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讲座题目：Global And Local Segmentation Of Images By Numerical Partial Differential Equations  

时间：12月24日上午10:00---12:00 

地点：理科楼407 

摘要：The imaging science as a research field is increasingly used in many disciplines (Mathematics,Statistics, Physics, Chemistry, Biology, Medicine, Engineering, Psychology, Computer and Information Science etc) because the imaging technology is   developed in a fast pace and widely available (with cost down and resolution up). The advance in imaging brings unprecedent challenges and demands on better image analysis techniques based on optimization, geometry and nonlinear partial differential equations, beyond the traditional filtering based linear techniques (FFT, wavelets,Wiener filters etc). Of course, in addition to modeling and analysis, there is an urgent need for advanced, accurate and fast omputational algorithms.
In this talk I shall first discuss variational models that are frequently used for detecting global
features in an image i.e. all objects and their boundaries. These include the Chan-Vese (2001) model of the Mumford-Shah (1989) type and other related models.
Such models lead to nonlinear partial differential equations (PDEs).  Since they are defined in a square domain, the finite difference method is commonly used. The uniqueness of PDEs is usally studied in convex analysis.  The issue of reformulating the non-convex model as a convex one is addressed. I then present some newer models that are designed to incorporate geometric constraints and detect local features in an image i.e. local objects and their boundaries. This kind of tasks is frequently met in medical imaging.  Finally I consider one way of reformulating the non-convex and local model as a convex one. 

报告人简介：陈柯，1962 年11 月出生于河南南阳. 79-83 年取得大连理工大学应用数学学士,85-86 年取得英国Manchester 曼彻斯特大学数值分析和计算硕士,87-90 年英国Plymouth 普利茅斯计算数学博士学位. 90-92 年间在英国Reading 里丁大学数学系进行博士后研究. 93 年直今就职于英国利物蒲大学数学科学系: 93 讲师,2001 高级讲师,2004 Reader, 2007 年起,升为正教授. 99-05年间每年定期访问加州大学洛衫矶分校和TＦChan教授合作.
他的研究领域为计算数学, 其国际领先的方向是微分方程数值中大型方程组的快速迭代算法.已发表了150 多篇学术文章,其中有90多专业杂志文章.另有剑桥大学出版社2005 年出的专著”矩阵预处理技术与应用”. 他于1995 年评为Chartered Mathematician 御批数学家; 2004 以来任7个国际数学杂志的编委(包括Springer的Numerical Algorithms)。2006 年起任英国国家工程和物理基金会评委; 2008 年5 月年兼利大”数学图像技术研究中心”主任. 他和北京中科院数学院, 九所,大连理工大学,复旦大学和香港中文大学有合作联系. 2007 年被大连理工大学聘为海天学者,博导; 2008 年起已在大工招收了三名博士生. 98 年直今已成功指导了13位博士生完成学位，目前带有5名在读博士生。2010年被评为利物蒲大学21位跨学科领军Champions人才之一。
个人网页：//www.liv.ac.uk/~cmchenke/  

欢迎各位教师、研究生和高年级的学生参加。