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Hierarchical Framework for Shape Correspondence

Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 245-261页

作者： Dan Raviv Anastasia Dubrovina Ron Kimmel Technion Israel Institute of TechnologyTechnion CityHaifa 32000Israel

Detecting similarity between non-rigid shapes is one of the fundamental problems in computer *** order to measure the similarity the shapes must first be *** opposite to rigid alignment that can be parameterized using a small number of unknowns representing rotations,reflections and translations,non-rigid alignment is not easily *** of the methods addressing this problem boil down to a minimization of a certain distortion *** complexity of a matching process is exponential by nature,but it can be heuristically reduced to a quadratic or even linear for shapes which are smooth *** we model the shapes using both local and global structures,employ these to construct a quadratic dissimilarity measure,and provide a hierarchical framework for minimizing it to obtain sparse set of corresponding *** correspondences may serve as an initialization for dense linear correspondence search.

关键词： Shape correspondence Laplace-Beltrami diffusion geometry local signatures

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Partial Shape Matching Without Point-Wise Correspondence

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Numerical Mathematics(Theory,Methods and Applications) 2013年第1期6卷 223-244页

作者： Jonathan Pokrass Alexander M.Bronstein Michael M.Bronstein School of Electrical Engineering Tel Aviv UniversityIsrael Institute of Computational Science Faculty of InformaticsUniversitàdella Svizzera Italiana(USI)LuganoSwitzerland

Partial similarity of shapes is a challenging problem arising in many important applications in computer vision,shape analysis,and graphics,*** one has to deal with partial information and acquisition *** problem is especially hard when the underlying shapes are non-rigid and are given up to a *** matching is usually approached by computing local descriptors on a pair of shapes and then establishing a point-wise non-bijective correspondence between the two,taking into account possibly different *** this paper,we introduce an alternative correspondence-less approach to matching fragments to an entire shape undergoing a non-rigid *** use region-wise local descriptors and optimize over the integration domains on which the integral descriptors of the two parts *** problem is regularized using the Mumford-Shah *** show an efficient discretization based on the Ambrosio-Tortorelli approximation generalized to triangular point clouds and meshes,and present experiments demonstrating the success of the proposed method.

关键词： Deformable shapes partial matching partial correspondence partial similarity diffusion geometry Laplace-Beltrami operator shape descriptors heat kernel signature Mumford-Shah regularization

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