© 1997 Stephen M Smith. LaTeX2HTML conversion by Steve Smith (firstname.lastname@example.org)
- The term
``statistical regularization'' is often used interchangeably with the
following: ``simulated annealing'', ``stochastic relaxation'' and
``global optimization''. Simulated annealing, as its name suggests,
finds a global minimum of a multi-dimensional function by allowing
random perturbations in the current state estimate; the probability of
changing state (analogous with temperature) decreases with time. The
change to the state is accepted if the total cost function is
decreased by it. As the ``temperature'' reaches zero, the system
should settle into the global minimum.
- Much research in this field has assumed that the only
one dimensional features of interest are step edges. However, there
exist many other types of feature. These include lines (ridges in the
image surface), ramp ends and roof edges. There are three main
reasons for the concentration on step edges. The first is that they
are the most common type of one dimensional change. The second is that
edges containing a step component are the most well localized one
dimensional features, that is, they are formed by a ``first order''
change. The third reason for working only with step edges is that some
proposed edge finders (such as Canny's) are easily extended to finding
other types of change once the theory for step edges has been
completed. Thus many detectors have been developed using rigorous
derivations of optimal algorithms using various criteria based on the
model of the ideal step edge.
- The problem with using image derivatives is that
differentiation enhances noise as well as edge structure, so most edge
detectors include a noise reduction stage. Thus the use of the
derivative of a Gaussian enables differentiation to take place at the
same time as the smoothing; this is allowable, as the two processes
commute. The problem of noise enhancement is even worse when
differentiation is performed twice.
higher level algorithms use Canny's method because of this
characteristic, as they work better with simple unconnected edges.
However, achieving full connectivity at junctions is clearly a
worthwhile goal as it correctly represents the scene. In 
Li et. al. suggest heuristic extensions to the Canny algorithm to
enable the joining of open contour ends with nearby contours. This
however produces some false edge extensions.
- Here model means the type of image
structure assumed to be present when discussing any particular aspect
of corner finding theory. Note that almost all approaches to corner
finding assume a simple corner model, whether or not they are