PERCEPTUAL COMPLETION OF OCCLUDED SURFACES

Researchers in computer vision have primarily studied the problem of v isual reconstruction of environmental structure that is plainly visibl e, In this paper, the conventional goals of visual reconstruction are generalized to include both visible and occluded forward facing surfac es, This larger fraction of the environment is termed the anterior sur faces, Because multiple anterior surface neighborhoods project onto a single image neighborhood wherever surfaces overlap, surface neighborh oods and image neighborhoods are not guaranteed to be in one-to-one co rrespondence, as conventional ''shape-from'' methods assume. The resul t is that the topology of three-dimensional scene structure can no lon ger be taken for granted, but must be inferred from evidence provided by image contours. In this paper, we show that the boundaries of the a nterior surfaces can be represented in viewer-centered coordinates as a labeled knot-diagram Where boundaries are not occluded and where sur face reflectance is distinct from that of the background, boundaries w ill be marked by image contours, However, where boundaries are occlude d, or where surface reflectance matches background reflectance, there will be no detectable luminance change in the image. Deducing the comp lete image trace of the boundaries of the anterior surfaces under thes e circumstances is called the figural completion problem. The second h alf of this paper describes a computational theory of figural completi on, In more concrete terms, the problem of computing a labeled knot-di agram representing an anterior scene from a set of contour fragments r epresenting image luminance boundaries is investigated. A working mode l is demonstrated on a variety of illusory contour displays. The exper imental system employs a two-stage process of completion hypothesis an d combinatorial optimization, The labeling scheme is enforced by a sys tem of integer linear inequalities so that the final organization is t he optimal feasible solution of an integer linear program. (C) 1996 Ac ademic Press, Inc.