Recently the concept of active regions as a way to combine both region and boundary information has been introduced. Examples of this approach, called hybrid active regions, are the works of Paragios and Deriche [21], and Chakraborty et al. [22]. This model is a considerable extension on the active contour model since it incorporates region-based information with the aim of finding a partition where the interior and the exterior of the region preserve the desired image properties.
The goal of image segmentation is to partition the image into
subregions with homogeneous properties in its interior and a high
discontinuity with neighbouring regions in its boundary. With the
aim of integrating both conditions, the global energy is defined
with two basic terms. Boundary term measures the probability that
boundary pixels are really edge pixels. Meanwhile, the region term
measures the homogeneity in the interior of the regions by the
probability that these pixels belong to each corresponding region.
Some complementary definitions are required: let
be a partition of the image into
non-overlapping regions, where
is the region
corresponding to the background region. Let
be the region boundaries of
the partition
. The energy function is then defined as
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(3) |
where is a model parameter weighting both terms: boundary
and region. This function is then optimised by a
region competition algorithm [23] which takes the
neighbouring pixels to the current region boundaries
into account to determine the next movement.
Specifically, a region aggregates a neighbouring pixel when this
new classification decreases the energy of the segmentation.
Intuitively, all regions begin to move and grow, competing for the
pixels of the image until an energy minimum is reached. When the
optimisation process finishes, if there is a background region
which remains without being segmented, a new seed is placed
in the core of the background and the energy minimisation starts
again. This step allows a correct segmentation when a region was
missed in the previous stage of initialisation. Furthermore, a
final step merges adjacent regions if this causes the energy
decrease.