Professor Wenwei Lin was invited to give a lecture

发布时间: 2023-11-15 21:30:00

Topic： Volumetric Stretch Energy Minimizationand Optimal Mass Transportwith Applications

Speaker：Wenwei Lin

Time：2023-11-14 15:00-16:00

Tencent Meeting ID： 656-4902-4546

Introduction：

    Volumetric stretch energy has been widely applied to the computation of volume-/mass-preserving parameterizations of simply connected tetrahedral mesh model;M. However, this approach still lacks theoretical support. In this talk, we providea theoretica  foundation for yolumetric stretch energy minimization (SEM to shothat a map is a precise volume-/mass-preserving parameterization from M to a regiorof a specified shape if and only if its yolumetric stretch energy reaches 3 M /2where M is the total mass of M We use VSEM to compute an  epsilon-volume-/mass-preserving map f* from M to a unit ball, where epsilon is the gap between the energyof f* and 3M/2. In addition.we prove the efficiency of the VSEM algorithm withguaranteed asymptotic R-linear convergence. Furthermore, based on the VSEM algorithm, we propose a projected gradientmethod for the computation of the epsion-volume-/mass-preserving optimal mass transport map with a guaranteed conver-the guaranteedgence rate of 0(1/m and combined with  esteroy-based acceleration.convergence rate becomes 0(1/m 2). Numerical experiments are presented to justifythe theoretical convergence behavior for variousexamples drawn from known bench-of themark models. Moreover, these numerical experiments show the effectiveness of the proposed algorithm, particularly in the processing of 3D medical MRI brain images.

Organizer

School of Mathematical Sciences, South China Normal University, Machine Learning and Optimization Computing Laboratory

Co-organizers

Guangdong Young Scientists Association

Guangdong Computational Mathematical Society