Image Denoising by Nonlinear Diffusing on Mixed Curvature

A basic problem in the image denoising is noise pressing and edge preserving, while it is difficult to do well in the two aspects at the same time. The Partial Differential Equation (PDE) based methods, such as nonlinear diffusing method, energy minimal method and active contour method, provide a new choice. Here, focus is put on the classic Total Variation and hypersurface minimal problems, which consider regularizing term of isolevel smoothing and mean curvature. In fact, Total Variation smoothing term works well for preserving clear edges and inefficiently in plain areas, while hypersurface minimal smoothing term does well on denoising in plain areas and excessively on edges causing blurring. A projected isolevel curvature is proposed here just as the Beltrami-Laplace operator to mean curvature, considering the gradient while smoothing and keeping edge sharp effectively. And a mixed curvature of mean curvature and projected isolevel curvature forms by a weighting variable. The new denoising method based on the mixed curvature, smoothing in plain areas of image like hypersurface minimal and on edges like a projected isolevel curvature diffusing. Results of relative experiments indicate the proposed mixed curvature denoising method possesses the merits of the two original.