Image Processing Reference
In-Depth Information
S H i
j
H i
S P ,
S P = {
H i } i = 1 , 2 ,..., p ,
S H i = {
} j = 1 , 2 ,..., p
(9.6)
are merged into one region if
S H i
j
ρ (
P
,
H i
)=
j = 1 , 2 ,..., k ρ (
max
H i
,
) ,
H i
M B
,
H i
M O
(9.7)
where
is the similarity measurement. M B and M O are the marker regions la-
beled as background and object respectively. N is the non-marker region set.
S Q
ρ
S i } i = 1 , 2 ,..., q is the formed set of Q 's adjacent regions. Obviously, this two-
stages process suffers from the complex implementation.
Considering the merit of CA based segmentation that can resolve complex tasks
with very simple implementation (evolution rule), a novel Regional Cellular Au-
tomaton merging (RCA) rule is presented to facilitate the region merging and
overcome the shortcoming of traditional pixel-wise method [10]. In the proposed
scheme, an initial mean shift segmentation is required to partition the image into
homogeneous regions. After desired object or background regions are labeled with
colored markers, the adjacent regions will be iteratively merged and labeled as ob-
ject or background. Once all the non-marker regions are classified correctly, the
object contour can then be readily extracted.
RCA tries to merge similar regions as many as possible until no merging oc-
curs (keeping a stable state). After pre-segmentation, the available regions are set
as cells in CA system, and the neighborhood is the adjacent region. This discrete
dynamical system consists of homogeneous cells that are synchronously updated in
discrete time steps t . The RCA scheme is summarized as: Each segmented homoge-
neous region (cell) p is assumed to have a eight-cell Moore neighborhood denoted
by N p = {
= {
q i } i = 1 , 2 ,..., 8 . At each time step t
+
1, a cell p
N p takes one of k possible
states considering its current state
p and that of neighbor cells. The cell state is up-
dated according to a transition function
σ
based on regional similarity. At start time
t 0 the cell states are set according to user imposed labels. Here k
Φ
.
The RCA segmentation is an evolving processing with regions attacking and merg-
ing rule.
After user marking, the marker regions cover only a small part of the object and
background. To completely extract the object contour, we need to automatically as-
sign each non-marker region with a correct label as either object or background.
Therefore, in the automatic region merging process, those regions that belongs to
the same class should be identified with highest probabilities and not be merged
with regions that belong to different class.
For the convenience of the following development, the set of marker and non-
marker regions are denoted as M and M respectively. Let q i be an adjacent region
of p and denoted by N p = {
=
2and
σ
∈{
0
,
1
}
p
q i } i = 1 , 2 ,..., k ,thesetof p 's adjacent regions. To guide the
following region merging process, Bhattacharyya coefficient [6] is used as regional
similarity descriptor. The Bhattacharyya coefficient is defined as:
Hist p · Hist q i
q i )=
θ (
p
,
(9.8)
 
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