Image Processing Reference
In-Depth Information
This is where the problem starts, as we now have 11 parameters (eight for the shapes and
three for the weighting coefficients). We could of course simply cycle through every
possible value. Given, say, 100 possible values for each parameter, we then have to search
10 22 combinations of parameters which would be no problem given multithread computers
with Terrahertz processing speed achieved via optical interconnect, but that is not now.
Naturally, we can reduce the number of combinations by introducing constraints on the
relative size and position of the shapes, e.g. the circle should lie wholly within the parabolae,
but this will not reduce the number of combinations much. We can seek two alternatives:
one is to use optimisation techniques. The original approach (Yuille, 1991) favoured the
use of gradient descent techniques; currently, the genetic algorithm approach (Goldberg,
1988) seems to be most favoured and this has been shown to good effect for deformable
template eye extraction on a database of 1000 faces (Benn, 1999) (this is the source of the
images shown here). The alternative is to seek a different technique that uses fewer parameters.
This is where we move to snakes that are a much more popular approach. These snakes
evolve a set of points (a contour) to match the image data, rather than evolving a shape.
6.3
Active contours (snakes)
6.3.1
Basics
Active contours or snakes (Kass, 1988) are a completely different approach to feature
extraction. An active contour is a set of points which aims to enclose a target feature, the
feature to be extracted. It is a bit like using a balloon to 'find' a shape: the balloon is placed
outside the shape, enclosing it. Then by taking air out of the balloon, making it smaller, the
shape is found when the balloon stops shrinking, when it fits the target shape. By this
manner, active contours arrange a set of points so as to describe a target feature by enclosing
it. Snakes are actually quite recent and their original formulation was as an interactive
extraction process, though they are now usually deployed for automatic feature extraction.
An initial contour is placed outside the target feature, and is then evolved so as to
enclose it. The process is illustrated in Figure 6.3 where the target feature is the perimeter
of the iris. First, an initial contour is placed outside the iris, Figure 6.3 (a). The contour is
then minimised to find a new contour which shrinks so as to be closer to the iris, Figure
6.3 (b). After seven iterations, the contour points can be seen to match the iris perimeter
well, Figure 6.3 (d).
(a) Initial contour
(b) After the first iteration
(c) After four iterations
(d) After seven iterations
Figure 6.3
Using a snake to find an eye's iris
 
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