“高顿杯”数学文化节报告

报告题目：Convex Shape Prior with Sublevel Set Representation and it’s Applications on CNN Image Segmentation

主 讲 人：刘 君

单 位：北京师范大学

时 间：11月5日14:00

腾 讯 ID：435 289 681

摘 要：

Convolutional Neural Networks (CNN) can well extract the features from natural images. However, the classification functions in the existing network architecture of CNNs are always simple and lack capabilities to handle important spatial information in a way that have been done for many well-known traditional variational models. Priors such as spatial regularization, object shapes and topology priors cannot be well handled by existing CNN architectures. We propose a novel Soft Threshold Dynamics (STD) based framework which can easily integrate many priors such as local and nonlocal image edges information, star/convexity shapes, topology priors (connectivity and holes) of the classic variational models into the DCNNs for image segmentation. The novelty of our method is to interpret the activation functions (including softmax, sigmoid, ReLU) as primal-dual variational problem, and thus many priors can be imposed in the dual space. By unrolling method, we can build several STD based network architectures which can enable the outputs of CNN to have many special priors. The proposed method is a general framework and it can be applied to any image segmentation CNNs. We will give some applications to show the efficiency of our method.

简 介:

刘君，北京师范大学副教授，博士生导师。曾受邀访问过美国UCLA、新加坡南洋理工、香港科技大学、香港浸会大学等高校。主要研究方向为变分法及深度学习相关的图像处理算法与应用。一些研究结果发表在图像处理与计算机视觉相关领域国际知名期刊如Int. J. Comput. Vis., IEEE T. Image. Process., IEEE T. Geosci. Remote, Pattern Recogn., SIAM J. Imaging Sci., J. Sci. Comput., J. Math. Imaging Vis. 等。研究成果曾获教育部高等学校优秀科研成果二等奖（团体）, 北京市科技进步奖二等奖（团体）。主持参与多项国家科研项目。