Gromov‐Hausdorff Stable Signatures for Shapes using Persistence

Chazal, Frédéric; Cohen-Steiner, David; Guibas, Leonidas J.; Mémoli, Facundo; Oudot, Steve

doi:10.1111/j.1467-8659.2009.01516.x

Cited by 203 publications

(197 citation statements)

References 35 publications

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“…Diffusion geometry approaches has been applied to shape matching problems based on the Laplace-Beltrami operator for establishing correspondences between shapes [55], [56]. The Gromov-Hausdorff distance has been used as a similar measure between shapes represented by point clouds [57].…”

Section: Introductionmentioning

confidence: 99%

Shape Matching Using Multiscale Integral Invariants

Hong

Soatto

2015

IEEE Trans. Pattern Anal. Mach. Intell.

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Abstract-We present a shape descriptor based on integral kernels. Shape is represented in an implicit form and it is characterized by a series of isotropic kernels that provide desirable invariance properties. The shape features are characterized at multiple scales which form a signature that is a compact description of shape over a range of scales. The shape signature is designed to be invariant with respect to group transformations which include translation, rotation, scaling, and reflection. In addition, the integral kernels that characterize local shape geometry enable the shape signature to be robust with respect to undesirable perturbations while retaining discriminative power. Use of our shape signature is demonstrated for shape matching based on a number of synthetic and real examples.

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Section: Introductionmentioning

confidence: 99%

Shape Matching Using Multiscale Integral Invariants

Hong

Soatto

2015

IEEE Trans. Pattern Anal. Mach. Intell.

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“…In general, such measures are reckoned to be beneficial for the organization of the huge collections of digital models produced nowadays through massive data acquisitions and shape modeling. In recent years, the development and study of topology-invariant metrics with stability properties has widely increased, as the numerous studies on similarity of non-rigid shapes testify (cf., e.g., [2,6]). …”

Section: Introductionmentioning

confidence: 99%

The natural pseudo-distance as a quotient pseudo-metric, and applications

Cagliari¹,

Fabio²,

Landi³

2013

Forum Mathematicum

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Abstract. The natural pseudo-distance is a similarity measure conceived for the purpose of comparing shapes. In this paper we revisit this pseudo-distance from the point of view of quotients. In particular, we show that the natural pseudo-distance coincides with the quotient pseudo-metric on the space of continuous functions on a compact manifold, endowed with the uniform convergence metric, modulo self-homeomorphisms of the manifold. As applications of this result, the natural pseudo-distance is shown to be actually a metric on a number of function subspaces such as the space of topological embeddings, of isometries, and of simple Morse functions on surfaces.

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“…Such an approach has been successfully used in a number of concrete problems concerning shape comparison and retrieval [4,5,8]. However, defining a (dis)similarity metric in the case of large databases can lead to considerable computational costs.…”

Section: Introductionmentioning

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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Gromov‐Hausdorff Stable Signatures for Shapes using Persistence

Cited by 203 publications

References 35 publications

Shape Matching Using Multiscale Integral Invariants

Shape Matching Using Multiscale Integral Invariants

The natural pseudo-distance as a quotient pseudo-metric, and applications

Multi-scale Approximation of the Matching Distance for Shape Retrieval

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