Image Processing Reference
In-Depth Information
(i)
(ii)
(iii)
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-
-
4-
4-
4-
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+
( a )
( b )
Fig. 5.13. Scanning mode and neighborhoods used for Algorithm 5.10 (fixed neigh-
borhood DT): ( a ) Scanning mode; ( b ) definition of neighborhoods.
(1) Introduction of variable neighborhood DT : In the DT of a 2D image, an al-
gorithm to use the 4-neighbor and the 8-neighbor alternately was proposed
and called the octagonal DT because the form of equidistance contour line
looks like an octagon. This idea was extended to a 3D image by using al-
ternatively two of the 6-, 18-, and 26-neighborhood and called by the name
of 6 / 26 octagonal DT, 18 / 26, and 6 / 18 octagonal DT [Borgefors84]. The
sequential type algorithm is realized in the same way as Algorithm 5.10
except that eight times of iteration (scanning of the whole of an input
image) are required.
(2) Modification of the distance value : The most important reason that the
distance value is significantly different from the value of the Euclidean
distance in any of the 6-, 18-, and 26-neighborhood distance is that
the distance to adjacent voxels is regarded as a uniform unit. The ef-
fect of this uniform distance assumption is decreased by using another
value that is closer to the true distance value. For instance, one possibil-
ity is to employ the Euclidean distance between center points of voxels
that are adjacent to each other. That is, the distance to a 6-adjacent,
18-adjacent, and 26-adjacent voxels are regarded as 1 , 2 ,and 3 ,
respectively. However, even this type of algorithm still cannot give ex-
act Euclidean distance values. Computation time will also increase be-
cause calculation among irrational numbers (or real numbers approxi-
mating them) is involved. Therefore weighting using only integers that
provide better approximation have been studied. A triplet of integers
( 3 , 4 , 5 ) instead of ( 1 , 2 , 3 ) is known as an example of relatively good
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