It is well know that the extraction of boundary information for textured images is a very tougher task. On the other hand, human performance in localising texture edges is excellent, if (and only if) there is a larger patch of texture on each side available. Hence, as Will et al.  noted, texture model of the adjacent textures are required to enable precise localisation. The previous initialisation step of the regions model allows to dispose of this required knowledge and to extract accurate boundary information.
We shall consider that a pixel constitutes a boundary between two adjacent regions, and , when the properties at both sides of the pixel are different and fit with the models of both regions. Textural and colour features are computed at both sides (referred as and its opposite as ). Therefore, is the probability that features obtained in the side belong to region , while is the probability that the side corresponds to region . Hence, the probability that the considered pixel is boundary between and is equal to , which is maximum when is exactly the edge between textures and because textures at both sides fit better with both models.
Four possible neighbourhood partitions (vertical, horizontal and two diagonals) are considered, similarly to the method of Paragios and Deriche . Therefore, the corresponding probability of a pixel to be boundary, , is the maximum probability obtained on the four possible partitions.