Mumford-shah Model Based On The Threshold

In this paper, the Mumford-Shah functional based on threshold (the threshold model) is discussed. In order to bypass the difficulty of discretizing the boundary r or the Lebesgue discontinuous set Su in the Mumford-Shah model, we use anedge-detector function and a threshold value to induce a thin-belt where the image boundary lie in and displace the length of the boundary by the area of the thin-belt approximatively.After having obtained the Euler-Lagrange equation of the threshold model, we compute this equation numerically by the method of gradient descent flows. Following a number of trials, we obtain a group of appropriate parameters and compare these data with several other groups of parameters according to the numerical results. We make some numerical experiments on images polluted by the random noises or the pepper-salt noises. The results show that the threshold model works well in denoising the random noises but works relatively poorly in denoising the pepper-salt noises.