Image segmentation and selective smoothing based on p-harmonic Mumford-Shah functional

In this work, we propose a p-harmonic Mumford-Shah (MS) functional with adaptive variable exponent 1 ≤ p(x) ≤ 2 according to image gray feature, which provides a model for image segmentation and smoothing. The paper analyzes the physical characteristics of the related p-harmonic equation in local coordinates and explains that diffusion behavior of p-harmonic is superior to that of anisotropic diffusion and isotropic diffusion in essence. Thus the proposed model is more suitable for segmentation and smoothing of noisy images with intensity inhomogeneities while simultaneously preserving edges than the piecewise smooth MS (PSMS) model. Then effective numerical scheme is constructed to handle its computation using level set method. The model is finally applied on a wide variety of image segmentation and smoothing. All these results show that the proposed model is effective.