The theory of the curvature-constraint line for amodal completion.

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.