Multivariate interpolation of arbitrarily spaced data by moving least squares methods
Journal of Computational and Applied Mathematics
ACM Transactions on Graphics (TOG)
Shape transformation for polyhedral objects
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
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
Machine Learning
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
An optimal algorithm for approximate nearest neighbor searching fixed dimensions
Journal of the ACM (JACM)
An equivalence between sparse approximation and support vector machines
Neural Computation
The approximation power of moving least-squares
Mathematics of Computation
Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
A survey of graph layout problems
ACM Computing Surveys (CSUR)
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Proceedings of the conference on Visualization '01
Conformal Surface Parameterization for Texture Mapping
IEEE Transactions on Visualization and Computer Graphics
Texture Mapping Using Surface Flattening via Multidimensional Scaling
IEEE Transactions on Visualization and Computer Graphics
Computer Aided Geometric Design
Watermarking 3D polygonal meshes in the mesh spectral domain
GRIN'01 No description on Graphics interface 2001
Normalized Cuts and Image Segmentation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Merging Polyhedral Shapes with Scattered Features
SMI '99 Proceedings of the International Conference on Shape Modeling and Applications
Spherical parametrization and remeshing
ACM SIGGRAPH 2003 Papers
Fundamentals of spherical parameterization for 3D meshes
ACM SIGGRAPH 2003 Papers
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
ACM SIGGRAPH 2003 Papers
Reanimating the dead: reconstruction of expressive faces from skull data
ACM SIGGRAPH 2003 Papers
Shape modeling with point-sampled geometry
ACM SIGGRAPH 2003 Papers
High-pass quantization for mesh encoding
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
Global conformal surface parameterization
Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
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
ACM SIGGRAPH 2004 Papers
Cross-parameterization and compatible remeshing of 3D models
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2004 Papers
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
Surface Reconstruction of Noisy and Defective Data Sets
VIS '04 Proceedings of the conference on Visualization '04
Optimal Global Conformal Surface Parameterization
VIS '04 Proceedings of the conference on Visualization '04
Local and Global Comparison of Continuous Functions
VIS '04 Proceedings of the conference on Visualization '04
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
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
3D scattered data interpolation and approximation with multilevel compactly supported RBFs
Graphical Models - Special issue on SMI 2003
Hierarchical Clustering for Unstructured Volumetric Scalar Fields
Proceedings of the 14th IEEE Visualization 2003 (VIS'03)
IEEE Computer Graphics and Applications
Robust spherical parameterization of triangular meshes
Computing - Geometric modelling dagstuhl 2002
Practical Spherical Embedding of Manifold Triangle Meshes
SMI '05 Proceedings of the International Conference on Shape Modeling and Applications 2005
Curvilinear Spherical Parameterization
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
SIMS: a Multi-Level Approach to Surface Reconstruction with Sparse Implicits
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
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
Unconstrained spherical parameterization
SIGGRAPH '05 ACM SIGGRAPH 2005 Sketches
Manifold splines with single extraordinary point
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Harmonic volumetric mapping for solid modeling applications
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A spectral approach to shape-based retrieval of articulated 3D models
Computer-Aided Design
Conformal Geometry and Its Applications on 3D Shape Matching, Recognition, and Stitching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Harmonic coordinates for character articulation
ACM SIGGRAPH 2007 papers
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Hierarchical error-driven approximation of implicit surfaces from polygonal meshes
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
GPU-assisted positive mean value coordinates for mesh deformations
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
Mesh parameterization methods and their applications
Foundations and Trends® in Computer Graphics and Vision
IEEE Transactions on Visualization and Computer Graphics
ACM SIGGRAPH 2008 papers
Volumetric parameterization and trivariate b-spline fitting using harmonic functions
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Globally Optimal Surface Mapping for Surfaces with Arbitrary Topology
IEEE Transactions on Visualization and Computer Graphics
Basis functions for concave polygons
Computers & Mathematics with Applications
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Computer-Aided Design
IEEE Transactions on Visualization and Computer Graphics
Towards a theoretical foundation for Laplacian-based manifold methods
Journal of Computer and System Sciences
MLS-based scalar fields over triangle meshes and their application in mesh processing
Proceedings of the 2009 symposium on Interactive 3D graphics and games
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Computing Teichmüller Shape Space
IEEE Transactions on Visualization and Computer Graphics
Coordinates for instant image cloning
ACM SIGGRAPH 2009 papers
Surface Mapping Using Consistent Pants Decomposition
IEEE Transactions on Visualization and Computer Graphics
Technical Section: A divide-and-conquer approach for automatic polycube map construction
Computers and Graphics
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
Surface Quasi-Conformal Mapping by Solving Beltrami Equations
