Fig. 1 illustrates an example of adaptive changes of the joint electrostatic force field during contour propagation. (Click on the following individual images for larger view of each, or here for the whole figure.)
Fig. 1(c) shows the initial vector force field and Fig. 1(d) is a closeup of the square region marked in 1(c) in the valley between the letters `V' and `S'. There are four critical points, indicated by thin blue circles, that can stop the snake from further propagation. A, C, and D are saddle points, while B is a divergent point. The thick red contours in Figs. 1(e)-1(h) are the progressing positions of the CACE snake. In 1(e), as the snake evolves in the valley, the saddle points A and C disappear. Notably, the divergent point B becomes a saddle point. Saddle point D stays approximately the same, as the snake is still far away from it. In 1(f), the snake has just passed the valley and is going to enter the deep concave in the letter `S'. In 1(g) the saddle point D is clearly moving away from the entrance of the concavity as the snake approaches. Finally in 1(h), the snake reaches the boundaries and the vector field takes a similar form as the initial state. The saddle points A and C re-emerge, saddle point D is back to the entrance of the concave, and B changes back into a divergent point. The corresponding CACE evolutions are shown in the last row of Fig. 1.