ACM Transactions on Graphics (TOG)
A spectral algorithm for envelope reduction of sparse matrices
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Point Signatures: A New Representation for 3D Object Recognition
International Journal of Computer Vision
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Spectral partitioning with multiple eigenvectors
Discrete Applied Mathematics - Special volume on VLSI
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Spectral compression of mesh geometry
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Watermarking 3D polygonal meshes in the mesh spectral domain
GRIN'01 No description on Graphics interface 2001
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
High-pass quantization for mesh encoding
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Butterworth Filtering and Implicit Fairing of Irregular Meshes
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
Discrete & Computational Geometry
Iso-charts: stretch-driven mesh parameterization using spectral analysis
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing
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
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
Pose-Oblivious Shape Signature
IEEE Transactions on Visualization and Computer Graphics
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Technical Section: Computing smooth approximations of scalar functions with constraints
Computers and Graphics
Harmonic functions for quadrilateral remeshing of arbitrary manifolds
Computer Aided Geometric Design - Special issue: Geometry processing
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
Laplace-Beltrami spectra as 'Shape-DNA' of surfaces and solids
Computer-Aided Design
A hierarchical segmentation of articulated bodies
SGP '08 Proceedings of the Symposium on Geometry Processing
A concise and provably informative multi-scale signature based on heat diffusion
SGP '09 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
Geometric characterization and clustering of graphs using heat kernel embeddings
Image and Vision Computing
COCOON'03 Proceedings of the 9th annual international conference on Computing and combinatorics
A multi-resolution approach to heat kernels on discrete surfaces
ACM SIGGRAPH 2010 papers
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
International Journal of Computer Vision
Multi-scale Feature Spaces for Shape Processing and Analysis
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Convergence, stability, and discrete approximation of Laplace spectra
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Uniform convergence of adaptive graph-based regularization
COLT'06 Proceedings of the 19th annual conference on Learning Theory
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
SHREC'10 track: robust shape retrieval
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
SHREC'10 track: feature detection and description
EG 3DOR'10 Proceedings of the 3rd Eurographics conference on 3D Object Retrieval
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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Recent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace-Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes.