Shape google: Geometric words and expressions for invariant shape retrieval
ACM Transactions on Graphics (TOG)
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
wFEM heat kernel: Discretization and applications to shape analysis and retrieval
Computer Aided Geometric Design
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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In digital geometry processing and shape modeling, the Laplace-Beltrami and the heat diffusion operator, together with the corresponding Laplacian eigenmaps, harmonic and geometry-aware functions, have been used in several applications, which range from surface parameterization, deformation, and compression to segmentation, clustering, and comparison. Using the linear FEM approximation of the Laplace-Beltrami operator, we derive a discrete heat kernel that is linear, stable to an irregular sampling density of the input surface, and scale covariant. With respect to previous work, this last property makes the kernel particularly suitable for shape analysis and comparison; in fact, local and global changes of the surface correspond to a re-scaling of the time parameter without affecting its spectral component. Finally, we study the scale spaces that are induced by the proposed heat kernel and exploited to provide a multi-scale approximation of scalar functions defined on 3D shapes.