The classic LSAC model directly determines the curve velocity function Vp based on the curve evolution theory, so that it moves from the initial position far away from the target to the target boundary at a certain speed. Take the GAC model as an example.

 

Since the edge stop function has a monotonous decline characteristic, when the curve is in a position with a small gradient (that is, a flat area) in the image, it will have a large moving speed; Zero, stop at the target boundary and form the image segmentation result. Image segmentation effect of GAC model. The black curve in the figure represents the position of the active contour curve in the image at different moments (indicated by the number of iterations) during the motion process from the initial position to the final stop. It can be seen that it undergoes topological changes gradually, and finally reaches the edge of the target, and the surrounding area is the foreground target.

 

Variational level set active contour models are another class of LSAC-like models. Firstly, the energy functional is defined and the corresponding Euler-Lagrangian equation and the gradient-descent flow equation are obtained by applying the variational method. Then, the gradient-descent flow equation is discretized on the space-time plane, and a certain numerical algorithm is used to solve it. Corresponding to the numerical solution process, the active contour curve undergoes topological changes on the image definition domain, and when it converges, the active contour curve stops at the target edge.