Philosophically speaking, it is impossible to define the goal of a texture segmentation algorithm, even if the question is restricted to one image taken from the natural world. Furthermore, our understanding of what constitutes a textured region is very limited, and no current model is expressive enough to cover the diversity of textures that one might encounter. Texture segmentation is not object segmentation; the human experience of observing a two-dimensional scene of textures and transforming it into a three- dimensional model of the physical world is quite different than the computer's experience through algorithms.
Nevertheless, texture does exist, it can be segmented to some extent, and much research is being conducted in this area, so it is equally fruitless to claim that nothing can be done. There are two general and currently popular approaches to the problem. One is to apply a bank of filters to an image, each one contributing one value to a feature vector. The other is to assume the pixel values belong to a probability distribution and to estimate the parameters of the distribution. Both operations involve local computations over large windows in an image.
From there the goal is to assign labels to feature vectors, each of which corresponds to a pixel in the image. This can be done by either pre-computing a set of representative vectors which partition the feature space into classes, or by using methods from statistics to perform clustering. In either case, attention must be paid to the image itself so that the final regions formed satisfy the implicit expectations of ``niceness'' that humans carry with them.