A statistical approach to hierarchical shape indexing

This paper describes the first stages of work aimed at developing a hierarchical framework for shape indexing in line images. The envisaged hierarchy is two-level. At the top-level of representation we construct a histogram of pairwise geometric attributes for line-structures extracted from the image. The lower level of the hierarchy is a constrained Delaunay graph which conveys detailed relational information concerning the arrangement of line structures. Our indexing scheme first compares the coarse-level representation provided by the geometric histogram. Rather than adopting the conventional least-squares comparison employed by M.J. Swain and D.H. Ballard (1990) or C. Dorai and A.K. Jain (1995), we use the methodology of statistical pattern recognition to compute a probabilistic distance measure between model and data histograms. With this evidential index to hand the second stage of indexing restricts its attention to the detailed graph search for images which return a high confidence of histogram match.