In this thesis, we address the challenge of computing correspondences between dissimilar shapes. This implies that, although the shapes represent the same class of object, there can be major differences in the geometry, topology, and part composition of the shapes as a whole. Additionally, the dissimilarity can also appear in the form of a shape that possesses additional parts that are not present in the other shapes. We propose three approaches for handling such shape dissimilarity. The first two approaches incorporate additional knowledge that goes beyond a direct geometric comparison of the shapes. In the first approach, of a supervised nature, the knowledge is provided by the user as a training set of manually segmented and labeled shapes. The training set is used in conjunction with shape descriptors to learn classifiers that distinguish different semantic classes of parts. The second approach, which is unsupervised, derives the knowledge automatically from a set of shapes. If all the shapes in the set roughly possess the same semantic part composition, we can derive their common structure by analyzing the shapes simultaneously, rather than individually. This is achieved by clustering shape segments in a descriptor space with a spectral method, which makes use of third-party connections between shape parts. We show that these approaches allow us to compute correspondences for shapes that differ significantly in their geometry and topology, such as man-made shapes. In the third approach, we compute partial correspondences between shapes that have additional parts in relation to each other. To address this challenge, we propose a new type of shape descriptor, called the bilateral map, whose region of interest is defined by two points. The region of interest adapts to the context of the two points and facilitates the selection of the scale and shape of this region, making this descriptor more effective for partial matching. We demonstrate the advantages of the bilateral map for computing partial and full correspondences between pairs of shapes.
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Thesis advisor: Zhang, Hao
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