Detection of grating patterns containing two spatial frequencies: a comparison of single-channel and multiple-channels models.

A NEURAL network in which there is excitatory and inhibitory interaction among neighboring units has been proposed as a model of human pattern vision and used, with some success, to explain such phenomena as the appearance of Mach bands and contrast sensitivity with periodic patterns (B&&Y, 1960 and RATLWF, 1965, for example). The network’s response is a two-dimensional transformation of the stimulus luminance pattern and is assumed to correspond to the perceived appearance of the pattern. A model of this kind implies that pattern vision is a function of a single neural network, and hence a single transfomation of the stimulus pattern. For this reason we will call it a single-chunnel model. A single-channel model of some kind underlies all attempts to characterize spatial interactions in human vision by a single modulation transfer function, or equivalently, a single spread function. Recently CAMPBELL and ROBSON (1968) have suggested a multiple-channels model of pattern vision. This model assumes that many channels simultaneously process the stimulus and that each channel is selectively sensitive to a different narrow range of spatial frequencies. Very roughly, being sensitive to a narrow range of spatial frequencies means responding best to a particular size of element in the pattern; a more precise definition of spatial frequency is given below. The study reported here compares the predictions of singleand multiple-channels models to results from a psychophysical pattern-detection experiment. The patterns were gratings in.which the luminance along any vertical line is constant and the luminance in the horizontal direction varies according to some periodic function. Figure 1 shows two examples of such gratings, along with the functions relating luminance to horizontal distance in each of the two gratings. In the left example, the function is a sinusoid added to a constant luminance (the mean luminance). In the right example, the function is the sum of two sinusoids added to a constant luminance. For gratings such as these, spatial frequency is easily defined: the spatial frequencies contained in a pattern are the frequencies (cycles/ unit distance) of the sinusoids that compose the function relating luminance to horizontal distance. Thus, in the left pattern of Figure 1, there is one spatial frequency. In the right pattern of Fig. 1, there are two spatial frequencies whose ratio is 3: 1. (The choice of this ratio of frequencies will be discussed later.) The amount of a component sinusoid at a particular frequency will be expressed by its contrast, where contrast is defined as one half