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学术报告
学术报告
香港浸会大学台雪成教授系列学术报告通知
发布人:系统管理员??威尼斯官方网站:2017-07-07?? 浏览次数:263

应威尼斯官方网站登录数学系邀请,香港浸会大学台雪成教授将于近期来访数学系并做一系列学术报告。欢迎感兴趣的老师和同学参加。此次活动是数学系SCI期刊编委校园行的一部分。

 

专题讲座:Variational Models and Fast Numerical Schemes in Image Processing and Computer Vision

报告时间和地点:

2017713 下午 2:003:30     正心217

2017713 下午 3:405:10     正心217

2017714 下午 2:003:30     正心217

2017714 下午 3:405:10     正心217

2017715 上午 8:3010:00   正心217

2017715 上午 10:1011:40 正心217

2017716 上午 8:3010:00   正心217

2017716 上午 10:1011:40 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 VisionSIAM J. Imaging ScienceSIAM J. Sci. Comput.IEEE Trans. on Image ProcessingIEEE Trans. on Visualization and Computer GraphicsSIAM J. Numer. Anal. 等国际顶级杂志和CVPRECCV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 MathematicsInverse Problems and ImagingAdvances in Numerical Analysis 的编辑,Numerical Mathematics: Theory, Methods and ApplicationsInternational Journal of Numerical analysis and modellingJournal of Algorithms & Computational TechnologyJournal of Information and Computing ScienceJournal of Mathematical Imaging and Vision的执行编辑。

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