应数学系邀请，挪威卑尔根大学和香港浸会大学台雪成教授，英国利物浦大学陈柯教授及香港中文大学Ronald Lok Ming Lui副教授将于近日来访我校，参加图像处理冬季论坛并做系列报告，以下是报告信息，欢迎感兴趣的师生参加。

报告时间和地点：2019年1月19日（星期六）上午 8:00开始格物楼 503

报告题目：A New Operator Splitting Method for Euler’s Elastica Model

报告人：台雪成

摘要：Euler’s elastica model has a wide range of applications in Image Processing and Computer Vision. However, the non-convexity, the non-smoothness and the nonlinearity of the associated energy functional make its minimization a challenging task, further complicated by the presence of high order derivatives in the model. In this article we propose a new operator- splitting algorithm to minimize the Euler elastica functional. This algorithm is obtained by applying an operator-splitting based time discretization scheme to an initial value problem (dynamical flow) associated with the optimality system (a system of multivalued equations). The sub-problems associated with the three fractional steps of the splitting scheme have either closed form solutions or can be handled by fast dedicated solvers. Compared with earlier ap- proaches relying on ADMM (Alternating Direction Method of Multipliers), the new method has, essentially, only the time discretization step as free parameter to choose, resulting in a very robust and stable algorithm. The simplicity of the sub-problems and its modularity make this algorithm quite efficient. Applications to the numerical solution of smoothing test problems demonstrate the efficiency and robustness of the proposed methodology.

报告题目：On variational models in Image Registration and their iterative methods

报告人：陈柯

摘要：In this talk we present three related variational models in image registeration (which is one of the major problems in image analysis) and discuss the application of the Gauss-Newton and ADMM framework.  The first model, based on the H1 seminorm regulariser, is commonly used and the latter two with newer and more elaborate control terms are refined models of the first that deliver a diffeomorphic map.

Such models, typical in registration, are challenging to analyse and solve, due to nonconvexity. We propose an ADMM for solving these models.

Initial results show that ADMM can speed up a Gauss-Newton solver by more than 50% for the first model while for the other two models the work is in progress. Some numerical results are shown.

报告时间和地点：2019年1月20日（星期日）上午 8:00开始格物楼 503

报告题目：Shape matching via quasiconformal maps

报告人：Ronald Lok Ming Lui

摘要：Shape matching is a process of finding meaningful dense correspondences between 3D shapes. It has important applications in imaging, computer graphics and visions. Quasiconformal theories provide a useful tool to compute shape matching with high accuracy, even if two shapes differ by a large deformation. In this talk, we will explore how quasiconformal maps can be used to tackle different shape matching problems, including the computation of large deformation shape registration, inconsistent shape matching and folded deformation. This work is support by HKRGC GRF (Project ID: 14304715).

报告人简介：台雪成，挪威卑尔根大学教授和香港浸会大学教授，第8届“冯康”计算数学奖获得者。台雪成教授的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，在SIAM J. Sci. Comput.、International Journal of Computer Vision、IEEE Transactions on Image Processing、IEEE Transactions on Visualization and Computer Graphics、SIAM J. Numer. Anal.等国际顶级杂志以及CVPR、ECCV等国际顶级会议共发表论文100多篇。担任多个国际会议的大会主席，并多次应邀做大会报告，目前担任Inverse Problems and Imaging，International Journal of Numerical analysis and modelling，Numerical Mathematics: Theory, Methods and Applications，Advances in Numerical Analysis, SIAM Journal on Imaging Sciences, Journal of Mathematical Imaging and Vision等多个国际知名期刊的编辑及执行编辑。

报告人简介：陈柯，英国利物浦大学终身教授，英国IMA Fellow、御批数学家。陈柯教授作为CMIT和LCMH创新团队负责人，主要研究方向为计算数学、应用数学、图像处理、医疗应用等，在SIA M Journal on Imaging Sciences、IEEE Transactions on Image Processing、Journal of Computationa
l Physics等国际权威期刊上发表超过170余篇学术论文。目前担任Numerical Algorithms，Journal of Mathematical Research and Exposition，Journal of Applied Mathematics ，International Journal of Computer Mathematics，Journal of Mathematical Research with Applications等多个国际知名期刊的编辑及执行编辑。

报告人简介：Ronald lok ming lui,香港中文大学副教授, 是计算数学与科学工程计算、图像处理与分析领域国际知名的青年学者。因其在科学计算方面的突出成就，曾获得晨兴数学银奖，香港数学学会“青年学者奖”。首次提出并分析了基于黎曼表面结构的参数化方法，该方法在医学图像领域被广泛引用并推广。他的研究兴趣包括保角几何计算，医学图像处理，数学形态分析等。他在相关研究领域中做出了杰出贡献，在国际高水平期刊和会议上发表了70余篇的学术论文，已成为其研究领域内年轻学者中的领军人物。