The wave kernel signature: A quantum mechanical approach to shape analysis

Aubry, Mathieu; Schlickewei, Ulrich; Cremers, Daniel

doi:10.1109/iccvw.2011.6130444

Cited by 611 publications

(573 citation statements)

References 24 publications

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“…As observed in Section 2.2, the proposed anisotropic Laplacian is not an isometry invariant; hence, its direct application in the computation of intrinsic descriptors [1,13] may not lead to an increase of performance in typical non-rigid matching scenarios.…”

Section: Shape Matchingmentioning

confidence: 99%

“…Computing the LB operator directly on meshes with approaches such as [18,15,20], numerous works exploit the information contained in its eigen-decomposition to build a new representation of a shape, either by explicit formulas [23,24,1] or by learning [13,22]. Based on these descriptors, several methods have been developed for segmentation purposes, for instance [14,21].…”

Section: Related Workmentioning

confidence: 99%

“…Since the theoretical guarantees of this signature come from the operator itself and its eigen-decomposition, subsequent studies have tried to use the same analytical objects to model different physical phenomena. These include the definition of new signatures such as the Wave Kernel Signature (WKS) [1], learning combinations of LB eigenfunctions to deal with more general classes of deformations [13], or directly employing the eigen-functions themselves for segmentation tasks [21]. However, all these works rely on the notion of an isotropic LB operator.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Shape Matchingmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Anisotropic Laplace-Beltrami Operators for Shape Analysis

Andreux

Rodolà

Aubry

et al. 2015

Computer Vision - ECCV 2014 Workshops

Self Cite

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“…1, middle), there remain only a finite, and often manageable, number of discrete ( , r)-symmetries. To extract these we use the fact that point-wise ( , r)-symmetries arise from an -approximate isometric mapping (correspondence) between two regions U and f (U), as defined in (2). Isometric mappings have a low number of degrees of freedom, which has been recently used to develop a direct region growing method for partial isometric correspondence [6].…”

Section: Overviewmentioning

confidence: 99%

“…Furthermore, we prune the remaining point pairs and directions using an isometry-invariant shape descriptor. We choose the state of the art Wave Kernel Signature (WKS) [2] as descriptor, and disregard point pairs whose WKS do not agree up to a threshold τ . Computing the WKS globally over the entire surface is not consistent with our partial symmetry model.…”

Section: Discrete R-symmetries By Isometric Region Growingmentioning

confidence: 99%

Characterization of Partial Intrinsic Symmetries

Shehu

Brunton

Wuhrer

et al. 2015

Computer Vision - ECCV 2014 Workshops

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Abstract. We present a mathematical framework and algorithm for characterizing and extracting partial intrinsic symmetries of surfaces, which is a fundamental building block for many modern geometry processing algorithms. Our goal is to compute all "significant" symmetry information of the shape, which we define as r-symmetries, i.e., we report all isometric self-maps within subsets of the shape that contain at least an intrinsic circle or radius r. By specifying r, the user has direct control over the scale at which symmetry should be detected. Unlike previous techniques, we do not rely on feature points, voting or probabilistic schemes. Rather than that, we bound computational efforts by splitting our algorithm into two phases. The first detects infinitesimal r-symmetries directly using a local differential analysis, and the second performs direct matching for the remaining discrete symmetries. We show that our algorithm can successfully characterize and extract intrinsic symmetries from a number of example shapes.

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Finding Homologous Points

2017

Theory and Applications of Image Registration

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The wave kernel signature: A quantum mechanical approach to shape analysis

Cited by 611 publications

References 24 publications

Anisotropic Laplace-Beltrami Operators for Shape Analysis

Anisotropic Laplace-Beltrami Operators for Shape Analysis

Characterization of Partial Intrinsic Symmetries

Finding Homologous Points

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