Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
SIAM Journal on Matrix Analysis and Applications
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Normalized Cuts and Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scientific Computations on Mathematical Problems and Conjectures
Scientific Computations on Mathematical Problems and Conjectures
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Towards a theoretical foundation for Laplacian-based manifold methods
Journal of Computer and System Sciences
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
A multi-resolution approach to heat kernels on discrete surfaces
ACM SIGGRAPH 2010 papers
International Journal of Computer Vision
Multi-scale Feature Spaces for Shape Processing and Analysis
SMI '10 Proceedings of the 2010 Shape Modeling International Conference
Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
Discrete Laplacians on general polygonal meshes
ACM SIGGRAPH 2011 papers
From graphs to manifolds – weak and strong pointwise consistency of graph laplacians
COLT'05 Proceedings of the 18th annual conference on Learning Theory
Point-Based Manifold Harmonics
IEEE Transactions on Visualization and Computer Graphics
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
Surface- and volume-based techniques for shape modeling and analysis
SIGGRAPH Asia 2013 Courses
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The heat diffusion distance and kernel have gained a central role in geometry processing and shape analysis. This paper addresses a novel discretization and spectrum-free computation of the diffusion kernel and distance on a 3D shape P represented as a triangle mesh or a point set. After rewriting different discretizations of the Laplace-Beltrami operator in a unified way and using an intrinsic scalar product on the space of functions on P, we derive a shape-intrinsic heat kernel matrix, together with the corresponding diffusion distances. Then, we propose an efficient computation of the heat distance and kernel through the solution of a set of sparse linear systems. In this way, we bypass the evaluation of the Laplacian spectrum, the selection of a specific subset of eigenpairs, and the use of multi-resolutive prolongation operators. The comparison with previous work highlights the main features of the proposed approach in terms of smoothness, stability to shape discretization, approximation accuracy, and computational cost.