Texture Segmentation is one of the most challenging areas of computer vision. One reason for this difficulty is the huge variety and variability of textures occurring in real world, making it very difficult to quantitatively study textures. One of the key tools used for texture segmentation is local invariant descriptors. Texture consists of textons, the basic building block of textures, that may vary by small nuisances like illumination variation, deformations, and noise. Local invariant descriptors are robust to these nuisances making them beneficial for texture segmentation. However, grouping dense descriptors directly for segmentation presents a problem: existing descriptors aggregate data from neighborhoods that may contain different textured regions, making descriptors from these neighborhoods difficult to group, leading to significant errors in segmentation. This work addresses this issue by proposing dense local descriptors, called Shape-Tailored Features, which are tailored to an arbitrarily shaped region, aggregating data only within the region of interest. Since the segmentation, i.e., the regions, are not known a-priori, we propose a joint problem for Shape-Tailored Features and the regions. We present a framework based on variational methods. Extensive experiments on a new large texture dataset, which we introduce, show that the joint approach with Shape-Tailored Features leads to better segmentations over the non-joint non Shape-Tailored approach, and the method out-performs existing state-of-the-art.