Snake Initialization

Fig. 3a shows the computed GVF ($\mu = 0.1$) for the line drawing square shown using gray lines in Figs. 3b and 3c. Figs. 3b and 3c show GVF snake results using initializations from the inside (Fig. 3b) and from the outside (Fig. 3c). The two final configurations are nearly indistinguishable from each other, indicating that the GVF snake can be initialized either inside or outside the desired boundary. It should be noted that, unlike pressure forces, the GVF snake does not require the a priori knowledge of whether to shrink or expand.

It can also be seen from Figs. 3b and 3c that the final configuration has slightly rounder corners than the square. This is one of the effects of $\mu$, the regularization parameter in the GVF formulation. Choosing $\mu$ smaller will tend to reduce this rounding, but will also reduce the strength of smoothing term. It should be noted, however, that this particular image has only $64\times 64$ pixels, and the rounded corner of the snake is still within one pixel of the original corner.

Figs. 4a and 4b demonstrate a further initialization insensitivity: the initial snake can cross the boundary. The result shown in Fig. 4a is nearly indistinguishable from that in Figs. 3b and 3c; and the result shown in Fig. 4b is nearly indistinguishable from that shown in Fig. 2c. Of course, there must be limits on the full range of possible valid GVF snake initializations. A full theoretical and empirical study of these limits is a subject for future research.