International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
o- intensity deviation of the same neighbouring region
as the above defined.
g(x,y,z) = the intensity value of the target voxel
x,y,z = the coordinates of the target voxel
h = a parameter which corresponds to control the
easiness of growing,
The results obtained by the vessel segmentation using the above
condition were not satisfactory ones in which many parts of
shortages were found. The main reason of this seems to be that
the intensity value changes widely in the vicinity of the branch
bifurcation.
We carried out a branch-based region growing as a trial to
check the actual intensity transition within blood vessels. The
voxels with more than 70 intensity level (max=255) are set as
the target voxels. Figure 6 shows the linkages between branches
and branch attributes (length, thickness and intensity value).
Each rectangle corresponds to each branch unit, i.e., region
between bifurcations. The brightness inside rectangles indicates
the intensity value of the corresponding branch unit, and its
length and width indicate the length and thickness of the branch
unit respectively.
This figure shows that the average values of the intensity and
the thickness of the vessel widely change in the vicinity of the
branch. The relation between the intensity and the thickness of
each branch is shown in Figure 7. The horizontal axis indicates
vessel thickness obtained by counting the number of voxels in
the cross section area and the vertical axis indicates the average
intensity of each branch unit.
We can see a close relation between the thickness and the
intensity on this figure. Especially, in the range of section area
(thickness) less than 30, this relation seems almost linear. On
the other hand, there exist several dots which don't fit to the
relation. They seem to correspond to the leak region. By getting
rid of these dots on branch units, we can get more proper results.
The following equation is proposed for this purpose:
C min + kd, (d, < d. ) (2)
Hm (d, 2 d,)
C nin s kd,
MW, = average intensity of i-th extracted branch
d; = average thickness of i-th extracted branch
Cmin = lower limits of the intensity of ROI
k = exclusive rate (if k=0, all branches are accepted)
d; = upper limits of the thickness range that the linear
relation between thickness and intensity is formed.
where
cos o thickness.
right IC
E intensity T
id / e e: c E
mmm,
Figure 6. Attributes and linkages of extracted branches.
gray - :
level
$ 150
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70 A
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0 10 20 30 40 50 60 70 pixel
average section area ofeach branch
Figure 7. Relation between the thickness and the intensity of
each branch unit.
2.5 Connection search over a gap
In the case of a narrow and long region like a blood vessel, a
break of growing often occurs because of missing voxels on the
way. This problem can be solved by extending the searching
area for vessels. But it increases over-extraction errors and
needs a lot of processing time.
In fact, the break occurs at the edge of the vessel, and it is
enough to search for vessels at that point only. In the branch-
based region growing, the growing stops at the each edge of the
vessel, and then starts seeking vessels over a gap. If a vessel to
be connected is found, the extracting process starts again,
otherwise, the process enters into the next branch extraction.
Figure 8 shows results of segmentation. The start point of the
region growing was set at a point inside the carotid artery. In
the case of this data, as the intensity of a posterior
communicating artery is partially low, the following vertebral
artery and some subsequent vessels are not extracted by the
conventional method shown in the left image. By using our
method presented above, those vessels are extracted and
moreover narrow vessels of parietal region are also detected as
shown in the right image.
