A General Framework for Relaxation Processes

This paper addresses a major problem in pattern recognition: the unambiguous identification of objects. Comparing the characteristics of objects with the characteristics of possible interpretations, the identification of objects is frequently ambiguous. To reduce ambiguous assignments one can include a) more characteristics or b) contextual information into the identification. We use contextual information. Various approaches are suggested in the literature to describe and generalize discrete or continuous relaxation processes concerning to several objectives and one can find a suitable approach for every problem. The wider problem addressed here is to find the best-suited relaxation process for a given assignment problem or, better still, to construct a task-dependent relaxation process. In this paper we describe an approach to generalizing relaxation processes. For this purpose, we develop a general framework for the theoretical foundations of relaxation processes in pattern recognition. The resulting structure enables 1) a description of all known relaxation processes in general terms and 2) the design of task-dependent relaxation processes. We show that the well-known standard relaxation formulas verify our approach.