Image Processing Reference
In-Depth Information
2
2
1 +
max
(
xx
- )
+ (
yy
- )
i
i
i
R
I
1(
R
) =
- 1
(8.10)
N
()
R
where x i and y i are co-ordinates of points within the region, x
and are the region's
centroid (its mean x and y co-ordinates), and N is the number of points within (i.e. the area
of) the region. The irregularity of the connected 0s, I 0( R ), is similarly defined. When this
is applied to the regions of 1s and 0s it gives two further geometric measures, IRGL 1( i ) and
IRGL 0( i ), respectively. To balance the contributions from different regions, the irregularity
of the regions of 1s in a particular plane is formed as a weighted sum WI 1(α
y
) as
()()
NI
RR
RB
()
WI
1(
) =
(8.11)
()
N
R
RP
giving a single irregularity measure for each plane. Similarly, the weighted irregularity of
the connected 0s is WI 0. Together with the two counts of connected regions, NOC 1 and
NOC 0, the weighted irregularities give the four geometric measures in SGF. The statistics
are derived from these four measures. The derived statistics are the maximum value of each
measure across all binary planes, M. Using m
) to denote any of the four measures, the
maximum is
M
= max (
m
(
))
(8.12)
i
1,
NB
the average m is
NB
1
m
=
255
m
()
(8.13)
=1
the sample mean s is
NB
1
s
=
m
()
(8.14)
NB
=1
()
m
=1
and the final statistic is the sample standard deviation ssd as
NB
1
2
ssd
=
( -
sm
)
( )
(8.15)
NB
=1
()
m
=1
The irregularity measure can be replaced by compactness (Section 7.3.1) but compactness
varies with rotation, though this was not found to influence results much (Chen, 1995).
In order to implement these measures, we need to derive the sets of connected 1s and 0s
in each of the binary planes. This can be achieved by using a version of the connect
routine in hysteresis thresholding (Section 4.2.5). The reformulation is necessary because
the connect routine just labels connected points whereas the irregularity measures require
a list of points in the connected region so that the centroid (and hence the maximum
distance of a point from the centroid) can be calculated. The results for four of the measures
(for the region of 1s, the maximum and average values of the number of connected regions
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