Snakes and Active Contours - Bezier and Splines in Image Processing and Machine Vision - page 203

Fig. 9.19. Refined segmentation of the connected object using a connected snake
network (from [168]).

9.8 Conclusions

Snakes use energy minimization techniques to form smooth curves. However,
snakes are mainly used for image segmentation and interpretation rather than
mathematical interpolation per se. Rather than interpolating between known
control points as is the case with Bernstein-Bezier splines, snakes find their
own control points using image features such as edges, lines, and line termi-
nations in an image under analysis. The formulation of internal snake energy
has a membrane term that provides a form of elasticity similar to an elastic
band, and a thin-plate term that provides a form of stiffness like a traditional
wooden spline.
Traditionally, a local gradient descent method is used to determine the
minimum energy contour. This leads to the well-known pitfalls in the appli-
cation of conventional snakes due to the inability to find satisfactory answers
to the following problems.

• How do we initialize the snake to find the best solution?

• When do we stop the snake evolving?

• How do we avoid unsatisfactory local minima?

Gunn and Nixon [71] argue that, “A weakness of the evolutionary, or
local minimum, approach is the sensitivity to initialization and diculty in
determining suitable parameters. This can be exaggerated by noise.” They
then advocate techniques based on global energy minimization rather than
local minimization.