Image Processing Reference
In-Depth Information
preserved finally ( FPV ). However, deletable voxels are not actually deleted at
the moment of detection. The deletion is executed simultaneously (all at once
and in parallel) for all these voxels, when all voxels of an input image have
finished being tested for deletability. A voxel is never deleted during any cycle
of the iteration once it has been selected to be preserved.
The most dicult and the most critical problem is the prevention of the
phenomenon that occurs when the whole of a figure with the two voxels width
disappears as a result of deletion regardless of only a deletable voxel being
deleted. This is a kind of degeneration. Let us show one example. Suppose
that an input figure is a cube consisting of 2
2 voxels. Then, any of
these eight voxels satisfies the deletability condition if the deletability of each
of them is tested independently from other voxels. Thus, if the deletion is
performed simultaneously at all of those eight voxels, then the input figure
will disappear.
The following three strategies have been known to avoid this type of de-
generation:
×
2
×
(1) To develop a better algorithm for detecting a set of deletable voxels so
that all of extracted voxels can be deleted all at once ( completely parallel-
processing type ).
(2) To classify first all border voxels into suitable subgroups and the deletabil-
ity test is applied to only one subgroup in one time of iteration. An exam-
ple of the grouping is how many 0-voxels are adjacent and in which side
of each border voxel. Each subgroup is processed according to the given
order. All deletable voxels in the same subgroup are deleted simultane-
ously. Therefore, deletion is done in parallel within the same subgroup,
and subgroups are processed sequentially ( subborder group type ).
(3) To divide all voxels in an input image into mutually exclusive subgroups
beforehand, the same processing as (2) above is applied in parallel within
the same subgroup. Each subgroup is processed sequentially according to
the predetermined order ( subfield type ).
The first strategy leads to a parallel type of procedure. However, it cannot
be realized by using a 3
×
3
×
3 or smaller neighborhood. An algorithm using
a 5
5 neighborhood is shown in [Ma95, Ma96]. The second idea is
essentially the same as the one employed in the subcycle system of thinning,
which was introduced to keep a thinned result at or near the center of an input
figure. This is a popular idea in the parallel type of algorithm used now. An
example of the third idea is found in [Bertrand94a, Bertrand94b, Bertrand95,
Saha94, Saha97], in which eight subfields are employed. Concrete algorithms
are given in those papers.
×
5
×
5.4.8 Experimental results
Let us show experimental results of surface/axis thinning in Fig. 5.6
5.9.
Algorithms used here are Algorithm 5.3 and the algorithm in [Tsao81]. Input
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