Spatial integration of compound gratings with various numbers of orientation components

The human foveal visual system in a detection task was recently modeled as a simple image processor comprising low-pass filtering due to the optical modulation transfer function of the eye, high-pass filtering (lateral inhibition) due to the neural modulation transfer function of visual pathways, addition of internal neural noise, and detection by a local matched filter, the efficiency of which decreases with increasing grating area. The applicability of this model was now tested by studying spatial integration for sums of various numbers of cosine gratings with different orientations.

Binocular root-mean-square contrast sensitivity was measured as a function of area for sums of cosine gratings (n = 1 to 16) with the same contrast, phase, and spatial frequency but with an orientation difference of 180/n between the components.

In agreement with the model, contrast sensitivity increased in proportion to the square root of grating area at small areas. When grating area exceeded its critical value, the increase saturated, and contrast sensitivity then became independent of area. The critical area and maximum contrast sensitivity of spatial integration first decreased with an increasing number of components, reaching minima at n = 5 to 6, but increased thereafter. A plausible explanation for the variation of critical area and maximum sensitivity could be the variation of the amount of contour and detail per unit area in the sums of cosine gratings. Critical area divided by maximum sensitivity squared refers to the contrast energy threshold at small grating areas. It was independent of the number of components but, because of lateral inhibition, decreased in inverse proportion to spatial frequency squared. Contrast energy threshold as a function of normalized grating area (grating area divided by critical area) also was independent of the number of components and decreased in inverse proportion to spatial frequency squared.

Within the framework of the local matched filter model, the dependency of contrast sensitivity on the grating area and number of orientation components resulted from the decrease in the efficiency of contrast energy collection, which was probably due to the increasing amount of contour and detail in the stimulus to be detected.