ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 178

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Fig. 5.18. Border surface of a 3D figure with the unit thickness.

5.6.3 Restoration of a figure

An original input figure is restored exactly from the result of border surface
following. We will present below a concrete form of an algorithm to realize
this.

Algorithm 5.18 (Restoration of a figure).
Input: One of the border voxels of the background (one voxel for each border
surface)
List of border voxels of a figure (output of Algorithm 5.17)
Output: Image

. (A 3D image. A restored binary image is stored after the
execution of the algorithm. Initial values are 0 for all voxels.)
TEMP: Work array (1D, a queue, or a stack)

F

[STEP 1] (Restoration of a border surface)
Pull out in turn each element of the border voxel list, and put the value 1
into a correspondent voxel of an output image.

[STEP 2] (Marking of border voxels of the background)
Denote by (

) a starting voxel pair corresponding to each border surface,
which is given as an output of Algorithm 5.17, and perform the following
steps, by starting at the 0-voxel of the above starting voxel pair.
(1) Substitute

x , y

1 to a voxel of an output image corresponding to the starting
voxel. Store the coordinate of the starting voxel to a work area TEMP (a
queue or a stack).
(2) Repeat the following (i)

−

(iii) until TEMP becomes empty.
(i) Read out the first element of TEMP.
(ii) Extract all voxels of the surface neighborhood of the value 1 .
(iii) Store coordinate values of extracted voxels to TEMP, and substitute
the value

∼

− 1 to voxels of an output image corresponding to voxels extracted

above.
(3) Go to [STEP 3]

[STEP 3] (Restoration of inner voxels and erasure of the mark)