In this paper, we propose a new framework for Binary Active Contours (AC) that incorporates a new texture descriptor. The texture descriptor is split into inside/ outside region descriptors. Both the inside and outside texture descriptors discriminate the texture using Kullback-Leibler distance. Using these two descriptors, the AC incorporates both learned textures. This formulation has two main advantages. Firstly, by discriminating independently the foreground/background textures. Secondly, by incorporating both the learned inside/outside texture. Our segmentation model based AC model is formulated in Total variation framework using characteristic function framework. We propose a fast Bregman split implementation of our segmentation algorithm based on the primal-dual formulation. Finally, we show results on some challenging images to illustrate texture segmentations that are possible.