Double-well Net for Image Segmentation
科研大讨论报告
报告题目(Title)：Double-well Net for Image Segmentation
报告人(Speaker)：台雪成 (挪威研究中心)
地点(Place)：#腾讯会议：523-208-021
时间(Time)：2024年6月14日 14:30-15:30
邀请人(Inviter)：王发强
报告摘要
In this study, our goal is to integrate classical mathematical models with deep neural networks by introducing two novel deep neural network models for image segmentation known as Double-well Nets. Drawing inspiration from the Potts model, our models leverage neural networks to represent a region force functional. We extend the well-know MBO (Merriman-Bence-Osher) scheme to solve the Potts model. The widely recognized Potts model is approximated using a double-well potential and then solved by an operator-splitting method, which turns out to be an extension of the well-known MBO scheme. Subsequently, we replace the region force functional in the Potts model with a UNet-type network, which is data-driven, and also introduce control variables to enhance effectiveness. The resulting algorithm is a neural network activated by a function that minimizes the double-well potential. What sets our proposed Double-well Nets apart from many existing deep learning methods for image segmentation is their strong mathematical foundation. They are derived from the network approximation theory and employ the MBO scheme to approximately solve the Potts model. By incorporating mathematical principles, Double-well Nets bridge the MBO scheme and neural networks, and offer an alternative perspective for designing networks with mathematical backgrounds. Through comprehensive experiments, we demonstrate the performance of Double-well Nets, showcasing their superior accuracy and robustness compared to state- of-the-art neural networks. Overall, our work represents a valuable contribution to the field of image segmentation by combining the strengths of classical variational models and deep neural networks. The Double-well Nets introduce an innovative approach that leverages mathematical foundations to enhance segmentation performance. This talk is based on joint work Raymond Chan, Hao Liu and Jun Liu.
主讲人简介
台雪成，挪威研究中心的首席科学家，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。台老师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)等国际顶级杂志以及CVPR、ECCV等国际顶级会议共发表论文100多篇（Google Scholar: citations 11740, h-index 51）。担任多个国际会议的大会主席，并多次应邀做大会报告，担任Inverse Problems and Imaging、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 numerical analysis等多个国际知名期刊的编辑及执行编辑。
