Edge Preserving Regularization for the Piecewise Smooth Mumford-Shah Model

In this paper, an improved segmentation algorithm for the piecewise smooth Mumford-Shah model is proposed. In which a new strategy for the computation of the diffusion item in the model is introduced that induces edge-preserving regularization thus also facilitate the image segmentation. Different from the previous approaches, at each iteration, the smoothing item in proposed algorithm is computed along an approximate contour that is obtained based on the difference between the two unknown functions u and u" that have been extended to the whole image domain. And a narrowband of the approximate contour also is given to reduce the area of the region to be smoothed. As a result, good edge preserving properties have been achieved. The improved approach not only addresses some drawbacks of the original algorithm such as the effect of the local characteristics of images on the curve evolving path and initial curve\´s effect on the segmentation results, but save computational cost greatly. The resulting algorithm has been implemented with Visual C++6.0, and several experimental results have been provided and compared with the original method. The result demonstrated the effectiveness of the proposed algorithm.