A new theoretical approach to relaxation, application to edge detection

The algorithm introduced by A. Rosenfeld, R.A. Hummel and S.W. Zucker (1976) is studied. Links between dynamic system concepts (equilibrium stability) and relaxation concepts (ambiguity and consistency) are established. It is proved that during the procedure the consistency increases and converges. An algorithm is then introduced in which labels no longer compete with one another at every site. This algorithm works far better every time a multiple labeling is necessary (edge detection, segmentation, etc.) or even possible. It is proved that the same properties hold for this procedure as for Rosenfeld et al.´s. An experimental study of edge detection. The problem of initial edge detection, is also reported. Compatibility choice, asymptotic behavior, and resistance of the algorithm to perturbations of the compatibilities are dealt with