Shape Analysis Using the Auto Diffusion Function

Katarzyna Gebal, Jakob Andreas Bærentzen, Henrik Aanæs, Rasmus Larsen

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    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.
    Original languageEnglish
    JournalComputer Graphics Forum
    Volume28
    Issue number5
    Pages (from-to)1405-1413
    ISSN0167-7055
    Publication statusPublished - 2009
    EventSymposium on Geometry Processing - Berlin
    Duration: 1 Jan 2009 → …

    Conference

    ConferenceSymposium on Geometry Processing
    CityBerlin
    Period01/01/2009 → …

    Keywords

    • eigensolutions
    • Reeb graphs
    • diffusion kernel
    • shape descriptor
    • Laplace-Beltrami operator
    • Auto Diffusion function

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