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.

Some 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 [57] 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 ``model-based''.

© 1997 Stephen M Smith. LaTeX2HTML conversion by Steve Smith (steve@fmrib.ox.ac.uk)