Scale-space representation of 3D models and topological matching

Abstract

Reeb graphs have been shown to be effective for topology matching of 3D objects. Their effectiveness breaks down, however, when the individual models become very geometrically and topologically detailed - as is the case for complex machined parts. The result is that Reeb graph techniques, as developed for matching general shape and computer graphics models, produce poor results when directly applied to create engineering databases. This paper presents a framework for shape matching through scale-space decomposition of 3D models. The algorithm is based on recent developments in efficient hierarchical decomposition of metric data 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.