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Amodal completion of partly occluded figures is analyzed as natural computation. Here amodal completion is shown to consist of four subproblems: representation, parsing, correspondence, and interpolation. Second, each problem is shown to be basically solvable on the basis of the generic-viewpoint assumption. It is also argued that the interpolation problem might be the key problem because of mutual interdependence among the subproblems. Third, a theory is described for the interpolation problem, in which the generic-viewpoint assumption and the curvature-consistency assumption are presumed. The generic-viewpoint assumption entails that the orientation and the curvature should not change at the point of occlusion. The curvature-consistency assumption entails that the hidden contour should have the minimum number of inflections to maintain continuity in orientation and curvature. The shape of the interpolated contour represented qualitatively in terms of the number of inflections can uniquely be determined when the location of the terminators and local orientation and curvature of the visible contours at the terminators are given. Fourth, it is shown in an instant psychophysics that the theory is highly consistent with human performance.

The effect of curvature on visual interpolation in partly occluded figures was examined. In experiments 1 and 2, the shape of a visually interpolated contour was measured by using a partially occluded triangle or a partially occluded circle as the target figure. The targets were cut off at both sides, with varying width from trial to trial. In experiment 1, the peak height, which was supposed to represent the shape of the interpolated contour, was measured for each target for each size of the visible part. A significant effect of curvature, as the difference in the peak height between the targets, was found when the width of the visible part was 10 to 20 min. The effect became stronger linearly with increasing length of the visible contour (the buildup effect). The effective curvature thus appeared to be measured along the visible contour in terms of the change of orientation. In experiment 2, the scale invariance of the buildup effect was examined with varying observation distance. It was found that the effect remained the same across scale if the effect was described in terms of visual angle of the visible arc, but not in terms of the proportion of the visible part to the whole figure. This suggests that the effect is derived from the visible contour, but not from the likelihood of the estimated shape of the partly occluded figure. It has been concluded that the curvature induces curved interpolation and that the curvature of the visible contour is measured along the contour as the change of orientation.

Binocular displacement of binocularly unpaired parts of the stimulus was examined by means of the Poggendorff figure. The Poggendorff figure can be used to investigate displacement since lateral displacement of the transversal may cause bias in judgments of its collinearity. In experiment 1, the transversal had a disparity, and thus binocularly unpaired parts, relative to the rectangle. The magnitude of the Poggendorff illusion should not have changed by addition of binocular disparity if displacement occurred. There was no or slight change when the transversal was seen behind the rectangle, but there was significant decrease when the transversal was seen in front of the rectangle, suggesting absence of displacement in this case. There were two possible explanations. One was that displacement depended on the positional relation between the unpaired stimuli and the binocularly presented rectangle, ie the occlusion constraint, which the case with the transversal in front did not satisfy. The alternative was that the decrease was due to the perceived front depth of the transversal, and not related to binocular displacement at all. In order to discriminate between these two possibilities, the transversal was reduced to only the unpaired parts, resulting in dichoptic stimulation in experiment 2. In this stimulus, the positional relation between the unpaired and the paired stimuli was the same as in the previous experiment, yet no front depth could be perceived. The results showed similar asymmetry as in experiment 1. Thus we conclude that binocular displacement depends on the positional relation between the unpaired and the paired stimuli, regardless of their perceived depth. This may imply that binocular displacement is not symmetric about the sign of disparity, hence that it is not just averaging but is a reconstruction of the spatial layout of objects in the outside world to keep the visual direction of the unsuppressed unpaired region veridical by using explicit cues to depth discontinuity.