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Proceedings of the nineteenth annual symposium on Computational geometry
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Topology Recognition of 3D Closed Freeform Objects Based on Topological Graphs
PG '01 Proceedings of the 9th Pacific Conference on Computer Graphics and Applications
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Optimal Global Conformal Surface Parameterization
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Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Topology driven 3D mesh hierarchical segmentation
SMI '07 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2007
Harmonic skeleton for realistic character animation
SCA '07 Proceedings of the 2007 ACM SIGGRAPH/Eurographics symposium on Computer animation
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
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ACM SIGGRAPH 2008 papers
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Harmonic functions for quadrilateral remeshing of arbitrary manifolds
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ACM SIGGRAPH ASIA 2009 Courses
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Technical Section: Fiedler trees for multiscale surface analysis
Computers and Graphics
ACM SIGGRAPH 2010 Courses
Shape comparison through mutual distances of real functions
Proceedings of the ACM workshop on 3D object retrieval
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
A new shape diffusion descriptor for brain classification
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Adaptive discrete Laplace operator
ISVC'11 Proceedings of the 7th international conference on Advances in visual computing - Volume Part II
Elements of geometry processing
SIGGRAPH Asia 2011 Courses
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CompIMAGE'10 Proceedings of the Second international conference on Computational Modeling of Objects Represented in Images
Eigenmodes of surface energies for shape analysis
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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Computer Aided Geometric Design
SMI 2012: Short Stable volumetric features in deformable shapes
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Computer Graphics Forum
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EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Affine-invariant photometric heat kernel signatures
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Equi-affine invariant geometries of articulated objects
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wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
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The Visual Computer: International Journal of Computer Graphics
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The Visual Computer: International Journal of Computer Graphics
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
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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.