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Greedy Algorithm (pg.2)
There were chosen so that the image gradient will have slightly more importance than either of the continuity terms in determining where points on the contour move.
Using |vi-vi-1|² causes the curve shrink; this minimizes the distance between points. It is also contributes to the problem of points bunching upon strong portions of the contour.
The tendency is for points to always be moved nearer the previous point which also moves a point farther from the following point. This causes a chain reaction, moving all points toward the previous one. In observing the behavior of the given algorithms, it became apparent that a term which encouraged even spacing of the points would reflect the desired behavior of the contours more than one which caused shrinking.
The algorithm uses the difference between the average distance between points, I, and the distance between the two points under consideration: I - |vi-vi-1| . Thus points having distance near the average will have the minimum value. The value of normalized by dividing by the largest value in the neighborhood to which the point may move, giving a value in [0,1].At the end of each iteration a new value of I is computed.
The formulation of the continuity term causes the point to be relatively evenly spaced |vi-1 -2vi +vi+1|². The constant term is not significant since this term, like the continuity term, is normalized by dividing by the largest value in the neighborhood giving a number from 0 to 1. His formula has the advantage that it is the most computationally efficient of the ones.
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