Title:  
Modeling, Analysis and Numerical Approximations of Image Processing 
and Computer Vision Problems: PDE and Variational Approach

Abstract: 
Image processing and computer vision have been traditional engineering 
fields, which have a broad range of applications in science, engineering 
and industry. Not long ago, statistical and ad hoc methods had been main tools 
for studying and analyzing image processing and computer vision problems. 
Recently, a new approach based on PDE and variational methods has emerged 
as a more powerful approach. Compared with old approaches, PDE and variational 
methods have remarkable advantages in both theory and computation. It allows 
to directly handle and process visually important geometric features 
such as gradients, tangents and curvatures, and to model visually 
meaningful dynamic process such as linear and nonlinear diffusions. 
Computationally, it can greatly benefit from the existing wealthy numerical 
methods for PDEs. Besides the practical advantages, the PDE and variational
approach also poses many new interesting and challenging mathematical problems 
in the areas of Calculus of Variation, PDE, Geometry and Computational Math. 
In this talk, I will first give a brief introduction to image processing 
and computer vision, and then highlight some recent developments 
on PDE and variational methods and their numerical approximations
for image processing and computer vision problems. The underlying 
mathematical problems and the required analytical and numerical tools 
for tackling those problems will be emphasized in the talk.