From filters to features: location, orientation, contrast and blur

Consider three main ideas about spatial filtering and feature coding in human spatial vision. (1) Computational theory: the representation of local luminance features--bars and edges--is a crucial step in human vision, forming the basis for many decisions in pattern discrimination. (2) Algorithm: features may be located and characterized in terms of polarity, blur and contrast by comparison of 1st, 2nd and 3rd spatial derivatives taken at a common point. Edges in compound (f + 3f) gratings are seen at or close to peaks of gradient magnitude. More tentatively, bars may be located at peaks of the 2nd derivative or at peaks in the Hilbert transform of the 1st derivative. Peaks of contrast energy do not predict all the features seen. An algorithm for recovering the blur of edges is derived as the square-root of the ratio of 1st to 3rd derivatives at the edge location. This successfully predicts blur matching between Gaussian edges and a variety of other test waveforms, including sine waves. Blur matching is (nearly) contrast invariant, as predicted by this ratio rule. (3) IMPLEMENTATION: experiments on the perception and discrimination of plaids imply that the outputs of tuned filters are combined before feature coding. The adaptive, weighted summation of bandpass filters may serve to synthesize the derivative operators while facilitating the segmentation of overlapping features and preventing the representation from being swamped by noise.