ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 124

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( a ) ( b ) ( c )

( d )

Fig. 5.4. Property of Algorithm 5.3 (surface/axis thinning). Condition of finally
preserved voxel and degeneration ( ◦ : deletable, × : preserved (not deletable) by the
condition C 1, • : preserved by the condition C 2).

J ≤ ( J − K +1) ≤ ( J − K +2)

K = 1 .

The above algorithm is a prototype of a 3D surface-thinning algorithm,
and has not been refined so much. In fact, it contains the surface thinning only.
One may expect that an axis-thinning algorithm is obtained by excluding the
condition C 1 in this algorithm. However, the problem is not so simple. For
example, a center line had to be obtained, even if a figure of the unit thickness
is given as an input figure. If a parallelepiped figure is given as an input figure,
it would be expected that the final result of a center line is obtained after an
intermediate result of the same shape as a result of the surface thinning is
reached. Let us give an example of such an algorithm in Algorithm 5.6.

5.4.5 Surface thinning algorithm accompanying the Euclidean
distance transformation

Another problem of the above algorithm is that a thinned result is affected
significantly by the rotation of an input figure. One major reason for this lies
in the order that the algorithm shaves surface voxels from an input figure.
Voxels at the unit distance from the background is tested for deletability and