Spatial visual channels in the Fourier plane.

Properties of human spatial visual channels were studied in two-dimensional form by a signal detection masking paradigm. Tuning surfaces of contrast threshold elevation induced by a sinusoidal mask were generated for four Subjects, interpolated from an 11 X 11 Cartesian grid over the Fourier plane, and numerically Fourier transformed in two dimensions to infer putative filter profiles in the 2D space domain. Among the main findings in the 2D frequency domain were: (1) Threshold elevation surfaces are highly polar nonseparable--they cannot be described as the product of a spatial frequency tuning curve times an orientation tuning curve. (2) Iso-half-amplitude contours of the spectral tuning surfaces have a length/width elongation ratio of about 2:1. (3) Necessarily, resolution for spatial frequency and for orientation are in fundamental competition with 2D spatial resolution. By calculating the occupied area of the inferred filters both in the 2D space domain and in the 2D frequency domain, it was estimated that these mechanisms approach within a factor of 2.5 of the theoretical limit of joint resolution in the two 2D domains that can be derived by 2D generalization of Gabor's famous Theory of Communication (1946). Other classes of 2D filters, such as an ideal 2D bandpass filter, have joint 2D entropies which are suboptimal by a factor of 13 or more. Subject to the inherent constraints on inference from these 2D masking experiments, the evidence suggests that 2D spatial frequency channels can be described as elongated 2D spatial wave-packets which crudely resemble optimal forms for joint information resolution in the 2D spatial and 2D frequency domains.