Shape Analysis Using the Auto Diffusion Function

Scalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion Function (ADF) which is a linear combination of the eigenfunctions of the Lap...

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Vydané v:	Computer graphics forum Ročník 28; číslo 5; s. 1405 - 1413
Hlavní autori:	Gȩbal, K., Bærentzen, J. A., Aanæs, H., Larsen, R.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Oxford, UK Blackwell Publishing Ltd 01.07.2009
Predmet:	3-D graphics Algorithms and systems Geometry I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling-Geometric algorithms I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Geometric algorithms, languages, and systems languages Studies
ISSN:	0167-7055, 1467-8659
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Popis
Shrnutí:	Scalar functions defined on manifold triangle meshes is a starting point for many geometry processing algorithms such as mesh parametrization, skeletonization, and segmentation. In this paper, we propose the Auto Diffusion Function (ADF) which is a linear combination of the eigenfunctions of the Laplace‐Beltrami operator in a way that has a simple physical interpretation. The ADF of a given 3D object has a number of further desirable properties: Its extrema are generally at the tips of features of a given object, its gradients and level sets follow or encircle features, respectively, it is controlled by a single parameter which can be interpreted as feature scale, and, finally, the ADF is invariant to rigid and isometric deformations. We describe the ADF and its properties in detail and compare it to other choices of scalar functions on manifolds. As an example of an application, we present a pose invariant, hierarchical skeletonization and segmentation algorithm which makes direct use of the ADF.
Bibliografia:	ArticleID:CGF1517 istex:E9A6DFE6F349B2B12DE83E9ECEC7FAB0251AFB4B ark:/67375/WNG-0PKFB0KR-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0167-7055 1467-8659
DOI:	10.1111/j.1467-8659.2009.01517.x