2017年7月13日 下午 2:00—3:30     正心217

2017年7月13日 下午 3:40—5:10     正心217

2017年7月14日 下午 2:00—3:30     正心217

2017年7月14日 下午 3:40—5:10     正心217

2017年7月15日 上午 8:30—10:00   正心217

2017年7月15日 上午 10:10—11:40 正心217

2017年7月16日 上午 8:30—10:00   正心217

2017年7月16日 上午 10:10—11:40 正心217

报告摘要：This course will introduce a number of problems in image processing and computer vision, and describe how they can be tackled by modern techniques based on calculus of variations and partial differential equations. We will focus especially(but not exclusively) on image reconstruction (denoising, deblurring, inpainting, as well as some inverse problems) and image segmentation. These procedures are fundamental in many applications, such as medical imaging and target recognition. Numerical solution of the models, which involve minimizing appropriate energies (often by solving associated partial differential equations) will be a major concern of the course: A variety of numerical techniques for this purpose, including level set and diffuse interface methods for evolving curves and surfaces, will be introduced and covered in detail. In addition, important theoretical questions about the various models and how they have been answered will be presented. We will try to cover some of the newest developments for these problems which have not been covered in any other standard text book.

Tentative outline.

1. Mathematical preliminaries.

(1)Some elementary partial differential equations.

(2)Basic about minimization and calculus of variations

(3)Functions of bounded variation.

2. Image restoration, inpainting and deblurring.

(1)The total variation model of Rudin, Osher, and Fatemi.

(2)Mumfor-Shah model

(3)Euler's Elastica model

(4)Higher oder methods of PDE nonlinear filters.

(5)Other geometrical models for image filters.

3. Fast numerical schemes

(1)Gradient decent method.

(2)Operator splitting and AOS schemes

(3)Dual approaches.

(4)Split-Bregman.

(5)Augmented Lagrangian approach.

(6)Other fast minimization approaches for image processing.

4. Image segmentation and geometrical PDEs

(1)Geodesic active contours; implementation using level-sets.

(2)Mumford-Shah and Chan-Vese models using level-sets.

(3)Piecewise Constant Level set method.

(4)Graph cut approach for interface problems and image segmentation.

(5)Recent fast numerical schemes and global minimizations

(6)Discussion of a few other vision problems.

报告人简介：

台雪成，香港浸会大学教授，挪威卑尔根大学数学系终身教授，挪威奥斯陆大学和挪威CIPR研究中心兼职教授，计算数学与科学工程计算、图像处理与分析领域国际知名学者。因其在科学计算方面的突出成就，曾获得第八届冯康奖。台教授研究领域主要包括数值PDE、优化技术、计算机视觉以及图像处理等，他在International Journal of Computer Vision、SIAM J. Imaging Science、SIAM J. Sci. Comput.、IEEE Trans. on Image Processing、IEEE Trans. on Visualization and Computer Graphics、SIAM J. Numer. Anal. 等国际顶级杂志和CVPR、ECCV等国际顶级会议上共发表论文100多篇，担任多个国际会议的大会主席，目前担任East Asia J. of Applied Mathematics、Inverse Problems and Imaging、Advances in Numerical Analysis 的编辑，Numerical Mathematics: Theory, Methods and Applications、International Journal of Numerical analysis and modelling、Journal of Algorithms & Computational Technology、Journal of Information and Computing Science、Journal of Mathematical Imaging and Vision的执行编辑。