ALGORITHM OF BINARY IMAGE PROCESSING - Fundamentals of Three-Dimensional Digital Image Processing - page 147

(Transformation III') Use the following equation instead of Eq. (5.4).

z )) 2 ; 1 s ijk =min

z {

h ijz +( β ( k − ≤ z ≤ N } . (5.9)

The following algorithm is obtained by combining Transformations I ∼ III

(orI,II',andIII').

Algorithm 5.7 (Squared Euclidean distance transformation).

[STEP 1] (Corresponds to Transformation I)
[STEP 1.1] Perform the following processing for each row.
Input image F = { f ijk } ( L × M × N ),

G = g ijk } Output image { ,

for all j, k do
d = 0
for i = 1 to L do
if f ijk

= 0
then d ← d + 1

else d ← 0

endif
g ijk ←

d 2

enddo
enddo
i is changed from 1 to L (from left to right in each plane of an image (forward
scan)).
[STEP 1.2] Perform the following processing for each row.
Input image

G = g ijk }

{ ,

Output image G = { g ijk } ,

for all j, k do
d = 0
for i = L to 1 do
if g ijk = 0

then d

← d + 1

else d ← 0

endif
g ijk ← g ijk ,d 2 } min {

enddo
enddo
i is changed from L to 1 (from right to left in each plane of an image (backward
scan)).

[STEP 2] (Corresponds to Transformation II)
Input image G = { g ijk } ,

Output image h ijk }

for all ( i, j, k ) do (Perform the following processing at each voxel)
h ijk ←

H = {

where r = √ g ijk g i ( j + n ) k + n 2 }

−r≤n≤r {

min