ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 122

C 1: None of arrangements in Fig. 5.3 (3D simplex) exists in the 3 × 3 × 3

neighborhood of a voxel ( i, j, k ).
C 2: A voxel ( i, j, k ) is not deletable in the m -connectivity.
(Main cycle processing)
[STEP 1] (Extraction and classification of border voxels)
Here a border voxel means a 1-voxel that has at least one 0-voxel in its 6-
neighborhood. Classify each border voxel as follows according to the location
of a 0-voxel in its 6-neighborhood.
for all ( i, j, k )s do (See Note)
if f ijk = 1 , then
if f i,j,k +1 = 0 , then f ijk ← 7

if f i,j +1 ,k = 0 , then f ijk ←

6

if f i +1 ,j,k = 0 , then f ijk ← 5

if f i− 1 ,j,k = 0 , then f ijk ← 4

if f i,j− 1 ,k = 0 , then f ijk ← 3

2
else no operation is performed
endif
enddo

if f i,j,k− 1 = 0 , then f ijk ←

(Subcycle processing)
[STEP 2] (Deletion of a voxel)
for bordertype = 2 to 7 do
[STEP 2.1] (Detection of finally preserved voxel ( FPV ))
Detect a voxel that is regarded as the unit thickness (surface voxel) and give
it a mark of FPV .
for all ( i, j, k )s do
if f ijk

=bordertype ∧ ( C 1 ∨ C 2)

10 ( FPV )
else no operation is performed
endif
enddo
enddo

then f ijk ←

[STEP 2.2] (Deletion of a 1-voxel)
Delete a deletable voxel.
for all ( i, j, k )s do
if f ijk

=bordertype

then
if ( i, j, k ) is deletable ( ¬ ( C 1 ∨ C 2) ∧ (not FPV ))

then f ijk ← 0 (deletion)

Note: Here “for all ( i, j, k )s do” means that each voxel is processed in the order
as shown in Fig. 2.13, and Fig. 5.1 (according to a raster scan given in the above
figures). This is the same in other algorithms presented in the following sections.
Note: ¬C 1 means logical negation of C 1.