A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
A Supernodal Approach to Sparse Partial Pivoting
SIAM Journal on Matrix Analysis and Applications
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Cutting 3D freeform objects with genus-n into single boundary surfaces using topological graphs
Proceedings of the seventh ACM symposium on Solid modeling and applications
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Discrete Laplace-Beltrami operators and their convergence
Computer Aided Geometric Design - Special issue: Geometric modeling and processing 2004
Feature-based surface parameterization and texture mapping
ACM Transactions on Graphics (TOG)
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Mesh Segmentation - A Comparative Study
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Laplace-Beltrami Eigenfunctions Towards an Algorithm That "Understands" Geometry
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Robust 3D Shape Correspondence in the Spectral Domain
SMI '06 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2006
Spectral surface quadrangulation
ACM SIGGRAPH 2006 Papers
Discrete differential forms for computational modeling
SIGGRAPH '05 ACM SIGGRAPH 2005 Courses
Families of cut-graphs for bordered meshes with arbitrary genus
Graphical Models
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
Laplace spectra as fingerprints for image recognition
Computer-Aided Design
Topological Generators and Cut-Graphs of Arbitrary Triangle Meshes
SMI '07 Proceedings of the IEEE International Conference on Shape Modeling and Applications 2007
Discrete laplace operators: no free lunch
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discrete quadratic curvature energies
Computer Aided Geometric Design
Global Medical Shape Analysis Using the Volumetric Laplace Spectrum
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
Discrete laplace operator on meshed surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
Global intrinsic symmetries of shapes
SGP '08 Proceedings of the Symposium on Geometry Processing
Global medical shape analysis using the Laplace-Beltrami spectrum
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
Semantic annotation of 3D surface meshes based on feature characterization
SAMT'07 Proceedings of the semantic and digital media technologies 2nd international conference on Semantic Multimedia
Technical Section: Fiedler trees for multiscale surface analysis
Computers and Graphics
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
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)
SMI 2011: Full Paper: Interactive 3D caricature from harmonic exaggeration
Computers and Graphics
Solving eigenvalue problems on curved surfaces using the Closest Point Method
Journal of Computational Physics
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
The hitchhiker's guide to the galaxy of mathematical tools for shape analysis
ACM SIGGRAPH 2012 Courses
A comparison of methods for non-rigid 3D shape retrieval
Pattern Recognition
Feature selection for enhanced spectral shape comparison
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
Heat diffusion approach for feature-based body scans analysis
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
SHREC'11 track: shape retrieval on non-rigid 3D watertight meshes
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Analytic Curve Skeletons for 3D Surface Modeling and Processing
Computer Graphics Forum
3D object classification using scale invariant heat kernels with collaborative classification
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part I
Equi-affine invariant geometries of articulated objects
Proceedings of the 15th international conference on Theoretical Foundations of Computer Vision: outdoor and large-scale real-world scene analysis
Anatomical structures segmentation by spherical 3d ray casting and gradient domain editing
MICCAI'12 Proceedings of the 15th international conference on Medical Image Computing and Computer-Assisted Intervention - Volume Part II
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Consistent approximations of several geometric differential operators and their convergence
Applied Numerical Mathematics
SMI 2013: Laplacians on flat line bundles over 3-manifolds
Computers and Graphics
Key-dependent 3D model hashing for authentication using heat kernel signature
Digital Signal Processing
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
| Hi-index | 0.01 |
Shape analysis plays a pivotal role in a large number of applications, ranging from traditional geometry processing to more recent 3D content management. In this scenario, spectral methods are extremely promising as they provide a natural library of tools for shape analysis, intrinsically defined by the shape itself. In particular, the eigenfunctions of the Laplace-Beltrami operator yield a set of real-valued functions that provide interesting insights in the structure and morphology of the shape. In this paper, we first analyze different discretizations of the Laplace-Beltrami operator (geometric Laplacians, linear and cubic FEM operators) in terms of the correctness of their eigenfunctions with respect to the continuous case. We then present the family of segmentations induced by the nodal sets of the eigenfunctions, discussing its meaningfulness for shape understanding.