A Mathematical Explanation of Unet
数学学科创建110周年系列报告
报告题目(Title)： A Mathematical Explanation of Unet
报告人(Speaker)：台雪成 (挪威研究中心）
地点(Place)：后主楼1124
时间(Time)：2025年6月26日 (周四) 下午16:50-17:30
邀请人(Inviter)：段玉萍
报告摘要
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 Unet. We explain what is the meaning and function of each of the components of Unet. We will show that Unet 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 UNet architecture. Connections between the proposed algorithm and general networks are also discussed. Our result shows that UNet 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.
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数学教授，香港浸会大学讲座教授兼数学系系主任，第8届冯康科学计算奖获得者。主要研究领域包括数值PDE、优化技术、计算机视觉以及图像处理等，在SIAM Journal on Scientific Computing, International Journal of Computer Vision, IEEE Transactions on Image Processing, IEEE Transactions on Visualization and Computer Graphics, SIAM Journal on Numerical Analysis 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。
