Bayesian-Inference-Based Convex Variant Mumford-Shah Model For Image Segmentation

In the research and application of images,people often only focus on a specific area of the image.In order to identify and analyze the area,we need to extract the area from the image,which is image segmentation.In recent years,with the development of medical,artificial intelligence,remote sensing and other fields,it has become very important to extract important information from images.As we all know,when we want to study a problem,our first task is to choose a suitable model.This article mainly studies the Mumford-Shah image segmentation model.The Mumford-Shah model is one of the most important image segmentation models,and has been extensively studied in the past thirty years.At present,many algorithms based on the Mumford-Shah model can get better segmentation results.However,these algorithms usually require repeated manual adjustments of model parameters to achieve better results.Therefore,there is a problem which is parameters need to be adjusted before segmentation each time for different images.This process not only wastes time,but also prevents the algorithm from performing well in practical applications well.In response to this problem,this paper studies how to handle the Mumford-Shah model and its parameter estimation.First,the article use a convex variant Mumford-Shah model for image segmentation,and then re-model the model from the perspective of probability distribution.Specifically,this paper treats the solution of the model and the parameters of the model as random variables.According to some prior information,the Bayesian theorem is used to obtain the posterior distribution of the solution of the model and the model parameters.When calculating the posterior distribution,we use the variational approximation method,and then use the alternate iteration method to obtain the optimal solution of the model and estimated parameters.In addition,for the optimization of the model solution,this article considers the primal dual proximal point algorithm for optimization,and for the estimation of the parameters,this article directly uses the properties of the Gamma distribution.Finally,we choose K-means clustering to obtain image segmentation results.Experimental results show that the method in this paper can still achieve a good segmentation results without manually adjusting the parameters.