学术报告
Fundamentals of Computational Conformal Geometry-顾险峰教授,Discrete Optimal Mass Transportation, Theory, ALgorithm and Applications-雷娜教授
Title: Fundamentals of Computational Conformal Geometry
Speaker: 顾险峰教授Prof. Xianfeng David Gu
简介：
顾险峰博士，于清华大学计算机系获得计算机科学与技术学士学位，哈佛大学计算机科学硕士和博士学位，师从国际著名微分几何大师丘成桐院士，现于纽约州立大学石溪分校计算机系和应用数学系任终身教授，清华大学丘成桐数学科学中心客座教授，大连理工大学海天学者。顾博士与丘成桐先生，以及国际著名数学家，计算机科学家共同创立发展了一门横跨数学和计算机科学的交叉学科：计算共形几何。计算共形几何应用现代几何理论于工程和医疗领域，特别是曲面参数化，曲面注册，人脸识别，形状分析，医学图像等等。顾博士为此获得了2013年世界华人数学家大会最高奖-晨兴应用数学金奖，美国NSF CAREER奖，NSFC 海外杰出青年基金等。顾博士著有《计算共形几何》，《离散曲面的变分原理》，《Ricci Flow for Shape Analysis and Surface Registration 》等专著。
摘要：Computational conformal geometry is an inter-disciplinary field between mathematics and computer science. This work introduces the fundamentals of computational conformal geometry, including theoretic foundation, computational algorithms, and engineering applications. Two computational methodologies are emphasized, one is the holomorphic differentials based on Riemann surface theory and the other is surface Ricci flow from geometric analysis.
The applications in Computer Graphics, Computer Vision, Geometric Modeling, Networking and Medical Imaging will be briefly covered as well.
Title: Discrete Optimal Mass Transportation, Theory, ALgorithm and Applications
Speaker: 雷娜教授Prof. Na Lei
简介：
雷娜博士，于吉林大学数学学院获得理学博士学位，现为大连理工大学软件学院教授，博士生导师，兼任中国工业与应用数学学会几何设计与计算专业委员会委员；中国数学会计算机数学专业委员会委员；美国数学会 Mathematical Review评论员；清华大学数学科学中心访问教授；曾为纽约州立大学石溪分校计算机系访问教授；德克萨斯大学奥斯汀分校计算工程与科学研究所research fellow；中科院数学与系统科学研究院访问学者。The Visual Computer, Journal of Computational and Applied Mathematics, Journal of Systems Science and Complexity, SCIENCE CHINA Mathematics等国际期刊审稿人。研究方向为：应用现代微分几何和代数几何的理论与方法解决工程及医学领域的问题，主要聚焦于计算共形几何、计算拓扑、符号计算及其在计算机图形学、计算机视觉、几何建模和医学图像中的应用
Abstract: Optimal mass transportation map transforms one probability measure to the other in the most economic way. If the domain and range are Euclidean regions, for L2 transportation cost, optimal transportation map is the gradient map of a convex energy. The equation governing the energy is the Monge-Ampere equation. In classical convex geometry, Monge-Ampere equation is closely related to Minkowski problem and Alexandrov problem. From this point of view, optimal mass transportation and Alexdrov problem are equivalent. This tutorial introduces a variational framework to solve the problem. A special convex energy is found, whose unique minimizer gives the optimal transportation map. The algorithm is closely related to upper envelope, power Voronoi diagram, power Delaunay triangulation in classical computational geometry. The discrete optimal mass transportation map offers a constructive proof for the Alexandrov theory in convex geometry. More importantly, discrete theories lead to computational algorithms, which can be applied to solve real problems, such as measure-preserving parameterization in graphics, surface/volume registration in vision, geometric clustering in pattern recognition and medical imaging.
时间：2016年9月23日（周五）13:30-16:30
地点：首都师大北二区教学楼136j教室
主办单位：
首都师范大学77779193永利官网
2011数学与信息交叉科学协同创新中心
北京成像技术高精尖创新中心
欢迎全体师生积极参加！
