ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 151

d ← min { f pqr , ( p, q, r ) ∈N bα (( i, j, k )) }

if d = M

then g ijk ← d + 1

else g ijk ← M

endif
endif
enddo

[STEP 3]
if when [STEP 2] finishes,

then stop
else

F = G

F ← G
endif
α

( α + 1 )mod n (Neighborhood sequence is used repeatedly)
go to [STEP 2]

←

[Explanation of the algorithm]
The basic idea of this algorithm is that we replace the value of each 1-
voxel P in an input image by

1 + the minimum in the neighborhood of

the current neighborhood number .Notehere

that in the initialization process we replace beforehand values of all 1-voxels
P in an input image by a suciently large value M (at least not smaller than
the expected maximum of the values of DT).
Thus, in the first iteration of [STEP 2], any 1-voxel that has a 0-voxel in
its neighborhood is given the value 1 . In the next iteration step, all voxels
that have at least one voxel of the value 1 in its neighborhood are given the
value 2 . The same procedure is iteratively performed until no voxel of the
value M remains, that is, a voxel of which value is to be replaced does not
exist.
The order of execution concerning ( i, j, k ) in [STEP 2] may be arbitrary.
In other words, calculation of g ijk at each voxel may be performed in parallel,
mutually independently at different voxels. However, an input image of the
i -th iteration had to be kept unchanged until [STEP 2] finishes for all voxels.
This means that an output image must be stored in an array different from an
input image. The k -times of processing is applied to the output image of the
( k

N bα (( i, j, k )) of the 1-voxel P

−

1) times of processing. If there is no voxel for which the value is replaced,
then the whole of processing terminates.
[STEP 3] is not essential. The output image of the previous iteration is
moved to an input image array for the convenience of the processing of the
next iteration.
Use of the value M and distinction of a voxel of a value M are only for
the ease of understanding. If care is not taken to prevent the possibility of
overflow, all voxels may be processed in the same way.
Different types of neighborhoods given in the neighborhood sequence are
used according to the order designated in the neighborhood sequence B ,start-