Image Processing Reference
In-Depth Information
provided at each iteration. The result of implementing the complete solution is illustrated
in Figure
6.7
. The initialisation, Figure
6.7
(a), is the same as for the Greedy algorithm, but
with 32 contour points. At the first iteration, Figure
6.7
(b), the contour begins to shrink and
moves towards the eye's iris. By the sixth iteration, Figure
6.7
(c) some of the contour
points have snagged on strong edge data, particularly in the upper part of the contour. At
this point, however, the excessive curvature becomes inadmissible, and the contour releases
these points to achieve a smooth contour again, one which is better matched to the edge
data and the chosen snake features. Finally, Figure
6.7
(e) is where the contour ceases to
move. Part of the contour has been snagged on strong edge data in the eyebrow whereas the
remainder of the contour matches the chosen feature well.
(a) Initialisation
(b) Iteration 1
(c) Iteration 6
(d) Iteration 7
(e) Final
Figure 6.7
Illustrating the evolution of a complete snake
Clearly, a different solution could be obtained by using different values for the snake
parameters; in application the choice of values for α , β and ∆ must be made very carefully.
In fact, this is part of the difficulty in using snakes for practical feature extraction; a further
difficulty is that the result depends on where the initial contour is placed. These difficulties
are called
parameterisation
and
initialisation
, respectively. These problems have motivated
much research and development.
6.3.4
Other snake approaches
There are many further considerations to implementing snakes and there is a great wealth
of material. One consideration is that we have only considered
closed
contours. There are,
naturally,
open contours
. These require slight difference in formulation for the Kass snake
(Waite, 1990) and only minor modification for implementation in the Greedy algorithm.
One difficulty with the Greedy algorithm is its sensitivity to noise due to its local
neighbourhood action. Also, the Greedy algorithm can end up in an oscillatory position
where the final contour simply jumps between two equally attractive energy minima. One
solution (Lai, 1994) resolved this difficulty by increasing the size of the snake neighbourhood,
but this incurs much greater complexity. In order to allow snakes to
expand
, as opposed to
contract a
normal force
can be included which inflates a snake and pushes it over unattractive
features (Cohen, 1991; Cohen, 1993). The force is implemented by addition of
F
normal
= ρ
n
(
s
) (6.38)
to the evolution equation, where
n
(
s
) is the normal force and ρ weights its effect. This is
inherently sensitive to the magnitude of the normal force that, if too large, can force the
contour to pass over features of interest. Another way to allow expansion is to modify the
elasticity constraint (Berger, 1991) so that the internal energy becomes
