International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
A) Normal (conventional) region growing
B) Branch-based region growing:
with searching process at the edge of the branch
C) Branch-based region growing
with searching process at the edge of the branch and
removing non-vessel region
On each data, we set the starting point at the bottom of the left
carotid artery. Growing condition c4, in eq.(2) is changed
every 5 steps in the feasible range. In method-C, parameters are
experimentally determined as &-0.5 and d, —20. In method-A
and method-B, parameters k, d. are unused. (k=d=0)
The extraction error of data-I is shown in Figure 11. Each bar
on the same growing condition corresponds to the method-A, -B,
-C respectively. The lower part of each bar (painted light grey)
reveals the shortage error and the upper part (dark grey) reveals
the excess error. As the tendency of every data was almost the
same, hereinafter, we talk about the evaluation of data-I as the
representative example.
A: use fixed criteria
! ~-B: search detached branch |— —
r- C: consider edge thickness
j excess / false positive
E []shortage / false negative
- JE] EP SE
= C8 I <q 4 HE
80 85 90
gray level
extraction error (x1000 pixels)
growing condition (Cmin)
Figure 11. Extraction error of data I.
3.3 Shortage error (false negative)
The shortage error in all methods increases as Cmin becomes
large. The following differences are appeared among the three
methods compared under the same Cmin,
The shortage error in method-B is less than that of method-A
for all Cmin, The reason is that the vessels beyond the gap are
connected and added to the extracted region in the method-B.
Especially, improvement at cmin=90 is conspicuous, this is
because of the addition of posterior communicating artery
(already shown in Figure 8).
In method-C, as the region to be extracted is restricted based on
the relation between the thickness and the intensity, the
shortage error is a little bit larger than that of method-B. This
tendency is more remarkable as c,,4, becomes smaller.
3.4 Excess error (false positive)
Excess error decreases as cy; becomes large in all methods.
The tendency of the excess error in each method is as follows.
800
The excess error of method-B is larger than that of method-A
under all conditions. This reason is that some connections to
non-vessel region are added accidentally. On the other hand, the
excess error of method-C is equal to or less than that of method-
A. This reason is that most of the accidental connections were
removed by the restriction based on the relation between
thickness and intensity.
3.5 Total error of extraction
Total error is obtained by summing up the shortage error (false
negative) and the excess error (false positive). As shown in
Figure 10, both errors are countable as the number of pixels in
line-shaped regions and the sum of the both error is treated as
the error index which is shown as the height of bars in Figure
H.
The evaluation of each method is performed by comparing their
total error on the same growing condition Cmin- In practical use;
as the Cmin which produces minimum error is often used for
segmentation, we made a comparative evaluation of their
superiority under the optimized Cmin-
As is clear from Figure 11, the optimized c,,;, of data-I is 70. As
to other data (IL, HII, IV, V), 55,55,70,75 are obtained as the
optimized c,;, respectively. Total error of each method under
its optimized cj, is shown in Figure 12. To help for comparison
among three methods, the vertical axis in this chart represents
the ratio of the total error to that of method-A.
- A:use fixed criteria excess / false positive
14 f ;
[ : r-B:search detached branch [J shortage / false negative
| p-C:consider edge thickness MH
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Cmin 7 70 Cmin = 55 Cmin = 55 Cmin = 70 Cmin = 75
Figure 12. Extraction error ratio under optimized C
min
As a whole, the shortage error of method-B is smaller than that
of method-A, but the excess error in method-B is always larger
than that of method-A. Consequently, the total error of method-
B is not always smaller than that of method-A. In these 5 data,
the results are as follows: almost the same (within 1%): 3,
improved: 1, deteriorate: 1. That is, the advantage of method-B
against method-A is not recognized.
Method-C decreases the shortage error and increases the excess
error as well as method-B. But the excess error of method-C is
quite smaller than that of method-B. And so, the total error of
method-C is always smaller than method-B and also smaller
than method-A in most cases.
The deteriorate ratios of total error of method-C to that of
method-A are 6.5, 7.4, 1.9, 1.7, 7.2[%]. These results lead us to
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