Statistical Relaxation Techniques

Relaxation methods have been particularly applied to optimisation problems. Such problems are very common in computer vision and so relaxation methods have been applied in a wide variety of ways to computer vision.

Relaxation methods have been applied to:

Edge linking

-- The probabilities of edge points lying on particular edges is determined by considering neighbouring edge points. Different labels are used for each edge, and a relaxation schedule is then used to find the appropriate label for each edge point.

Line labelling techniques

can be expressed a relaxation problem.

• Label lines as belonging to a certain class of edge (occluding, concave or convex).
• Probabilities can be assigned to each type of labelling fairly easily.
• Only certain sets of edge labellings are mutually compatible at line junctions.
• These restrictions can be expressed as constraints when the conditional probabilities for the particular labels are estimated.

Segmentation

can be interpreted in two slightly different ways here:

• The process of grouping pixels into regions of similarity. Here the relaxation processes amount to self-organisation of the image. The regions are simply labelled as .
• The process of labelling regions of image as belonging to recognised physical entities such as sky, grass, trees, car and road.