Stable Segmentation of Digital Image

Abstract: In the paper the optimal image segmentation by means of piecewise constant approximations is considered. The optimality is defined by a minimum value of the total squared error or by equivalent value of standard deviation of the approximation from the image. The optimal approximations are defined independently on the method of their obtaining and might be generated in different algorithms. We investigate the computation of the optimal approximation on the grounds of stability with respect to a given set of modifications. To obtain the optimal approximation the Mumford-Shuh model is generalized and developed, which in the computational part is combined with the Otsu method in multi-thresholding version. The proposed solution is proved analytically and experimentally on the example of the standard image.