Numerical Geometry of Non-Rigid Shapes

Bronstein, Alexander M.; Bronstein, Michael M.; Kimmel, Ron

doi:10.1007/978-0-387-73301-2

Cited by 457 publications

(441 citation statements)

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“…Shapes from the TOSCA [31] and Princeton [32] datasets were used in our experiments. Textured shapes acquired with a multicamera system were taken from the INRIA Grenoble dataset [8].…”

Section: Resultsmentioning

confidence: 99%

Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching

Wang

Bronstein

et al. 2012

Lecture Notes in Computer Science

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Abstract. Similarity and correspondence are two fundamental archetype problems in shape analysis, encountered in numerous application in computer vision and pattern recognition. Many methods for shape similarity and correspondence boil down to the minimum-distortion correspondence problem, in which two shapes are endowed with certain structure, and one attempts to find the matching with smallest structure distortion between them. Defining structures invariant to some class of shape transformations results in an invariant minimum-distortion correspondence or similarity. In this paper, we model shapes using local and global structures, formulate the invariant correspondence problem as binary graph labeling, and show how different choice of structure results in invariance under various classes of deformations.

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“…Shapes from the TOSCA [31] and Princeton [32] datasets were used in our experiments. Textured shapes acquired with a multicamera system were taken from the INRIA Grenoble dataset [8].…”

Section: Resultsmentioning

confidence: 99%

Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching

Wang

Bronstein

et al. 2012

Lecture Notes in Computer Science

Self Cite

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“…The database is divided into 12 classes, each containing 19 elements obtained as follows: A null model taken from the Non Rigid World Benchmark [3] is considered together with six non-rigid transformations applied to it at three different strength levels. An example of the transformations and their strength levels is given in Table 1.…”

Section: Resultsmentioning

confidence: 99%

Multi-scale Approximation of the Matching Distance for Shape Retrieval

Cerri

Fabio

Medri

2012

Computational Topology in Image Context

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Abstract. This paper deals with the concepts of persistence diagrams and matching distance. They are two of the main ingredients of Topological Persistence, which has proven to be a promising framework for shape comparison. Persistence diagrams are descriptors providing a signature of the shapes under study, while the matching distance is a metric to compare them. One drawback in the application of these tools is the computational costs for the evaluation of the matching distance. The aim of the present paper is to introduce a new framework for the approximation of the matching distance, which does not affect the reliability of the entire approach in comparing shapes, and extremely reduces computational costs. This is shown through experiments on 3D-models.

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“…In this section we investigate the practical benefits of adopting the proposed operator in two problems commonly arising in shape analysis, namely stable region detection and matching of deformable shapes, using the datasets [5,4].…”

Section: Methodsmentioning

confidence: 99%

Anisotropic Laplace-Beltrami Operators for Shape Analysis

Andreux

Rodolà

Aubry

et al. 2015

Computer Vision - ECCV 2014 Workshops

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Abstract. This paper introduces an anisotropic Laplace-Beltrami operator for shape analysis. While keeping useful properties of the standard Laplace-Beltrami operator, it introduces variability in the directions of principal curvature, giving rise to a more intuitive and semantically meaningful diffusion process. Although the benefits of anisotropic diffusion have already been noted in the area of mesh processing (e.g. surface regularization), focusing on the Laplacian itself, rather than on the diffusion process it induces, opens the possibility to effectively replace the omnipresent Laplace-Beltrami operator in many shape analysis methods. After providing a mathematical formulation and analysis of this new operator, we derive a practical implementation on discrete meshes. Further, we demonstrate the effectiveness of our new operator when employed in conjunction with different methods for shape segmentation and matching.

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Numerical Geometry of Non-Rigid Shapes

Cited by 457 publications

References 0 publications

Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching

Discrete Minimum Distortion Correspondence Problems for Non-rigid Shape Matching

Multi-scale Approximation of the Matching Distance for Shape Retrieval

Anisotropic Laplace-Beltrami Operators for Shape Analysis

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