One of the original applications for snakes as envisioned by Kass, Witkin, and Terzopoulos [1] was to reconstruct subjective contours. Subjective contours are edges that are not actually present in an image, but are perceived nevertheless. Fig. 5 gives an example of a subjective contour. In the object shown in Fig. 5a, we mentally connect the left and right parts of the upper and lower horizontal edges. This gives the impression that we are looking at a closed figure, perhaps the shape of a room with two open doors and two bay windows.
The GVF field (
)
for the shape in
Fig. 5a is shown in Fig. 5b,
and a converging sequence of growing snakes is shown in
Fig. 5c. Clearly, the snake has converged to what
we would think of as the subjective boundary. It is interesting to note
that while the snake did not ``leak'' out the ``doors'' on the top and
bottom, it did grow out into the ``bay windows'' at the left and
right, capturing the protruding boundary accurately. Thus, the GVF field
seems to implicitly differentiate the open boundary from the protruding
boundary.
An immediate extension of this idea is to consider a collection of scattered points in the plane, as shown in Fig. 6a. The GVF field for this image is shown in Fig. 6b, and the converging snake sequence is shown in Fig. 6c. Again, the snake has converged to what we would consider to be the subjective contour connecting these points. While much more investigation needs to be done, this approach appears to have promise in curve and surface interpolation, a common problem in both science and engineering.