Reciprocal interactions between occlusion and motion computations

Abstract

The "aperture problem" refers to the inherent ambiguity of the motion generated by an untextured contour moving within an aperture. The limited spatial extent of the receptive fields of neurons in cortical areas like V1 and MT render them susceptible to this problem. Most psychophysical experiments have probed how the visual system overcomes the aperture problem by presenting moving contours behind one or more simulated apertures. The assumption has been that the computational ambiguities that arise in resolving these displays are equivalent to the computational problems created by receptive fields that sample a small region of visual space. Evidence is presented here that challenges this view. We demonstrate that a fundamental computational difference in the interpretation of contour terminators arises in these two variants of the aperture problem. When the aperture is a receptive field, and a moving contour extends beyond its boundaries, the contour "terminators" delimit the boundaries of the receptive field, not the ends of the contour. In contrast, when a moving contour is viewed through a simulated aperture, the contour terminators are generated by the occluding edges of the aperture. In a series of experiments, we show that reciprocal interactions arise between computations of occlusion and those of motion direction and integration. Our results demonstrate that the visual system solves the aperture problem by decomposing moving contours into moving segments, and unpaired terminators that arise from the accretion and deletion of contours behind occluding edges, generating both coherent motion and illusory occluding surfaces.

Figure 1

A schematic of two aperture problems and the computations that they entail. (a) The ambiguity in motion speed and direction generated when an untextured contour is either sampled by a receptive field smaller than the contour’s length or when a contour moves behind an aperture in the environment. Two discrete time frames are presented (t₁ and t₂), which may be regarded as either the temporal sampling limit of the visual system or a limit on the presentation rate of the display device (e.g., a computer monitor). (b) The unique computational problem that arises when a contour moves behind an occluding surface in the environment. Three possible interpretations of motion direction are shown (arrows and solid black contour segments). Note that regions of the contour will either be accreted (dashed segments) or deleted (dotted segments) in all possible directions of motion and therefore will not have corresponding elements in the two views. (Also see † footnote)

Figure 2

A schematic of the motion displays used in experiment 1. (a) Three frames of the motion sequence used in the experiment. As the lines and dots translated to the right, the length of the lines increased, and the small dots on the lines translated to the right in phase with the lines. This display appeared as two lines that grew in length while they translated (depicted schematically in d). (b) Same as a, except that small squares were placed in the surround and translated in the opposite direction of the lines. This display generated vivid illusory contours, and the lines appeared to be progressively uncovered behind an occluding surface (depicted schematically in e). (c) If the lines did not change in length during their translation, no illusory contours were observed. (f) Mean ratings of 10 observers of the strength of apparent occlusion generated by the displays depicted in a–c (where more vivid occlusion is represented as larger ratings).

Figure 3

(a) The setup used to generate the sequence shown in b. The diamond oscillated horizontally behind occluders that had the same gray level as the background. There is no physical significance to the depth differences among the occluders, diamond, and background shown in this figure. They are indicative only of the relative depth ordering used to generate the sequences. The displays subtended 7° of visual angle at a viewing distance of 80 cm. The diamond’s speed of oscillation was 0.7°/s. (c) The setup used to generate the sequence shown in d. The four point features attached to the moving diamond serve to disambiguate its motion. (e) The percept with sequence b—four lines oscillating vertically. No occluding contours are perceived. (f) The percept with sequence d. The four lines are seen as being part of a partially occluded diamond translating horizontally; strong subjective contours are reported at the indicated locations. As shown in the enlarged Inset, the illusory contours coincide with the discontinuities in the horizontal motion field. The reported contours were not precisely vertical but were slightly curved, possibly due to a bias toward orthogonality to the inducing contour. (g) A summary of the results obtained with the two sequences.

Figure 4

(a) The same sequence as the one shown in Fig. 3b, except the occluders are explicitly defined by contrast differences. (b) A sequence with subjectively defined occluders. (c) The dominant percept with sequences a and b: a partially obscured diamond translating horizontally behind three opaque strips. (d) A comparison of the results obtained with the sequence shown in Fig. 3b and sequences a and b shown here. The explicit indication of occluding surfaces (contrast defined or subjective) strongly biased the percept from being one of motion in the vertical direction to one of coherent horizontal motion. Both the contrast and subjectively defined occluders generated a much stronger bias for perceiving coherent horizontal motion when compared with the display that contained only the moving contour segments (pairwise t test, P < 0.001).