Image Processing Reference
In-Depth Information
( a )
( b )
Fig. 5.5. Property of Algorithm 5.5 (surface thinning of a 2D plane figure in 3D
space).
: Preserved by the condition C 1and C 2,
: preserved by the condition C 1.
replaced by a 0-voxel if deletable. The 6-neighbor distance used in the algo-
rithm is significantly affected by the orientation of an input figure, although
the distance is recalculated in each main cycle. This effect of the rotation will
be reduced if the squared Euclidean distance is used instead of the 6-neighbor
distance. Computation load will become too much, however, if the Euclidean
distance is calculated directly according to its definition. One possible solu-
tion to overcome this diculty is the application of the Euclidean distance
transformation as a preprocess. Let us show an example of how to implement
this idea [Saito95, Saito96]. The distance transformation will be explained in
detail in the next Section 5.5.
Algorithm 5.4 (Surface thinning accompanied by squared Euclidean
distance transformation).
N ).
f ijk =densityvalueofavoxel( i, j, k )whichtakes 0 or 1 .Asetof1-voxels
is considered as a figure.
m = type of the connectivity ( m = 6 , 18 , 18 , 26 ).
Output:
F
{
f ijk }
= input binary image ( L
×
M
×
Input:
=
= result of surface thinning is stored when the algorithm
finishes. Also this is used to store intermediate results (values of distance
transformation, labels, etc.) produced during execution. Physically the
same array as the one that stores an input image is assigned.
Conditions for a finally preserved voxel ( FPV ): A border voxel ( i, j, k )satis-
fying at least one of the following C 1and C 2 is called FPV , and is never
deleted in the subsequent procedure (same as in Algorithm 5.3).
C 1: None of arrangements in Fig. 5.3 (3D simplex) exists in the 3
F
=
{
f ijk }
×
3
×
3
neighborhood of a voxel ( i, j, k ).
C 2: A voxel ( i, j, k ) is not deletable in the m -connectivity.
[STEP 1] (Squared Euclidean distance transformation)
for all ( i, j, k )s do (See Note)
Note: de (( i, j, k ) , ( p, q, r )) means the Euclidean distance between voxels ( i, j, k )
and ( p, q, r ). For squared Euclidean distance transformation and details of its
algorithm, see Section 5.5
Search WWH ::




Custom Search