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報告題目：Image segmentation using Bayesian inference for convex variant Mumford-Shah variational model

主講人：文有為教授（湖南師范大學）

時間：2023年4月19日（周三）15:30 p.m.

地點：北院卓遠樓305會議室

主辦單位：統計與數學學院

摘要：

The Mumford-Shah model is a classical segmentation model, but its objective function is non-convex. The smoothing and thresholding (SaT) approach is a convex variant of the Mumford-Shah model, which seeks a smoothed approximation solution of the Mumford-Shah model. The idea of SaT is to separate the segmentation into two stages: a convex energy function is first minimized to obtain a smoothed image and then a thresholding technique is applied to segment the smoothed image. The energy function consists of three weighted terms and the weights are called the regularization parameters. It is important to select the appropriate regularization parameters to obtain a good segmentation result. Traditionally, the regularization parameters are usually chosen by trial-and-error, which is a very time-consuming procedure and is not practical in real applications.

In this talk, we apply Bayesian inference approach to infer the regularization parameters and estimate the smoothed image. We analyze the convex variant Mumford-Shah variational model from the statistical perspective and then construct a hierarchical Bayesian model. Mean field variational family is used to approximate the posterior distribution. The variational density of the smoothed image is assumed to have Gaussian density, and the hyperparameters are assumed to have the Gamma variational densities. All the parameters in the Gaussian density and Gamma densities are iteratively updated, hence the proposed method is parameter-free.

Experimental results show that the proposed approach can obtain good segmentation results. Although the proposed approach contains an inference step to estimate the regularization parameters, it requires less CPU running times to obtain the smoothed image comparing to previous methods.

主講人簡介：

文有為，湖南師范大學數學與統計學院教授，博導，湖南省計算數學與應用軟件學會副理事長。獲香港大學博士學位，曾在新加坡國立大學、香港中文大學從事訪問研究員、博士后等工作。主要研究方向為科學計算、數字圖像處理與計算機視覺，在SIAM J. Sci. Comput., SIAM J. Imaging Sciences, Multiscale Model. Simul., SIAM J. Matrix Anal., IEEE Trans. Image Process.等期刊發表論文30余篇，主持國家自然科學基金4項。以第一完成人身份，獲2019年湖南省自然科學獎二等獎。