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報(bào)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(xué)）

時(shí)間：2023年4月19日（周三）15:30 p.m.

地點(diǎn)：北院卓遠(yuǎn)樓305會(huì)議室

主辦單位：統(tǒng)計(jì)與數(shù)學(xué)學(xué)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(jiǎn)介：

文有為，湖南師范大學(xué)數(shù)學(xué)與統(tǒng)計(jì)學(xué)院教授，博導(dǎo)，湖南省計(jì)算數(shù)學(xué)與應(yīng)用軟件學(xué)會(huì)副理事長(zhǎng)。獲香港大學(xué)博士學(xué)位，曾在新加坡國(guó)立大學(xué)、香港中文大學(xué)從事訪問(wèn)研究員、博士后等工作。主要研究方向?yàn)榭茖W(xué)計(jì)算、數(shù)字圖像處理與計(jì)算機(jī)視覺(jué)，在SIAM J. Sci. Comput., SIAM J. Imaging Sciences, Multiscale Model. Simul., SIAM J. Matrix Anal., IEEE Trans. Image Process.等期刊發(fā)表論文30余篇，主持國(guó)家自然科學(xué)基金4項(xiàng)。以第一完成人身份，獲2019年湖南省自然科學(xué)獎(jiǎng)二等獎(jiǎng)。