Transformation Invariant Shape Similarity Comparison of Solid Models

This paper presents two complementary approaches to comparing the shape and topology of solid models. First, we develop a mapping of solid models toModel SignatureGraphs (MSGs)— labeled, undirected graphs that abstract the boundary representation of the model and capture relevant shape and engineering attributes. Model Signature Graphs are then used to de ne metric spaces over arbitrary sets of solid models. This paper introduces two such metric spaces: rst, a mapping of MSGs to a high-dimension vector space where euclidean distance measures are applied; second, a distance computation performed between graph spectra constructed fromMSGs using spectral graph theoretic techniques. In practice, exact computation of the edit distance between model signature graphs is believed to be an NP-hard problem. We show that properties of the design signature graph's spectra, derived from the eigenvalues of its adjacency matrix, can be used as a ef cient and tractable approximation of the edit distance. Lastly, we provide empirical results using real test data from the National Design Repository (http://www.designrepository.org) to validate our approach. We argue comparisons among solid models in these metric space are immune to problems caused by inexactness and ambiguity arising from basic modeling transformations (scale, translation, rotation, sheer, etc.). It is our belief that this work contributes to a growing body of techniques for comparing models and indexing CAD media types in database systems.