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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Growing Point
Growing Points
ivl
Start Point
a
Start Point
Figure 2. Comparison of region-growing method:
ce Pe c i
left: ordinary method, right: branch based method.
2.2 Branch based region-growing
The branch-based region growing performs the region-growing
branch by branch and if growing point reaches a branch
bifurcation part, let it go into only one side of the branches.
Figure 3 shows an example of the growing at a branch
bifurcation. The left figure shows the ordinary region growing
and the right figure shows branch-based region growing. The
number written in a voxel means the order of extraction step.
When growing point reaches an edge of the vessel, the growing
stops, and then, it starts again from the latest branch bifurcation
point as shown in Figure 4.
i s growing is
5 P growing areas oS ee
are divided ti suspended
12 | 391 2th cycle tostack 1.
12 [11 [12 ZI
1t on Je | x noli
soin 4
g [9 lofi ie >
3 [9 hof [12]
9 [10 [11 14|15|
8 9 [10]t1 Zh IC
819 hol 2113]
3
6
61718 617 3
314/[5|6]|7]8 41516 8 continue
25415 [6 2 bM 5 growing
[ke ja
Figure 3. Processing of growing at the branch connection:
left: ordinary method, right: branch based method.
the orderofedge extraction
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E [8] [8] (81 [8] [8] [8 [3] 1.7
contents of the stack (coordinates of @ in the left figure)
Figure 4. Order of the branch extraction and the contents of the
stack.
2.3 Detection of branch bifurcation
In every growing cycle, the connectivity of the region added at
the cycle is examined to find a branch bifurcation. This process
is done as follows:
797
l. Start the region growing from one of the voxels in the
added region. In this growing, the targets (voxels to be
extracted as the connected object of added region) are
the voxels which have the same cycle number.
2. After the growing finishes, voxels in a part of the added
region are labelled as new parent voxels of the next
cycle of branch-based region growing.
3. The voxels which are not connected are treated as the
branch to be traced later.
To reduce over-dividing of branches, the region growing for
checking connectivity are modified by the following
modifications:
1. Use 26-neighbourhood to grow diagonal directions.
(Original region growing uses 6-neighbourhood.)
2. Extend the range of the target cycle number of grouping to
2 from 1 as shown in Figure 5.
The number of branches detected according to the growing
conditions described above is shown in Table 1.
detected as individual edge
{total 4 edges)
detected as combined edge
(total 2edges)
12
12]11
11110, [t2
9 110111112
319 10/1
12
12 11
1110| 412
9 10[11 12
S 19 [10111
(a) 12thonly (b) both 11thand 12th
Figure 5. Voxels incorporated as connected region.
Growing condition number of
thickness | neighbours branches
1 6 96390
1 26 204
2 6 159
2 26 115
Table 1. Number of detected branches under several growing
conditions.
2.4 Dynamical change of the growing conditions
Next step for the branch based region-growing is how to change
the growing condition.
One of methods commonly used is to modify growing
conditions according to the grey level intensity value of the area
extracted recently. A typical example for this type of the
growing condition is to use the following equation:
-ho € g(x,y,z) (1)
where pu = average intensity of the neighbouring region
during a certain duration of the resent growing steps.
