Image Processing Reference
In-Depth Information
Table 4.3. All possible 3D line elements and their lengths.
4.5.4 Voxel state and connectivity index
All possible values of the connectivity number and the connectivity index were
shown in Table 4.2. The state of a 1-voxel
x 0 is classified using these values
also. Several examples are presented below ( m denotes the type connectivity)
and in Fig. 4.9.
is called an interior voxel if R ( m ) (
(1) Interior voxel :A1-voxel
x
x
)= 1 ,
H ( m ) (
)= 0 ,and Y ( m ) (
)= 1 ,thus Nc ( m ) (
x
x
x
)= 2 . The cavity index
Y ( m ) (
is an interior voxel. All voxels in the
m -neighborhood of an interior voxel are 1-voxels for the m -connectivity
case (Fig. 4.9).
(2) Boundary voxel : A 1-voxel that is not a 3D interior voxel is called a 3D
boundary ( border ) voxel . A boundary voxel for the m -connectivity case has
at least one 0-voxel in its m -neighborhood.
(3) Connecting voxel :A1-voxel
x
) is positive if and only if
x
at which Nc ( m ) (
)= 1 and ( R ( m ) (
) ,H ( m )
x
x
x
) ,Y ( m ) (
(
has
two connected components in its m -neighborhood mutually connected by
x
x
x
)) = ( 2 , 0 , 0 ) is called a 3D connecting voxel because
x
.
(4) Isolating voxel :A1-voxel
at which Nc ( m ) (
)= 0 and ( R ( m ) (
) ,H ( m ) (
x
x
x
x
) ,
Y ( m ) (
)) = ( 0 , 0 , 0 ) is called an isolating voxel . An isolating voxel has no
1-voxel in its m -neighborhood for the m -connectivity case.
x
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