In our first experiment, we computed the GVF field for the line drawing
of Fig. 2a using 
.
Comparing the
resulting field, shown in Fig. 2b, to the
potential force field of Fig. 1b, reveals several key
differences. First, the GVF field has a much larger capture range. It
is clear that in order to get this extent using traditional potential
force fields, one would have to use a large 
in the Gaussian filter.
But this would have the effect of blurring (or perhaps even
obliterating) the edges, which is not happening in the GVF
field. A second observation is that the GVF vectors are pointing
somewhat downward into the top of the U-shape, which should cause an
active contour to move farther into this concave region. Finally, it is
clear that the GVF field behaves in an analogous fashion when viewed
from the inside. That is, the vectors are pointing toward the boundary
from as far away as possible and are pointing upward into the concave
regions (the fingers of the U-shape) as viewed from the inside.
Fig. 2c shows the result of applying a GVF snake
with parameters
and
to the line drawing
shown in Fig. 2a (using the external GVF field of
Fig. 2b). In this case, the snake was
initialized farther away from the object than the initialization in
Fig. 1c, and yet it converges very well to
the boundary of the U-shape. It should be noted that the blocky
appearance of the U-shape results from the fact that the image is only
pixels. The snake itself moves through the continuum (using
bilinear interpolation to derive external field forces which are not at
grid points) to arrive at a sub-pixel interpolation of the boundary.