Reeb graphs for shape analysis and applications
Theoretical Computer Science
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Toward an efficient triangle-based spherical harmonics representation of 3D objects
Computer Aided Geometric Design
Topology-Invariant Similarity of Nonrigid Shapes
International Journal of Computer Vision
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Streaming 3D meshes using spectral geometry images
MM '09 Proceedings of the 17th ACM international conference on Multimedia
ACM SIGGRAPH ASIA 2009 Courses
Spectral conformal parameterization
SGP '08 Proceedings of the Symposium on Geometry Processing
Shape analysis using the auto diffusion function
SGP '09 Proceedings of the Symposium on Geometry Processing
Approximating gradients for meshes and point clouds via diffusion metric
SGP '09 Proceedings of the Symposium on Geometry Processing
Full and Partial Symmetries of Non-rigid Shapes
International Journal of Computer Vision
Technical Section: Fiedler trees for multiscale surface analysis
Computers and Graphics
International Journal of Computer Vision
International Journal of Computer Vision
ACM SIGGRAPH 2010 Courses
Parallel Poisson disk sampling with spectrum analysis on surfaces
ACM SIGGRAPH Asia 2010 papers
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Inelastic deformation invariant modal representation for non-rigid 3D object recognition
AMDO'10 Proceedings of the 6th international conference on Articulated motion and deformable objects
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Heat kernel smoothing using laplace-beltrami eigenfunctions
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part III
Intra-patient supine-prone colon registration in CT colonography using shape spectrum
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Wave interference for pattern description
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
Pose-consistent 3D shape segmentation based on a quantum mechanical feature descriptor
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
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
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part I
A correspondence-less approach to matching of deformable shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Photometric heat kernel signatures
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Deformable shape retrieval by learning diffusion kernels
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
SMI 2012: Short Stable volumetric features in deformable shapes
Computers and Graphics
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
Discrete heat kernel determines discrete Riemannian metric
Graphical Models
Continuous and discrete Mexican hat wavelet transforms on manifolds
Graphical Models
A novel approach for high dimension 3D object representation using Multi-Mother Wavelet Network
Multimedia Tools and Applications
Affine-invariant photometric heat kernel signatures
EG 3DOR'12 Proceedings of the 5th Eurographics conference on 3D Object Retrieval
Stable spectral mesh filtering
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
A multiresolution descriptor for deformable 3D shape retrieval
The Visual Computer: International Journal of Computer Graphics
Pose analysis using spectral geometry
The Visual Computer: International Journal of Computer Graphics
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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One of the challenges in geometry processing is to automatically reconstruct a higher-level representation from raw geometric data. For instance, computing a parameterization of an object helps attaching information to it and converting between various representations. More generally, this family of problems may be thought of in terms of constructing structured function bases attached to surfaces. In this paper, we study a specific type of hierarchical function bases, defined by the eigenfunctions of the Laplace-Beltrami operator. When applied to a sphere, this function basis corresponds to the classical spherical harmonics. On more general objects, this defines a function basis well adapted to the geometry and the topology of the object. Based on physical analogies (vibration modes), we first give an intuitive view before explaining the underlying theory. We then explain in practice how to compute an approximation of the eigenfunctions of a differential operator, and show possible applications in geometry processing.