Discrete relaxation

Edwin R. Hancock, Josef Kittler

Abstract: In this paper we are concerned with the approach to discrete relaxation that regards the global consistent labelling of objects as maximum a posteriori probability (MAP) estimation. We commence by reviewing existing work and draw attention to some of the technical difficulties that limit the applicability of the technique. The difficulties originate from the distinct requirements that the final labelling is both a global optimum and globally consistent. We demonstrate how it is possible to achieve a globally consistent MAP estimate by iterative label replacement without sacrificing the representational capacity of the label process. The computational realisation of the proposed approach admits a conceptual ingredient hitherto not present in discrete relaxation schemes, namely, that of a label error process. This process naturally leads to a measure of congruency between initial inconsistent labellings and physically occurring dictionary items. The use of congruency provides a means of resolving labelling ambiguities and inconsistencies which would otherwise remain unresolved if the conventional models of the label process were employed. The performance of the technique is demonstrated for the highly structured problem of edge labelling.