Biomedical Engineering Reference
In-Depth Information
Figure 10.18:
A shape and its boundary (a harmonic curve).
using
r
=
a
+
b
cos(
m
θ
+
c
)
,
(10.41)
where
r
is the length from any edge point to the center of the shape,
a
,
b
,
and
c
remain constant, and
m
can be used to produce different numbers of
'bumps'; in this case
m
=
6. We added varying amounts of noise and measured
the accuracy of fit (i.e. boundary description) after convergence. The accuracy
was computed using maximum radial error (MRE), i.e. the maximum distance
in the radial direction between the true boundary and each active contour.
Impulse noise was added to the original image from 10% to 60% as shown in
the first column of Fig. 10.19. The region segmentation data used for RAGS is in
the second column (without any post-processing to close gaps, etc.). The third,
fourth, and fifth columns show the converged snake for the standard geomet-
ric, the GGVF, and RAGS snakes respectively. A simple subjective examination
clearly demonstrates the superior segmentation quality of the proposed snake.
The initial state for the standard geometric and RAGS snakes is a square at the
edge of the image, while for the GGVF it is set close to the true boundary to en-
sure better convergence. At low percentages of noise, all snakes could find the
boundary accurately enough. However, at increasing noise levels (
>
20%), more
and more local maxima appear in the gradient flow force field, which prevent the
standard geometric and GGVF snakes from converging to the true boundaries.
The RAGS snake has a global view of the noisy image and the underlying region
force pushes it toward the boundary. The MRE results are shown in Table 10.1.
These verify RAGS error values to be consistently and significantly lower than
the other two snake types for noise levels
>
10%.
10.9.4 Results on gray level images
Figures 10.20-10.22 demonstrate RAGS in comparison to the standard geomet-
ric and GGVF snakes on various gray level images. Figure (10.20) shows a good
example of weak-edge leakage on the lower side of the object of interest. While
