Fast Image Segmentation with Lv Distance between Local Cumulative Histograms

This paper presents two new region-based active contour models in a variation framework for image segmentation. In these models, to quantify the similarity measurement between two regions, we propose to compare their respective cumulative histograms with theL_1, L_2, L_∞ distances which are often applied in image comparison. For example, to compute the similarity, the Kolmogorov-Smirnov test by using the L_∞ distance is the most popular one. Our first energy model is based on minimizing L_v distance between two cumulative histograms of different regions, together with a geometric regulation term that penalizes the length of region boundaries. The second model is the localization of the first model with the popular local method. To solve these models, we describe a fast minimization algorithm with the Split-Bregman method, which can find the global minimizer. Finally, to illustrate the robust and accurate segmentations with the proposed models, we show some experimental results on some images.