In this paper, we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model. We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction. This is often the case of natural images composed of both homogeneous and textured regions. Because these images cannot be in general directly processed by the gray-level information, we propose a new texture descriptor which intrinsically defines the geometry of textures using semi-local image information and tools from differential geometry. Then, we use the popular Kullback-Leibler distance to design an active contour model which distinguishes the background and textures of interest. The existence of a minimizing solution to the proposed segmentation model is proven. Finally, a texture segmentation algorithm based on the Split-Bregman method is introduced to extract meaningful objects in a fast way. Promising synthetic and real-world results for gray-scale and color images are presented.