Algorithms Of Edge Detection Based On Mumford-Shah Model In Image Processing

21th century is an era of information expanding. As the basis of people feeling and knowing the world, images are the major tools by which we get, impress and transfer the information. Images processing is the technology, which images are analyzed and computed by computers, so that we can get the results of what we need. Edge Detection is a significant part in image processing, because edges are dividing lines of background and target of what we extract. Only extracting the edges can we separate the target and background. So studying algorithms of edge detection based on Mumford-Shah(MS) model in image processing shows a big significance.In this paper, we proposed a Modified Mumford-Shah(MMS) model with L1-norm according to the classical MS model and the previous MMS model with L2-norm and constructed theoretical derivation and numerical experiments to this new model. First, we use fixed point iteration in the process of getting recovered image. In the following step of extracting the edges, two famous algorithms are used:Proximity Method and Split Bregman(SB) Method. Besides, with the purpose of accelerating the speed of iteration, we apply Threshold and Truncation method so that we get the results more fast and accurate. As for the numerical experiments, comparisons between the new proposed model and the famous Ambrosio-Tortorelli(AT) model are made. According to the experiments, we found not only MMS model with L1 norm could remove the noise better, but also showed more clear edges to the impulse noise. Another experiment is we integrate the two optimized methods with the above two algorithms. From the images and tables, we observe the algorithms with optimized methods can protect more edges and reduce times of iteration so that improve computational efficiency. Besides, proof of convergence of our model are given.