Perceptual completion of occluded surfaces

PERCEPTUAL COMPLETION OF OCCLUDED SURFACES February 1994 LANCE R. WILLIAMS B.S., Pennsylvania State University M.S., University of Massachusetts Amherst Ph.D., University of Massachusetts Amherst Directed by: Professor Allen R. Hanson Researchers in computer vision have primarily studied the problem of visual reconstruction of environmental structure that is plainly visible. In this thesis, 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. Because multiple anterior surface neighborhoods project onto a single image neighborhood wherever surfaces overlap, surface neighborhoods and image neighborhoods are not guaranteed to be in one-to-one correspondence, as conventional \shape-from" methods assume. The result is that the topology of threedimensional scene structure can no longer be taken for granted, but must be inferred from evidence provided by image contours. Where boundaries are not occluded and where surface re ectance is distinct from that of the background, boundaries will be marked by image contours. However, where boundaries are occluded, or where surface re ectance matches background reectance, 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 called the gural completion problem. vi In this thesis, we show that the boundaries of the anterior surfaces can be represented in viewer-centered coordinates as a labeled knot diagram. The interior neighborhoods of the anterior surfaces are explicitly represented by a combinatorial model called a paneling, which is produced from a labeled knot diagram by means of a straightforward construction. Conventional \shape-from" methods formulated as variational problems and de ned over image neighborhoods can be applied to the neighborhoods of the paneling equally well. The labeling scheme and paneling construction provide a solid theoretical foundation for a working experimental system which computes surface representations from illusory contour displays, including well known gures from the visual psychology literature. The experimental system employs a two stage process of completion hypothesis and combinatorial optimization. The labeling scheme is enforced by a system of integer linear inequalities so that the nal organization is the optimal feasible solution of an integer linear program. vii TABLE OF CONTENTS Page ACKNOWLEDGMENTS : : : : : : : : : : : : : : : : : : : : : : : : : : : : : iv ABSTRACT : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : vi LIST OF TABLES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : x LIST OF FIGURES : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : xi CHAPTER