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Abstract
This paper presents an improved algorithm for the partial differential equation (PDE)-based piecewise smooth Mumford–Shah approach, in which we integrate Mumford–Shah segmentation with the anisotropic diffusion, leading to better edge preserving regularization. Considering that the energy function in the piecewise smooth Mumford–Shah functional is non-convex, evolution of the curve does not completely depend on the global properties of the image, and some local information also affects the segmentation result. Based on this idea, the anisotropic diffusion is integrated into it to enhance boundaries and denoising, and the edges (high gradient points) are smoothed at the isophote direction. Consequently, the problems such as low convergence rate and boundary leakage can be solved. Compared with previous works, since the smoothing operation is calculated only within the narrowband domain around the evolving curve, it is not expensive computationally. The proposed algorithm has been implemented and tested by several cases, and promising results are obtained.