Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
(d)
Figure 8.
Illustration of dynamic discrete contour evolution on a cropped region from an
MR image of brain. (a,c) Initial contour drawn manually. (b,d) Segmentation result from
the contours of (a) and (c), respectively. Reprinted with permission from [20]. Copyright
c
1995, IEEE.
should be zero for parts of the contour with constant curvature. To accomplish this,
the dot product of the local
c
i
at point
i
is computed
and convolved with a discrete filter
f
. The idea here is to reduce the high-frequency
component and rather retain only the DC component. Thus, the choice of filter
needs to be such that the result of convolution is zero. This approach results in
a smoother contour and also allows an open contour to evolve within the snake
framework. Figure 8 shows the results of deformation using the dynamic discrete
contour.
r
i
and global radial vectors
3.1. Gradient Orientation
A different problem arises when two strong disconnected edges come close
to each other. In these cases, the strong gradient acts independently to attract
the contour. The final result thus becomes dependent on a number of factors
like the contour's relative location with respect to the participating edges, their
strengths, and possibly on all other force factors in the neighborhood. In many
˜
cases, the resulting contour alternates between the two strong edges. Falcao et al.
[21, 22] addressed this problem in their proposed “live-wire” framework. The
“live-wire” uses the gradient orientation information to detect the “true” boundary
and avoids the possibility of getting trapped by strong edges. Similarly, the gradient
orientation can be used in the snake framework [23]. Instead of using the gradient
force without any reference to the contour, the external energy due to the gradient
can be defined by the contour orientation and gradient direction. The idea is to
make the “false” boundary invisible to the contour, so that it does not snap onto the
“false” edge. Here, the direction of gradient is defined as whether it is a step-down
or a step-up gradient. Now, this direction depends on the point from which we
are looking at the gradient and the orientation of the contour. For example, in
Figure 9, if we observe the edge marked green from the blue point, it seems to be
a step-down gradient, while if it is observed from the red point, the gradient is a
step-up gradient.
