We present an approach for unsupervised segmentation of natural and textural images based on active contour, differential geometry and information theoretical concept. More precisely, we propose a new texture descriptor which intrinsically defines the geometry of textural regions using the shape operator borrowed from differential geometry. Then, we use the popular Kullback-Leibler distance to define an active contour model which distinguishes the background and textural objects of interest represented by the probability density functions of our new texture descriptor. We prove the existence of a solution to the proposed segmentation model. Finally, a fast and easy to implement texture segmentation algorithm is introduced to extract meaningful objects. We present promising synthetic and real-world results and compare our algorithm to other state-of-the-art techniques.