讲座题目：A Mathematical Explanation of U-Net

主讲人：台雪成

讲座时间：2025年1月2日 上午10:00

讲座地点：龙湖校区国际教育学院国际会议室306

主讲人简介：台雪成，挪威研究中心首席科学家，曾任挪威卑尔根大学教授和香港浸会大学讲座教授和系主任，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，IJCV，IEEE Trans.（TIP，TOG）等国际等级杂志以及CVPR、ECCV等国际顶级会共发表论文200多篇（Google Scholar：citations 11740，h-index 51）。担任多个国际会议大会主席，并多次应邀做大会报告，担任 Inverse Problems and lmaging、International Journal of Numerical Analysis and Modelling、Advances in Continuous and Discrete Models: Theory and Applications、 Advances in Numerical Analysis、SIAM Journal on Imaging Sciences、Journal of Mathematical Imaging and Vision、SIAM Journal on Numerical Analysis等多个国际知名期刊的编辑及执行编辑。

内容摘要：The U-Net architecture has transformed image segmentation. U-Net’s versatility and accuracy have driven its widespread adoption, significantly advancing fields reliant on machine learning problems with images. In this work, we give a clear and concise mathematical ex- planation of U-Net. We explain what is the meaning and function of each of the components of U-Net. We will show that U-Net is solving a control problem. We decompose the control variables using multigrid methods. Then, operator-splitting techniques is used to solve the problem, whose architecture exactly recovers the U-Net architecture. Connections between the proposed algorithm and general networks are also discussed. Our result shows that U-Net is a one-step operator-splitting algorithm for the control problem. This talk is based on joint works with: Liu Hao, Raymond chan and Lingfeng Li.

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研究生处、数学与信息科学学院

2024年12月26日