快速发展的信息科学和医学科学技术加速了计算机技术在医学领域的应用。作为一种普便存在的曲面结构，曲面共形结构的计算研究可以帮助医学图像处理中曲面注册及形态分析的计算。同时，基于李代数的多元张量分析也为我们提供了一种稳定的形态学比较的研究工具。我将简单汇报近几年来我与我的同事们在应用共形几何和基于多元张量计算的形态学分析在人类核磁共振脑图自动化信息处理的若干心得。
Historically, biology and medicine have been primarily descriptive science.  The rapid advance of information and medical technology will accelerate the trend towards more quantitative science and help achieve an integrated understanding of anatomy, genetics and illness prevention and treatment. Mathematically, all metric oriented surfaces have conformal structures and can be corformally mapped to either sphere, Euclidean plane or the Poincaré disk. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable. It provides a rigorous framework for representing, matching and measuring general surfaces. The obtained conformal grids are beneficial for PDE-based signal processing and the induced conformal invariants - the Teichmüller space coordinates and Beltrami coefficients are stable shape indices for statistical analysis. In this talk, I will introduce how to apply conformal geometry and multivariate tensor-based morphometry (MTBM) to analyze brain structures effectively. With harmonic energy minimization, holomorphic 1-form and discrete curvature flow (Ricci/Yamabe flow) methods, we can parameterize brain surfaces onto various canonical domains for brain surface registration. I will also show that the analysis of parametric brain surfaces can be made more powerful by analyzing the full multivariate information on surface morphometry.  Applications on structural MRI image analysis of Alzheimer’s disease, HIV/AIDS, Williams syndrome, childhood acute Leukemia, preterm baby, imaging genetics, and Schizophrenia will be discussed.

王雅琳博士现任亚利桑那州州立大学计算机科学系助理教授。他分别于1994 和1996年从我系获得学士和硕士学位（硕士导师：唐龙教授）。他于2002年于美国华盛顿大学（Univ. of Washington）电机工程系获得博士学位（博士导师：Robert Haralick）。毕业后，他曾师从丘成桐和陈繁昌教授进行博士后研究。他目前从事计算机视觉方向的研究并已经发表了80余篇学术论文（个人网页：http://gsl.lab.asu.edu）。
Dr. Yalin Wang is an assistant professor at School of Computing, Informatics, Decision Systems Engineering and an affiliate assistant professor in the BioDesign Institute at Arizona State University.  He got his MS and BS in Computer Science at Tsinghua Univ. in 1996 and 1994, respectively. He got his PhD degree in Electrical Engineering at Univ. of Washington in 2002 (adviser: Robert Haralick). He took his postdoc training with the Fields medalist, Shing-Tung Yau and Dr. Tony F. Chan, the current president of Hong Kong University of Science and Technology. He was a cofounder and served as the CTO of Geometric Informatics, Inc. between 2004 and 2008. He was also a founding member and key investigator at UCLA Center for Computational Biology. Currently, his research focuses on the engineering applications of differential geometry, medical imaging, and clinical aspects of neuroimaging and brain mapping. He has published over 80 peer-reviewed technical papers (more information is available at http://gsl.lab.asu.edu).