The active contour model algorithm, first introduced by Kass et al., deforms a contour to lock onto features of interest within in an image [27]. Usually the features are lines, edges, and/or object boundaries. Kass et al. named their algorithm, ``Snakes'' because the deformable contours resemble snakes as they move.
Given an approximation of the boundary of an object in an image, an active contour model can be used to find the ``actual'' boundary. Active contour models should be able to find the intracranial boundary in MR images of the head when an initial guess is provided by a user or by some other method, possibly an automated one.
An active contour is an ordered collection of 
points in the
image plane:
The points in the contour iteratively approach the boundary of an
object through the solution of an energy minimization problem. For
each point in the neighborhood of 
, an energy term is
computed:
where 
is an energy function dependent on the shape
of the contour and 
is an energy function dependent
on the image properties, such as the gradient, near point .
and 
are constants providing the relative
weighting of the energy terms.
, 
, and 
are matrices. The value at the
center of each matrix corresponds to the contour energy at point
. Other values in the matrices correspond (spatially) to the
energy at each point in the neighborhood of .
Each point, , is moved to the point, 
, corresponding
to the location of the minimum value in . This process is
illustrated in Figure 5.1. If the energy functions
are chosen correctly, the contour, 
, should approach, and stop
at, the object boundary.
Figure 5.1: An example of the
movement of a point, , in an active contour. The point,
, is the location of minimum energy due to a large gradient
at that point.