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Fast Nonrigid 3D Retrieval Using Modal Space Transform
"... Nonrigid or deformable 3D objects are common in many application domains. Retrieval of such objects in large databases based on shape similarity is still a challenging problem. In this paper, we first analyze the advantages of functional operators, and further propose a framework to design novel sha ..."
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Nonrigid or deformable 3D objects are common in many application domains. Retrieval of such objects in large databases based on shape similarity is still a challenging problem. In this paper, we first analyze the advantages of functional operators, and further propose a framework to design novel shape signatures for encoding nonrigid object structures. Our approach constructs a contextaware integral kernel operator on a manifold, then applies modal analysis to map this operator into a lowfrequency functional representation, called fast functional transform, and finally computes its spectrum as the shape signature. Our method is fast, isometryinvariant, discriminative, and numerically stable with respect to multiple types of perturbations.
ON EUCLIDEAN DISTANCE MATRICES OF GRAPHS ∗
"... Abstract. In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. It is proven that distance matrices of paths and cycles are EDMs. The proofs are constructive and the generating points of studied EDMs are given in a closed form. A generalizatio ..."
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Abstract. In this paper, a relation between graph distance matrices and Euclidean distance matrices (EDM) is considered. It is proven that distance matrices of paths and cycles are EDMs. The proofs are constructive and the generating points of studied EDMs are given in a closed form. A generalization to weighted graphs (networks) is tackled.
ELA AN IMPROVED ESTIMATE FOR THE CONDITION NUMBER ANOMALY OF UNIVARIATE GAUSSIAN CORRELATION MATRICES
, 2015
"... An improved estimate for the condition number anomaly of univariate Gaussian correlation matrices ..."
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An improved estimate for the condition number anomaly of univariate Gaussian correlation matrices