Shape discrimination for rectangles defined by disparity alone, by disparity plus luminance and by disparity plus motion

Abstract

We measured the just-noticeable difference in aspect ratio a/b for dotted rectangles defined entirely by disparity (DD rectangles), dotted rectangles defined by both disparity and luminance contrast (DD + LD rectangles) and rectangles defined by both disparity and relative motion (DD + MD rectangles) over a wide range of uncrossed (0–126 min arc) and crossed (0–126 nun arc) disparities. The rectangle's height and width were, respectively, a and b. Vergence was monitored by nonious lines, fusion was monitored by a fusion line, and subjects were instructed to look at the rectangle. We conclude that for DD rectangles, aspect ratio discrimination for crossed and uncrossed disparities cannot be compared accurately unless (a) ocular vergence is monitored, (b) a wide range of crossed and uncrossed disparities are investigated and (c) trials are repeated until threshold has stabilized for the entire range of both crossed and uncrossed disparities. Intersubject variations in fixation disparity is the reason for (a). The reason for (b) is that the effect of disparity on aspect ratio discrimination threshold is different for crossed and uncrossed disparities. The reason for (c) is that, for some subjects, the lowest discrimination threshold continues to fall with practice for uncrossed disparities beyond the point at which the lowest threshold has effectively stabilized for crossed disparities. We report that aspect ratio discrimination threshold for a DD rectangle first decreased and then levelled out as its disparity was progressively increased from zero, while the perceived depth of the rectangle increased smoothly and approximately linearly. We found that the lowest value of aspect ratio discrimination threshold was the same for both crossed and uncrossed disparities. This lowest value occurred at or just before the disparity at which fusion was lost for the dots surrounding the rectangle. The lowest value of discrimination threshold was lower for DD + LD and for DD + MD rectangles than for DD rectangles. The lowest value of discrimination threshold for DD rectangles was 4.0, 3.4, 7.4 and 3.1% for our four subjects. If we assume that a and b are encoded directly, then a 3.1% discrimination threshold implies that the precision of encoding a and b is better than 1 min arc—considerably better than the 9 min arc mean dot separation, and considerably better than the 3–5 c/deg estimate for cyclopean grating acuity.