ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 140

Fig. 5.11. An example of voxels used in deletability test in surface/axis thinning
in [Tsao81, Tsao82a, Tsao82b]. A current voxel is denoted with ◦ . Solid lines show
check planes of 3 × 3 voxels.
(vii) Subsidiary information : Various subsidiary information is used to im-
prove the quality of a thinned result and to achieve higher performance
of algorithms. For example, the computation time can be significantly
reduced by extracting border voxels and storing those coordinates in a
list beforehand as in Algorithms 5.5 and 5.6. This is due to the fact that
an object of deletion is only a border voxel. The use of distance trans-
formation is also effective as in Algorithm 5.4. For example, a voxel of
a smaller distance value may be deleted earlier, a skeleton voxel is con-
sidered as a candidate of a voxel to be deleted, and appearance of false
branches in an output of thinning is controlled by using skeleton voxels
[Saito01, Toriwaki01].
(viii) Control of a finally preserved voxel ( FPV ): A user may wish that a spe-
cific voxel will remain in an output figure, or that a resulting line figure
will pass specific voxels. These requirements are satisfied by giving a mark
of FPV to those voxels beforehand.Thinning with an anchor point is an
example of this and is effectively used for controlling the appearance of
spurious branches. See Remark 5.7 [Ragnemalm90, Saito01, Toriwaki01].
Remark 5.7. Study of surface/axis thinning of a 3D image began in around
1980. Papers in those years are listed in [Toriwaki85a]. Papers [Tsao81,
Kawase85] showed the conditions of topology preservation explicitly and pro-
vided a prototype of research in related fields. After these, a few papers
have been published and are given in the reference list in the end of this
topic. Comparative studies have not been reported. A deletability test in
[Kawase85, Saito95] is the one presented in Chapter 4, and those in other
papers were similar to [Tsao81]. Comparative study on the quality of thinned
results is very sparse. According to experimental results by the author's group,
the method accompanied by Euclidean distance transformation seems to be
better than others. The reason is perhaps that the deviation from the Eu-