MINDS Seminar Series | Moo K. Chung (University of Wisconsin–Madison) - Fast Polynomial Approximation of the Hodge-Laplacian for Diffusion of Vector Fields on Manifolds

MINDS SEMINAR

period : 2024-12-17 ~ 2024-12-17

time : 13:30:00 ~ 14:30:00

개최 장소 : Math Bldg 404 & Online streaming (Zoom)

Topic : Fast Polynomial Approximation of the Hodge-Laplacian for Diffusion of Vector Fields on Manifolds

개요

Date	2024-12-17 ~ 2024-12-17	Time	13:30:00 ~ 14:30:00
Speaker	Moo K. Chung	Affiliation	University of Wisconsin–Madison
Place	Math Bldg 404 & Online streaming (Zoom)	Streaming link	ID : 688 896 1076 / PW : 54321
Topic	Fast Polynomial Approximation of the Hodge-Laplacian for Diffusion of Vector Fields on Manifolds
Contents	Heat diffusion using the Laplace-Beltrami operator has been extensively applied to surface mesh fairing, mesh regularization, regression, and data smoothing. Since its introduction in 2001 for denoising brain cortical data in brain imaging, it has been established as the fundamental baseline approach for denoising scalar data on manifolds. Leveraging discrete exterior calculus (DEC), which discretizes differential geometric operations, we extend this method to denoise noisy vector fields using the Hodge Laplacian. To accelerate computation, we employ polynomial approximation for heat diffusion—the same technique utilized in the rapid computation of diffusion wavelets and convolutional graph neural networks. We propose that our method represents the fastest possible diffusion solver on triangle meshes for closed surfaces. This work is ongoing joint research with Jae-Hun Jung and Ilwoo Lyu of POSTECH. The talk is partially based on Huang et al. 2020, IEEE TMI 39:2201-2212 (https://pages.stat.wisc.edu/~mchung/papers/huang.2020.TMI.pdf) and Anand and Chung 2023 IEEE TMI 42:1563-1573 (https://github.com/laplcebeltrami/hodge/blob/main/anand.2023.pdf).

MinDS · 2024-12-16 13:12 · Views 421

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