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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Bibliographic Details
Published in:Computer graphics forum Vol. 28; no. 5; pp. 1405 - 1413
Main Authors: Gȩbal, K., Bærentzen, J. A., Aanæs, H., Larsen, R.
Format: Journal Article
Language:English
Published: Oxford, UK Blackwell Publishing Ltd 01.07.2009
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:ArticleID:CGF1517
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ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01517.x