A theoretical framework for relaxation processes in pattern recognition: application to robust nonparametric contour generalization

While various approaches are suggested in the literature to describe and generalize relaxation processes concerning to several objectives, 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. For this, 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. Referring to the common problem of generating a generalized description of a contour we demonstrate the applicability of the suggested generalization in detail. Important characteristics of the constructed task-dependent relaxation process are: (1) the independency of the segmentation from any parameters, (2) the invariance to geometric transformations, (3) the simplicity, and (4) efficiency.