Active Contours (Snakes) Gradient Decent

Question

I am doing research on the active contour (snake) using gradient decent which was implemented by Kass. The two pieces of documentation that I have been reading can be found here: Original paper and A more descriptive version

My question is in regards to gradient decent. How does the algorithm determine when an edge is met and should stop trying to minimize at that point? What is preventing the snake from continuing to minimize?

Any thoughts or answers will be very much appreciated! Thanks

Answer 1

To put it simply: when there is no change.

If you change the variable x

x_i+1=x_i+dx

and the corresponding function

f(x_i+1)=f(x_i)+D

does not change, i.e.

|f(x_i+1)-f(x_i)|<e

you stop. The snake will continue to minimize if you let it (if you dont put a highest number of iterations) or it reaches a minimum (as stated above).

You plug this in to the larger equations that you have there and you arrive at your answer.