Image Processing Reference
In-Depth Information
4.6 Calculation of connectivity index and connectivity
number
4.6.1 Basic ideas
The following three principles are instrumental in the calculation of the Euler
number, the connectivity number, and the connectivity index. We can employ
any of them according to application.
(a)
Local pattern matching
: Local patterns or arrangement of 0- and 1-voxels
in the neighborhood are detected by local pattern matching. Features
are obtained from the types of patterns detected. Algorithms for pattern
matching may vary according to input image and features required.
(b)
Use of arithmetic expression
: Valuesofvoxelsin
) are represented
by binary valuables. We derive mathematical equations of those variables
based upon definitions of features to be calculated. Since variables are
binary, those expressions are pseudo-Boolean. The calculation of equations
is performed at each voxel.
(c)
Image processing algorithm
: Regarding a local pattern in
N
333
(
x
)asa
binary image, we can apply image processing algorithms to obtain results.
For example, the number of connected components in
N
333
(
x
N
333
(
x
)isknown
by applying the labeling algorithm to
N
333
(
x
).
The second method will be most convenient for execution by computer,
but suitable expressions are not always available.
4.6.2 Calculation of the connectivity index
The connectivity index (
R
(
m
)
(
)
,H
(
m
)
(
)
,Y
(
m
)
(
x
x
x
)) at each 1-voxel
x
is cal-
culated by the following procedure.
(1)
Component index
R
(
m
)
(
):
R
(
m
)
(
x
x
) is equal to the number of connected
components connected to
x
presented in Definition 4.11. Labeling is performed first in a subarea in-
cluding
x
, existing in the suitable neighborhood of
and its neighborhood presented above. Next, we extract all
1-voxels having the same label as that of
x
x
in the above subarea. Finally,
after deleting the 1-voxel
, we again perform labeling on a set of the re-
maining 1-voxels. The resulting number of connected components equals
R
(
m
)
(
x
).
(2)
Cavity index
Y
(
m
)
(
x
):
Y
(
m
)
(
)=
0
(voxel) for all configurations except
for an interior voxel (Fig. 4.9) and
Y
(
m
)
(
x
x
)=
1
for an interior voxel. The
interior voxel is found easily by testing whether all adjacent voxels are
1-voxels or not.
(3)
Hole index
H
(
m
)
(
x
x
):
H
(
m
)
(
x
) is obtained by substituting into Eq. 4.14
values of
R
(
m
)
(
x
)and
Y
(
m
)
(
x
) calculated by the above procedures and
the value of
Nc
(
m
)
(
x
) determined by the method presented later.
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