Variational Partial Differential Equations and Implicit Geometry
Student No.:50
Time:Thu./Fri. 08:00-09:50
Instructor:Ye Duan  [University of Missouri - Columbia]
Place:Conference Room 3, Floor 2, Jin Chun Yuan West Building (近春园西楼)
Starting Date:2012-7-12
Ending Date:2012-8-10

Course description:
Variational Partial Differential Equations (PDEs) and Implicit Geometry are emerging techniques for representing, deforming, and recovering structures in an arbitrary dimension across different fields (such as mathematics, fluid dynamics, graphics, imaging, and vision). Advances in numerical analysis have led to computationally efficient tools for computing and analyzing interface motion within variational PDEs frameworks in a host of application settings. This course will introduce students to both the theoretical foundations and technical aspects of implicit geometry and level set methods as well as the state-of-the-art in applying variational PDEs techniques in areas such as medical imaging, computer animation, computer graphics, computer vision and virtual reality, etc. We will explore current research issues and will cover in depth the associated computational and numerical techniques. This course should be appropriate for graduate students in all areas as well as advanced undergraduate students.


Calculus, Linear Algebra


Reference for the course:
[1]. Level Set Method and Dynamic Implicit Surfaces (2003), by S. Osher and R. Fedkiw.
[2]. Level Set Methods and Fast Marching Methods (1996, 1999), by J. Sethian.
[3]. Geometric Level Set Methods in Imaging, Vision, and Graphics, Stanley Osher, Nikos Paragios, Springer, 2003.
[4]. Geometric Partial Differential Equations and Image Analysis, Guillermo Sapiro, Cambridge University Press, 2001.
[5]. Handbook of Mathematical Models in Computer Vision, Nikos Paragios, Yunmei Chen, Olivier Faugeras, Springer 2006.
[6]. Image Processing and Analysis - Variational, PDE, wavelet, and stochastic methods, Tony F. Chan and Jianhong (Jackie) Shen, SIAM 2005.
[7]. Mathematical Problems in Image Processing, Gilles Aubert and Pierre Kornprobst, Springer 2001.