Shape Analysis Using the Auto Diffusion Function

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dc.contributor.authorGebal, K.en_US
dc.contributor.authorBaerentzen, J. A.en_US
dc.contributor.authorAanaes, H.en_US
dc.contributor.authorLarsen, R.en_US
dc.date.accessioned2015-02-23T15:43:29Z
dc.date.available2015-02-23T15:43:29Z
dc.date.issued2009en_US
dc.description.abstractScalar 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.en_US
dc.description.number5en_US
dc.description.seriesinformationComputer Graphics Forumen_US
dc.description.volume28en_US
dc.identifier.doi10.1111/j.1467-8659.2009.01517.xen_US
dc.identifier.issn1467-8659en_US
dc.identifier.pages1405-1413en_US
dc.identifier.urihttps://doi.org/10.1111/j.1467-8659.2009.01517.xen_US
dc.publisherThe Eurographics Association and Blackwell Publishing Ltden_US
dc.titleShape Analysis Using the Auto Diffusion Functionen_US
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SGP09: Eurographics Symposium on Geometry Processing