@ARTICLE\{IMM2009-05794,
    author       = "K. Gebal and J. A. B{\ae}rentzen and H. Aan{\ae}s and R. Larsen",
    title        = "Shape Analysis Using the Auto Diffusion Function",
    year         = "2009",
    pages        = "1405-1413",
    journal      = "Computer Graphics Forum",
    volume       = "28",
    editor       = "",
    number       = "5",
    publisher    = "Wiley-Blackwell Publishing",
    url          = "http://www2.compute.dtu.dk/pubdb/pubs/5794-full.html",
    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}.",
    isbn_issn    = "ISSN: 0167-7055"
}