Nonparametric Statistical Level Set Snake Based on the Minimization of the Stochastic Complexity

In this paper, we focus on the segmentation of objects not necessarily simply connected using level set snakes and we present a nonparametric statistical approach based on the minimum stochastic complexity principle. This approach allows one to get a criterion to be optimized with no free parameter to be tuned by the user. We thus propose to estimate the probability law of the gray levels of the object and the background of the image with a step function whose order is automatically determinated. We show that coupling the probability law estimation and the segmentation steps leads to good results on various types of images. We illustrate the robustness of the proposed nonparametric statistical snake on different examples and we show on synthetic images that the segmentation results are equivalent to those obtained with a parametric statistical technique, although the technique is nonparametric and without ad hoc parameter in the optimized criterion.