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. [20] 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 [21]. Therefore, the corresponding
probability of a pixel to be boundary,
, is the
maximum probability obtained on the four possible partitions.