity. These properties are demonstrated without assuming particular two-dimensional filter functional forms; rather, they are shown as general principles associated with certain broad categories of two-dimensional filters. Such an analysis enhance theoretical understanding of the two-dimensional receptive field organization of neurons in the visual cortex and permits the rejection of some candidate organizational principles on two-dimensional spectral grounds.