Shape similarity and clustering for engineering design repositories

Shape-based similarity and matching of 3D models has been an area of active research in the past decade in disciplines such as computer vision, computer graphics, mechanical engineering, molecular biology, and chemistry. Advances in robust algorithms for geometry-based representations and shape matching algorithms have enabled comparison of objects on both global shape as well as local shape. While past research has focused on developing meaningful shape representations, there is limited literature on benchmarking various shape representations, and developing automatic indexing and clustering techniques, especially for the mechanical engineering domain. Indexing techniques such as multi-dimensional R-trees have been used for indexing 3D models [1], however they are not readily applicable to more recently developed shape representations such as skeletal graphs and other view-based representations, including Light Field Descriptors (LFD) [2], and Multiple Levels of Detail (MLD) representations [3] which showed superior retrieval performance compared to several other methods. These shape representations are embedded in arbitrary metric spaces, rather than in feature space, thereby rendering traditional indexing and clustering algorithms unsuitable in this context. In this thesis we have proposed using a multidimensional scaling strategy to convert the data from arbitrary metric spaces to lower dimensional feature spaces which can be easily handled by existing indexing and clustering techniques. We have evaluated several different shape descriptors with respect to shape retrieval and automatic clustering. Evaluations were performed on two different benchmark datasets - an Engineering Shape Benchmark (ESB) and the Princeton Shape Benchmark (PSB). Additionally, we evaluated the retrieval performance of these representations on two smaller datasets from the National Design Repository. Results from both these experiments suggest that the new view-based shape representations can be used for clustering and indexing large databases. A clustering effectiveness study was also performed to compare the effectiveness of various shape descriptors on the ESB