Snakes and Active Contours - Bezier and Splines in Image Processing and Machine Vision - page 199

9.6 Problems and Pitfalls
Traditional snakes minimize energy within a local search space only. This leads
to diculties in many applications because the snakes become stuck on local
minima rather than on finding global solutions that may be preferable for fully
automated image segmentation. As a result of the gradient descent nature of
the traditional snake, the answer obtained is very dependent on initialization
and stopping criteria, and these criteria, may be very dicult to determine in
general.
An example of this diculty with a traditional closed snake or balloon
on the cell image segmentation problem is shown in Figure 9.15, where the
contour is stuck in a local minimum. If we increase the deflationary force,
we may be able to contract the contour down on to the nuclear membrane.
Unfortunately, we may also run the very real risk of the contour being pushed
right inside the membrane—especially if the image gradient on the nuclear
membrane is less than on the surrounding artifacts.
Gunn and Nixon [72] attempt to address this issue by using a dual active
contour model. Their idea is to initialize balloons both inside and outside
the object of interest. The inner balloon would then expand and the outer
balloon would contract. If the two balloons did not meet, the inflationary and
deflationary forces would be increased until the balloons were forced together.
This approach has the advantage of clear initialization and stopping criteria,
but does not necessarily yield the optimal minimal energy solution in general.
The dual active contour process is illustrated in Figure 9.16 on the cell image
problem.
9.7 Connected Snakes for Advanced Segmentation
Snakes can be used to segment quite complicated images with a little guidance
from a human expert. Usually only one snake is evolved, but some situations
call for a far more complex segmentation where many snakes must be evolved
simultaneously. Figure 9.17 shows a set of connected objects and an initial
hand-drawn rough segmentation. Our goal is to use snakes to refine the rough
object segmentation into an acceptable segmentation with good boundary
delineation. This approach was developed by Walford [168] to fuse spatial
LIDAR information with image data for the automatic analysis of rock wall
faces in a mine.
We treat each section of the boundary between the joins as an open-ended
snake as illustrated in Figure 9.18. Now our problem is to find the minimum
energy configuration of snakes by evolving all snakes simultaneously. At first
glance, this appears to be a very challenging problem. Nevertheless, a good
solution can be found if we decouple the problem by taking advantage of the
mid-point heuristic as described in Section 9.5.