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        Intrinsic mesh matching for near-isometric deformations using double-order affinities

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        Publication date
        2015
        Author
        Koutsoumpas, I.
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        Summary
        Shape matching is among the most basic research fields in digital geometry processing, with applications ranging from industrial design to three-dimensional medical image analysis. Our focus is restricted to triangle meshes undergoing deformations that can be described by intrinsic isometries, that is, near-isometric changes. In this thesis, we propose a shape matching algorithm comprised by a feature detection and feature matching phase. Specifically, a shape descriptor is introduced, called the vicinity area descriptor, based on the surface area around each vertex bounded by an isoring for a given geodesic radius. We improve the distinctiveness of the local signature by extending it from a scalar to a vector descriptor referring to arbitrary number of areas defined by inner isorings. The most descriptive points are then extracted using non-maximum suppression. By also considering the preservation of geodesic distances among the corresponding pairs of features, we compute a double-order affinity matrix. This combinatorial affinity matrix encodes the pointwise and pairwise relations of features regarding the two meshes. This matrix is then fed to the spectral matching algorithm, a graph matching method, in order to establish correspondences between the two surfaces. Experiments include benchmarks under various conditions regarding internal variables and state-of-the-art methods comparisons. It is showed that the proposed framework is robust over near-isometric deformations and keeps well against modern algorithms.
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        https://studenttheses.uu.nl/handle/20.500.12932/19661
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