Efficient solution of parabolic equations by Krylov approximation methods
SIAM Journal on Scientific and Statistical Computing
Point Signatures: A New Representation for 3D Object Recognition
International Journal of Computer Vision
Using Spin Images for Efficient Object Recognition in Cluttered 3D Scenes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Topology matching for fully automatic similarity estimation of 3D shapes
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Laplacian Eigenmaps for dimensionality reduction and data representation
Neural Computation
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
Discrete & Computational Geometry
A Theoretical and Computational Framework for Isometry Invariant Recognition of Point Cloud Data
Foundations of Computational Mathematics
Salient geometric features for partial shape matching and similarity
ACM Transactions on Graphics (TOG)
Persistence-sensitive simplification functions on 2-manifolds
Proceedings of the twenty-second annual symposium on Computational geometry
Data Fusion and Multicue Data Matching by Diffusion Maps
IEEE Transactions on Pattern Analysis and Machine Intelligence
Pose-Oblivious Shape Signature
IEEE Transactions on Visualization and Computer Graphics
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Multi-scale features for approximate alignment of point-based surfaces
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Laplace-Beltrami eigenfunctions for deformation invariant shape representation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Analysis of scalar fields over point cloud data
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Technical Section: Computing smooth approximations of scalar functions with constraints
Computers and Graphics
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
Spectral-Driven Isometry-Invariant Matching of 3D Shapes
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
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
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)
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
SMI 2013: Heat diffusion kernel and distance on surface meshes and point sets
Computers and Graphics
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 heat diffusion kernel. In this paper, we focus our attention on the properties (e.g., scale-invariance, semi-group property, robustness to noise) of the wFEM heat kernel, recently proposed in Patane and Falcidieno (2010), and its application to shape comparison and feature-driven approximation. After proving that the wFEM heat kernel is intrinsically scale-covariant (i.e., without shape or kernel normalization) and scale-invariant through a normalization of the Laplacian eigenvalues, we experimentally verify that the wFEM heat kernel descriptors are more robust against shape/scale changes and provide better matching performances with respect to previous work. In the space F(M) of piecewise linear scalar functions defined on a triangle mesh M, we introduce the wFEM heat kernel K"t, which is used to increase the degree of flexibility in the design of geometry-aware basis functions. Furthermore, we efficiently compute scale-based representations of maps on M by specializing the Chebyshev method through the solution of a set of sparse linear systems, thus avoiding the spectral decomposition of the Laplacian matrix. Finally, the scalar product induced by K"t makes F(M) a Reproducing Kernel Hilbert Space, whose (reproducing) kernel is the linear FEM heat kernel, and induces the FEM diffusion distances on M.