Research On Edge Detection Method Based On Mumford-Shah Model

Digital image processing first appeared in 1950s, followed by the development of the computer. It is mainly through the computer to analyze and calculate the image. However, the amount of digital image data is very large, which contains a lot of irrelevant information, how to extract the basic and constant information from a large amount of data is one of the basic techniques of digital image processing. And the edge of the image is often carrying the majority of information of the image. Therefore, the edge of the image has an important impact for image processing. The image edge detection algorithm based on Mumford-Shah (MS) model has important significance in image processing.In this paper, we propose our new model based on the classical MS model, and integrate the Modified Mumford-Shah (MMS) model proposed by Wang et al., as well as the two improved models proposed by Shi et al. which were based on the MMS model. We also carried out the relevant theoretical derivations and numerical experiments. We use the fixed point iteration method when we get the recovery image, and we use the Proximity algorithm to calculate the edges. Finally, in the numerical experiments, we compare with the classical Ambrosio-Tortorelli (AT) model and the original model. We find that our model is more stable and the edges obtained by our model are more efficient, continuous and clear.