Shape Analysis Using the Auto Diffusion Function
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Date
2009
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing Ltd
Abstract
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.
Description
@article{10.1111:j.1467-8659.2009.01517.x,
journal = {Computer Graphics Forum},
title = {{Shape Analysis Using the Auto Diffusion Function}},
author = {Gebal, K. and Baerentzen, J. A. and Aanaes, H. and Larsen, R.},
year = {2009},
publisher = {The Eurographics Association and Blackwell Publishing Ltd},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2009.01517.x}
}