Image Processing Reference
In-Depth Information
2
13
12
6
10
4
7
15
11
9
Update
partitions
3
1
8
Exit?
Start
Update
centers
5
14
Fig. 16.3. The graph on the
left
represents some feature vectors to be clustered. On the
right
the processing flow to achieve a partitioning is shown
level
L
, we can define a label image
Γ
(
r
k
,L
) in which each pixel receives the label
of the corresponding prototype vector in the feature space. Note that even the label
image
Γ
is also defined as a pyramid, albeit the high-resolution levels are yet to
be determined. At the lowest resolution level, rough boundaries can be observed
between the different classes in
Γ
. Let
N
8
(
r
k
) be the 8
-connected neighborhood
of
a pixel at location
r
k
composed of the 8-closest neighbors on a square grid.
3
A pixel
r
k
is considered as spatially misclassified if
Γ
(
r
k
,L
) is different from all the labels
in its
N
8
(
r
k
).
Next, we consider
insignificant classes
, which are small and scattered classes
that need to be reassigned to their neighboring classes. This is because a class in the
feature space is distributed in one or more subregions in
Γ
(
r
k
,L
), even the largest of
which may not be more than a few pixels. A class is considered as “insignificant” if
its largest subregion contains no more than a threshold (nine in the discussions here).
Thus, the idea is to give a preference to classes that are spatially distributed into large
and compact subregions rather than the inverse. It is, however, clear that the mean-
ing of “insignificant classes” is closely related to the height of the pyramid, i.e., for
a low value of
L
, the actual size of an insignificant class is smaller than for higher
values of
L
. We discuss a possible implementation of this by the illustration in Fig.
16.4. Representing the largest regions of their respective classes, the hatched regions
are assumed to be insignificant classes on the grounds of their size (because they are
fewer than 9 pixels each) and have to be reassigned to either one of the surrounding
classes or, in the cases of (b) and (c), possibly even between themselves. Thus there
are two types of insignificant classes:
isolated insignificant class
, as exemplified by
(a), and
touching insignificant class
, as exemplified by (b) and (c). The isolated class
N
8
(
r
k
). In that case, it is reassigned to the most common class in
3
That is,
N
8
(
r
k
) represents the set of points in a 3
×
3 neighborhood around the current
point
r
k
, excluding the latter.
