Coordinate descent optimization for one-to-one correspondence and supervised classification of 3D shapes

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Recent developments in shape analysis and retrieval play an important role in a wide variety of applications that potentially require matching of objects with different geometries. In shape classification, there is no natural way to represent an object but the similarity measure, distance between representations or descriptors, depends heavily on the strategy of computing optimal correspondences. In this paper we introduce a new numerical method for registering surfaces. Thus, finding an optimal one-to-one correspondence between their shapes. Unfortunately, solving this type of optimization problem is generally hard because the solutions space is nonlinear with no natural manifold structure on it. To overcome such limitations we make use of recent methods to represent objects then we find optimal correspondences using a discretized approximation of the search space. The proposed method has the advantage of extending the Riemannian analysis of 3D curves in a natural way for surfaces. We demonstrate the proposed algorithms using different public datasets for 2D and 3D objects matching and classification. <\p>