ALGORITHMS FOR PROCESSING CONNECTED COMPONENTS WITH GRAY VALUES - Fundamentals of Three-Dimensional Digital Image Processing - page 190

L, M, N : Image size (numbers of rows, columns and planes of an image) (con-
stant)
α :Weightcoecient
t : Work variable

[STEP 1] (Initialization)
for all ( i, j, k )s do
if f ijk = 0
then g ijk ← 0 ;

else g ijk ← Suciently large integer;

endif
enddo

[STEP 2] (Iteration)
for all ( i, j, k )s do
if f ijk > 0
for all ( p, q, r ) ∈N [26] (( i, j, k )) do

√ 3
if ( p, q, r )

α ←

∈N [18] (( i, j, k ))

√ 2

then α

←

else
if ( p, q, r ) ∈N [6] (( i, j, k ))

then α ← 1

endif
endif
t ∈N [26] (( i, j, k ));

← α × g ijk + f ijk , ( p, q, r )

if t<g ijk
then g ijk ← t ;

endif
enddo
endif
enddo

[STEP 3] (Test of terminating rule)
if (no gray value in

G changed) stop

else go to [STEP 2]
endif

Remark 6.1. The parallel processing of algorithms and operator expressions
by use of the minimum filter [Yokoi81, Naruse77b] is immediately extended
to a 3D image. See also Remarks 5.12, 5.17 in Chapter 5 concerning a binary
image.

Note: In the calculation of the distance, the distance to a 18-adjacent voxel, and
the distance to a 26-adjacent voxel are multiplied by √ 2 and √ 3 , respectively,
to reduce the amount of gap between the Euclidean distance.