Scale-Space Representation and Classification of 3D Models

Abstract

This paper presents a framework for shape matching and classification through scale-space decomposition of 3D models. The algorithm is based on recent developments in efficient hierarchical decomposition of a point distribution in metric space (p,d) using its spectral properties. Through spectral decomposition, we reduce the problem of matching to that of computing a mapping and distance measure between vertex-labeled rooted trees. We use a dynamic programming scheme to compute distances between trees corresponding to solid models. Empirical evaluation of the algorithm on an extensive set of 3D matching trials demonstrates both robustness and efficiency of the overall approach. Lastly, a technique for comparing shape matchers and classifiers is introduced and the scale-space method is compared with six other known shape matching algorithms.