报告题目 (Title)：保度计算几何与脑肿瘤影像处理
报告人 (Speaker)：林文伟 教授（上海数学与交叉学科研究院）
报告时间 (Time)：2026年6月4日（周四）10:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：王卿文
主办部门：理学院数学系
报告摘要：
In this talk, we first introduce the conformal parametrization (CP) and the equiareal (area-preserving) parametrization (EP) between a 2D-surface and a sphere or a disc. We propose a conformal energy minimization (CEM) and a stretch energy minimization (SEM) with southern and northern hemisphere alternating iteration techniques to compute CP and EP, respectively, and show both CEM and SEM have asymptotically R-linear convergence. For 3D manifolds, we introduce a volume stretch energy minimization (VSEM) to find a volume-preserving parametrization (VPP) between a 3D manifold and a ball or a cube. We prove that the set of volume-stretch energies of all orientation preserving functions has a minimum m_0, and f_* attain the minimum if and only if f_* is volume-/mass-preserving. For applications in medical images, we first introduce the volume optimal mass transport (VOMT) problem and develop the projected gradient method for VOMT to efficiently find a OMT map between a 3D irregular domain and a ball or a cube. We efficiently apply the VOMT method on brain tumor segmentation in MICCAI 2023 international challenges and successfully get the top-ranking results.
