On the disparity gradient limit for binocular fusion.

Abstract

Recently, Burt and Julesz (1980) have measured the limits of single versus double vision (diplopia) in binocular stereopsis. They found that the extent of the fusional limits is not fixed spatially and argued that a limit on the disparity gradient, rather than the absolute disparity magnitude usually associated with the notion of Panum' s fusional area, is the critical factor when two or more objects occur near each other in the (cyclopean) visual field. Their main result was that fusion was never observed when the disparity gradient (defined as the ratio of disparity difference and angular separation as shown in Figure 1) exceeded a critical value of approximately 1. They concluded that this invariant limit captures the role of object interaction in binocular fusion. Despite some criticism (Krol, 1982; Krol & van de Grind, 1980), the concept of limiting disparity gradient would seem to have a rather secure basis in a geometrical analysis of the binocular viewing situation (Kass, 1984; Terzopoulos, 1984) and is currently being used as a major theoretical construct in at least one computational approach to binocular stereomatching (Pollard, Mayhew, & Frisby, 1984). We have found, however, that fusion and single vision can be achieved in situations in which the disparity gradient exceeds, by a factor of 2 to 3, the critical value reported by Burt and Ju1esz(1980). As a demonstration, compare the displays in Figure 2. In general, our experiments revealed that when the context consisted of dots of the same contrast polarity, the limiting disparity gradient (0.96±0.2) was close to the previously reported values. When one of the interacting dots was larger than the other (by a factor of 2) the gradient was elevated to 1.4±0.23 (see also Braddick, 1979). When the interacting dots had opposite contrast polarity and one of the dots was larger than the other, the critical value increased to 2.1 ± 0.3; that is, the gradient below which single vision was experienced increased and larger disparity differences could be tolerated for a given object separation.i Rather than questioning the concept of limiting disparity gradient, our results may be suggesting that the notion of a purely geometrically defined gradient is not satisfactory. Object properties other than mutual separation seem to participate in the interaction context. Burt and