The image is a set of pixels, domains are spatially compact subsets of the image. They may represent interesting parts of the scene and it is the task of segmentation to isolate them. If two domains have a common border, pixel properties at both sides of the border are different and the border can be detected. In many applications human operators perform image segmentation using their visual system. Of course they easily detect domains that are characterized by grey value, or of which the borders are characterized by difference in grey value, but they see the borders between domains of different texture just as easily.
Texture is a domain property rather than a pixel property.
There is a smallest area on which it can be defined. In order to detect a texture a test window of at least tile size must be analyzed. If the test window lies within a domain, there is no problem. If the test window is positioned over a domain border the detection will be ambiguous or will totally fail. The human visual system suppresses this and delivers as crisp borders as between grey value domains.