ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 131

endif
endif
enddo
enddo

[STEP 5] (Test of the terminating rule)
N ← length of the list

mind the minimum of the distance values in the list (the minimum value

in all values over 20 )
if (mind < maxd or N> 0 )
then go to [STEP 3]
endif

←

[STEP 6] (Postprocessing)
for all ( i, j, k )s do
if ( f ijk

= 0 )
then f ijk ← 1

endif
enddo

Remark 5.6. A kind of trade-off exists in a surface/axis-thinning algorithm
between the appearance of false (undesired) branches and occurrence of de-
generation. Here a false branch tends to appear in a thinned result due to
small irregularities on a border surface. Degeneration means that a thinned
result shrinks too much or becomes shorter than we naturally expect. An algo-
rithm with a better performance concerning degeneration is likely to produce
more false branches and vice versa. Both of them are affected by the subject
in evaluation to some extent. In Algorithm 5.3 and 5.4, this trade-off is con-
trolled only a little by the number of 1-voxels existing in the 26-neighborhood
of each 1-voxel. For example, the deletion is applied according to the order
of the number of 1-voxels in the 26-neighborhood. One method to control
this trade-off more successfully is given in [Saito01]. Prevention of degenera-
tion is important in a thinning algorithm, but is not solved easily. Incorrect
strategies may cause the disappearance of the whole of a figure with the spe-
cific orientation. Many problems still remain to be solved in the prevention of
degeneration.

(b) Axis thinning

Let us show an example of the axis thinning algorithm. As was stated, it is
not always necessary to terminate the iteration procedures in an algorithm
concerning axis thinning at the moment that an input figure becomes a plane
of the unit thickness. A 1-voxel is given the mark of a finally preserved voxel

Note: Integers 0 ∼ 20 are used as labels.