Perceptual completion of occluded surfaces

Researchers in computer vision have primarily studied the problem of visual reconstruction of environmental structure that is plainly visible. In this paper, the conventional goals of visual reconstruction are generalized to include both visible and occluded forward facing surfaces. This larger fraction of the environment is termed the anterior surfaces. In this paper, we show that the boundaries of the anterior surfaces can be represented in viewer-centered coordinates as a labeled knot diagram. Where boundaries are not occluded and where surface reflectance is distinct from that of the background, boundaries will be marked by image contours. However, where boundaries are occluded, or where surface reflectance matches background reflectance, there will be no detectable luminance change in the image. Deducing the complete image trace of the boundaries of the anterior surfaces under these circumstances is termed the figural completion problem. The second half of this paper describes a computational theory of figural completion. A working model is demonstrated on a variety of illusory contour displays. The experimental system employs a two stage process of completion hypothesis and combinatorial optimization. The labeling scheme is enforced by integer linear inequalities so that the optimal feasible solution of an integer linear program defines a typologically valid surface organization