Image Processing Reference
In-Depth Information
Table 4.2.
Possible values of connectivity number and connectivity index.
Remark 4.14.
A local feature called the connectivity number (CN) was pro-
posed in [Yokoi75] for a 2D image. The significance of this feature is summa-
rized in four points stated below:
(i) The value of CN at a 1-pixel
represents the number of connected com-
ponents existing in the 8-neighborhood of
x
.
(ii) The value of CN is equal to the amount of change in the Euler number
+
1
caused by the deletion of a pixel
x
and connected to
x
x
.
(iii) A 1-pixel
is deletable if and only if the value of CN =
1
.
(iv) The value of CN is equal to the number of times for a 1-pixel
x
to be
passed when the border of a figure is traced by the specific border following
algorithm.
x
Extension of the CN to a 3D image inheriting all of these properties is
almost impossible. In this chapter the CN of a 3D image was defined so that
the second property is preserved. As a result, the first and the third properties
do not hold. To compensate this limitation, a new feature, the component
index, was added here; the fourth point cannot be extended to a 3D image.
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