fig. 2.4. Contour contracting for square.pgm
First of all, theoretically, to get a very good (a perfect) contour of
an object, the initial boundary points should be obtained from the even
distributed points along the initial boundary. And each point should be
assigned a pair of (alpha, beta, gamma) of its own, and these values can
be modified during the contour contracting process. I have NOT
done in either because I can not afford in time. Even so, the results are
good enough to deserve "analysis" and "discussion".
1. Sensitivity to the initial contour points: the
following two images are produced with exact same parameters as the fig.
2.2. except only one: the left with the same intial points as that in fig.
2.2. but the right one with the initial contour points in modelB.dat in which the points are more
far away from the object than in the former case.
fig. 2. 6. Two contours obtained with different initial contour points.
It is a reasonable result: with the same snake window size and
the apha-beta-gamma values, if the initial points, to some
degree, are out of the reach of the first hits in the snake contour contracting
process, those points can NOT get closer to the object and furthermore affects
the contracting thereafter, as shown in the above (fig. 2.6. ) animated
image. Our question is: can we improve the "contracting" only by increasing
the snake window size? The answer is: yes, as shown in the
following.
2. Sensitivity to neighborhood (snake window) size: increasing
snake window size can improve the performance of the contour contracting.
The following two images are obtained with the same bad initial
points as that in fig. 2.6. (and also same other parameters as in fig.
2. 2. ) but they show different results with different snake window
size: left window size = 7 and right window size = 13.
fig. 2. 7. Improvement of contour with the increase of neighborhood size.
3. Sensitivity to alpha: alpha forces
the contour to be continuous (the elasticity) along the object contour. The
following images (fig. 2. 8.) show such effect: under the same conditions,
the left image has an alph of 0.80 and the right one of alpha as 1.36. The
larger the alpha, more stretched the contour along the object's true contour.
This also illustrates the alpha as one of the two factors that ajust the
"inner" energy of the image contour.
fig. 2. 8. Contours with different alpha's (other parameters are
same): left (0.80), right (1.36)
4. Sensitivity to beta: beta controls
the curvature (whether the contour looks smooth or stiff).
From the following images (fig. 2. 9.) we can see the effect of beta: with
a larger beta in the right image (the other parameters are same), the contour
tried to increase the smoothness of the whole contour. The
beta is another factor that affects the "inner" energy of the image contour,
also shown in fig. 2.9.
fig. 2.9. Contours with different beta's (other parameters are same):
left (1.31) right (2.0)
5. Sensitivity to gamma: gamma controls
the degree of the contracting of contour: it attracts the contour toward
the closest image edge. In the following animated image, the contour starts
from a near convex polygon far away from the object edge (in the center of
the image) with gamma = 0.06 to a boundary very close to the object's true
contour with gamma = 0.74 (gammas between the two are: 0.16, 0.26, 0.29,
0.35, 0.41, 0.51 and 0.61), the other parameters are the same as in fig.
2.2, that is: alpha = 0.80, beta = 0.80, and window size = 7. This animated
images also display the "external" energy characteristic of gamma in the deformable
contour.
fig. 2.10. Contour changing with the increase of gamma.
In all, anyone of the parameters (the snake window size,
initial points, alpha, beta, and gamma) can have a certain effect on the
production of contour according to their functionality in the contracting
process. But it is the combination of all these parameters
that determine the final effect. How to get a perfect contour for
an object demands vast amount of experiments in addition to our knowledge
of the parameters (just as shown in the above).