The symmetric eigenvalue problem
The symmetric eigenvalue problem
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
Morse-smale complexes for piecewise linear 3-manifolds
Proceedings of the nineteenth annual symposium on Computational geometry
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Hierarchical mesh decomposition using fuzzy clustering and cuts
ACM SIGGRAPH 2003 Papers
Deformation transfer for triangle meshes
ACM SIGGRAPH 2004 Papers
Segmentation of 3D Meshes through Spectral Clustering
PG '04 Proceedings of the Computer Graphics and Applications, 12th Pacific Conference
Laplace-spectra as fingerprints for shape matching
Proceedings of the 2005 ACM symposium on Solid and physical modeling
Stability of persistence diagrams
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Hierarchical mesh segmentation based on fitting primitives
The Visual Computer: International Journal of Computer Graphics
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
Extreme Elevation on a 2-Manifold
Discrete & Computational Geometry
Efficient Computation of Isometry-Invariant Distances Between Surfaces
SIAM Journal on Scientific Computing
Laplace spectra as fingerprints for image recognition
Computer-Aided Design
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Global Medical Shape Analysis Using the Volumetric Laplace Spectrum
CW '07 Proceedings of the 2007 International Conference on Cyberworlds
Surface matching using consistent pants decomposition
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Fast mesh segmentation using random walks
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Describing shapes by geometrical-topological properties of real functions
ACM Computing Surveys (CSUR)
Extending Persistence Using Poincaré and Lefschetz Duality
Foundations of Computational Mathematics
Technical Section: Discrete Laplace-Beltrami operators for shape analysis and segmentation
Computers and Graphics
Discrete Laplace--Beltrami operators and their convergence
Computer Aided Geometric Design
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
A hierarchical segmentation of articulated bodies
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
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
On bending invariant signatures for surfaces
IEEE Transactions on Pattern Analysis and Machine Intelligence
Technical Section: Fiedler trees for multiscale surface analysis
Computers and Graphics
Data-driven suggestions for creativity support in 3D modeling
ACM SIGGRAPH Asia 2010 papers
Affine puzzle: realigning deformed object fragments without correspondences
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Learning shape segmentation using constrained spectral clustering and probabilistic label transfer
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part V
Matching 2D and 3D articulated shapes using the eccentricity transform
Computer Vision and Image Understanding
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Fast brain matching with spectral correspondence
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Pose-consistent 3D shape segmentation based on a quantum mechanical feature descriptor
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
SMI 2012: Full Spectral computations on nontrivial line bundles
Computers and Graphics
A comparison of methods for non-rigid 3D shape retrieval
Pattern Recognition
SHREC'11 track: shape retrieval on non-rigid 3D watertight meshes
EG 3DOR'11 Proceedings of the 4th Eurographics conference on 3D Object Retrieval
Spectral demons --- image registration via global spectral correspondence
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
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
Fast nonrigid 3D retrieval using modal space transform
Proceedings of the 3rd ACM conference on International conference on multimedia retrieval
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
SMI 2013: Laplacians on flat line bundles over 3-manifolds
Computers and Graphics
Diffeomorphic spectral matching of cortical surfaces
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Key-dependent 3D model hashing for authentication using heat kernel signature
Digital Signal Processing
A Class of Generalized Laplacians on Vector Bundles Devoted to Multi-Channel Image Processing
Journal of Mathematical Imaging and Vision
From a Non-Local Ambrosio-Tortorelli Phase Field to a Randomized Part Hierarchy Tree
Journal of Mathematical Imaging and Vision
Spectral Log-Demons: Diffeomorphic Image Registration with Very Large Deformations
International Journal of Computer Vision
3D-model retrieval using bag-of-features based on closed curves
3DOR '13 Proceedings of the Sixth Eurographics Workshop on 3D Object Retrieval
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This work introduces a method to hierarchically segment articulated shapes into meaningful parts and to register these parts across populations of near-isometric shapes (e.g. head, arms, legs and fingers of humans in different body postures). The method exploits the isometry invariance of eigenfunctions of the Laplace-Beltrami operator and uses topological features (level sets at important saddles) for the segmentation. Concepts from persistent homology are employed for a hierarchical representation, for the elimination of topological noise and for the comparison of eigenfunctions. The obtained parts can be registered via their spectral embedding across a population of near isometric shapes. This work also presents the highly accurate computation of eigenfunctions and eigenvalues with cubic finite elements on triangle meshes and discusses the construction of persistence diagrams from the Morse-Smale complex as well as the relation to size functions.