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

Myself • Researcher at CNR-IMATI & Member of the “Shape and Seman2cs Modelling Group” (since 2001) Responsible of the research line “Numerical Geometry and Signal Processing” • Spectral Methods for • NaDonal ScienDfic HabilitaDon Geometry Processing & Shape Analysis – Full Professor in Computer Science (INF01) – Full Professor in S ystems for Informa3on Processing (ENG-09/H1) • My research and training interests lie at the intersec2on of – Computer Science: Computer Graphics & Mul2media, Machine Learning – Engineering : Informa2on & Signal Processing Giuseppe Patanè – Applied MathemaDcs : Numerical Analysis CNR-IMATI, Genova - Italy ERC Sector: PE6 Computer Science & InformaDcs • patane@ge.imati.cnr.it IntroducDon IntroducDon Geometric & Laplacian spectral Topological approaches approaches Remeshing/skeletonisa2on/segmenta2on/etc Remeshing/skeletonisa2on/segmenta2on/etc ( ∆ , ϕ ) ApplicaDons ApplicaDons FuncDonal FuncDonal approaches approaches Laplacian & Hamiltonian Laplacian spectral spectral funcDons kernels and distances • Harmonic func2ons • Commute 2me & biharmonic • Laplacian/Hamiltonian eigenfunc2ons • Diffusion & wave • … • Diffusive func2ons Shape Descriptors FuncDons, Kernels & Distances Laplacian spectral funcDons, kernels & distances

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ie., independent of data – sparse representaDons , by choosing a low number of basis func2ons in order to embedding/representa2on achieve a target approxima2on accuracy Different postures – mulD-scale definiDon , in order to encode – compression , by quan2sing the representa2on coefficients local and global shape features k – invariance to shape transformaDons ; eg., X f = α i ϕ i isometries for pose invariance i =1 f = ( x, y, z ) k = 3 , 20 , 50 , . . . – compact support & localisaDon at feature/ Different & parDal representaDons seed points for encoding local geometry MulD-scale/sparse proper2es & saving memory space representaDon – efficient, stable, and parameter-free computaDon Compression IntroducDon IntroducDon • Working on the space of scalar funcDons defined on the input domain (eg., surface, • Working on the space of scalar funcDons defined on the input domain (eg., surface, volume), we can address volume), we can address – shape deformaDons , by modifying the coefficients that express the geometry of – the defini2on of Laplacian spectral kernels and distances , as a filtered the input surface in terms of geometry-driven or shape-intrinsic basis funcDons combina2on 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