Myself Researcher at CNR-IMATI & Member of the Shape and - PowerPoint PPT Presentation

Myself • Researcher at CNR-IMATI & Member of the “Shape and Seman<cs Modelling Group” (since 2001) Laplacian Spectral Functions, Kernels, and Distances • Responsible of the research line “Numerical Geometry and Signal Processing” • NaHonal ScienHfic HabilitaHon Theory & Applications to Geometry Processing – Full Professor in Computer Science (INF01) & Shape Analysis – Full Professor in S ystems for Informa3on Processing (ENG-09/H1) My research and training interests lie at the intersec<on of • – Computer Science: Computer Graphics & Mul<media, Machine Learning – Engineering : Informa<on & Signal Processing Giuseppe Patanè – Applied MathemaHcs : Numerical Analysis CNR-IMATI, Genova - Italy ERC Sector: PE6 Computer Science & InformaHcs • patane@ge.imati.cnr.it IntroducHon IntroducHon Geometric & Laplacian spectral Topological approaches approaches Remeshing/skeletonisa<on/segmenta<on/etc Remeshing/skeletonisa<on/segmenta<on/etc ( ∆ , ϕ ) ApplicaHons ApplicaHons FuncHonal FuncHonal approaches approaches Laplacian & Hamiltonian Laplacian spectral kernels and distances spectral funcHons • Harmonic func<ons • Commute <me & biharmonic • Laplacian/Hamiltonian • Diffusion & wave eigenfunc<ons • … • Diffusive func<ons Shape Descriptors FuncHons, Kernels & Distances Laplacian spectral funcHons, kernels & distances

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Different & parHal representaHons seed points for encoding local geometry MulH-scale/sparse proper<es & saving memory space representaHon – efficient, stable, and parameter-free computaHon Compression IntroducHon IntroducHon Working on the space of scalar funcHons defined on the input domain (eg., surface, Working on the space of scalar funcHons defined on the input domain (eg., surface, • • volume), we can address volume), we can address – shape deformaHons , by modifying the coefficients that express the geometry of – the defini<on of Laplacian spectral kernels and distances , as a filtered the input surface in terms of geometry-driven or shape-intrinsic basis funcHons combina<on of the Laplacian spectral basis (eg., harmonic barycentric coordinates) X f = α i ( t ) ϕ i i q seed point p X d 2 ( p , q ) := α i | ϕ i ( p ) − ϕ i ( q ) | 2 Global basis Local basis i