Proceedings of the 13th IMA International Conference on Mathematics of Surfaces XIII
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
Ricci Flow for 3D Shape Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
A hierarchical segmentation of articulated bodies
SGP '08 Proceedings of the Symposium on Geometry Processing
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Polyhedral finite elements using harmonic basis functions
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
Controllable conformal maps for shape deformation and interpolation
ACM SIGGRAPH 2010 papers
A multi-resolution approach to heat kernels on discrete surfaces
ACM SIGGRAPH 2010 papers
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Technical Section: Feature-aligned harmonic volumetric mapping using MFS
Computers and Graphics
ACM Transactions on Graphics (TOG)
International Journal of Computer Vision
International Journal of Computer Vision
Hexahedral shell mesh construction via volumetric polycube map
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Direct-Product Volumetric Parameterization of Handlebodies via Harmonic Fields
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Visual Similarity Based 3D Shape Retrieval Using Bag-of-Features
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Multi-scale Feature Spaces for Shape Processing and Analysis
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Generalized PolyCube Trivariate Splines
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Volumetric modeling with diffusion 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
Shape analysis of planar objects with arbitrary topologies using conformal geometry
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Supine and Prone Colon Registration Using Quasi-Conformal Mapping
IEEE Transactions on Visualization and Computer Graphics
Editable polycube map for GPU-based subdivision surfaces
I3D '11 Symposium on Interactive 3D Graphics and Games
Bounded biharmonic weights for real-time deformation
ACM SIGGRAPH 2011 papers
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping
Computers and Graphics
Cultural Heritage: Symmetry and template guided completion of damaged skulls
Computers and Graphics
Boundary aligned smooth 3D cross-frame field
Proceedings of the 2011 SIGGRAPH Asia Conference
Interpolated eigenfunctions for volumetric shape processing
The Visual Computer: International Journal of Computer Graphics - Special Issue on 3DOR 2010
Consistent spherical parameterization
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part II
Functional maps: a flexible representation of maps between shapes
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Restricted Trivariate Polycube Splines for Volumetric Data Modeling
IEEE Transactions on Visualization and Computer Graphics
Fast orthogonal least squares algorithm for efficient subset modelselection
IEEE Transactions on Signal Processing
SMI 2012: Full Local approximation of scalar functions on 3D shapes and volumetric data
Computers and Graphics
Fragmented skull modeling using heat kernels
Graphical Models
Generalized Swept Mid-structure for Polygonal Models
Computer Graphics Forum
An automatic assembly and completion framework for fragmented skulls
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Efficient Optimization of Common Base Domains for Cross Parameterization
IEEE Transactions on Visualization and Computer Graphics
Point-Based Manifold Harmonics
IEEE Transactions on Visualization and Computer Graphics
All-hex meshing using singularity-restricted field
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Part analogies in sets of objects
EG 3DOR'08 Proceedings of the 1st Eurographics conference on 3D Object Retrieval
Visual vocabulary signature for 3D object retrieval and partial matching
EG 3DOR'09 Proceedings of the 2nd Eurographics conference on 3D Object Retrieval
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
Interactively visualizing procedurally encoded scalar fields
VISSYM'04 Proceedings of the Sixth Joint Eurographics - IEEE TCVG conference on Visualization
Computer Graphics Forum
IEEE Transactions on Visualization and Computer Graphics
Efficient spherical parametrization using progressive optimization
CVM'12 Proceedings of the First international conference on Computational Visual Media
Multi-resolutive sparse approximations of d-dimensional data
Computer Vision and Image Understanding
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
Biharmonic Volumetric Mapping Using Fundamental Solutions
IEEE Transactions on Visualization and Computer Graphics
Surface Mesh to Volumetric Spline Conversion with Generalized Polycubes
IEEE Transactions on Visualization and Computer Graphics
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
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Extending a shape-driven map to the interior of the input shape and to the surrounding volume is a difficult problem since it typically relies on the integration of shape-based and volumetric information, together with smoothness conditions, interpolating constraints, preservation of feature values at both a local and global level. In this context, this course revises the main out-of-sample approximation schemes for both 3D shapes and d-dimensional data, and provides a unified discussion on the integration of surface- and volume-based shape information. Then, it describes the application of shape-based and volumetric techniques to shape modeling and analysis through the definition of volumetric shape descriptors; shape processing through volumetric parameterization and polycube splines; feature-driven approximation through kernels and radial basis functions. We also discuss the Hamilton's Ricci flow, which is a powerful tool to compute the conformal structure of the shapes and to design Riemannian metrics of manifolds by prescribed curvatures and shape descriptors using conformal welding. We conclude the presentation by discussing applications to shape analysis and medicine, open problems, and future perspectives.