Shape Analysis Using the Auto Diffusion Function

Publication: Research - peer-reviewConference article – Annual report year: 2009

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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
Issue number5
Pages (from-to)1405-1413
StatePublished - 2009
EventSymposium on Geometry Processing - Berlin


ConferenceSymposium on Geometry Processing
Period01/01/2009 → …


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