Increasing availability of large repositories of 3D models has triggered a lot of research interests in 3D shape analysis and creation. One of the most fundamental shape analysis problems is to understand the high-level structure of a shape. Recent works on this problem have applied a variety of data-driven approaches to learn structural invariants from shapes belonging to the same category. Such a co-analysis framework has been deployed in various relevant applications (e.g., segmentation, shape collection organization and exploration). Most of them work on homogeneousshape collections which share a lot of similarity in both geometry and structure. However, there are fewer works analysing heterogeneous shape collections which imply abundant information of structure and the functionality attached.In this dissertation, we introduce an unsupervised analysis of both homogeneous and heterogeneous shape collections, aiming at organizing shapes based on their similarity in structure. Wederive the idea of graph representation of shape structure from the state of the art and a novel graph editing distance based on structure matching cost is defined. For any arbitrary pair of shapes, we propose a searching scheme to find the best matching pair of graphs with the minimal cost in a proper level of structural contraction. The core problem is to cluster shapes based on the matchingcost, meanwhile, select a set of representative graphs per cluster to exhibit the structural invariants within each cluster and the relationships between clusters. We formulate this problem as a new version of multiple instance clustering where the clustering is coupled with the process of representative selection. We also demonstrate that this multiple instance learning scheme also can be applied to cluster other digital assets e.g., image, video and reveal key semantics in a unsupervised manner.
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Thesis advisor: Zhang, Hao
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