Relational matching by discrete relaxation

Abstract

This paper describes a symbolic approach to relational matching. The novelty of the method lies in its Bayesian modelling of relational consistency which leads to a global matching criterion with a unique mathematical structure and robustness to error. Unlike many alternatives in the literature, the method is not limited to the use of binary constraints; it can accommodate N-ary relations of varying order. In consequence of this assumed model, the consistency of match is gauged by a compound exponential function of a higher-order Hamming distance between symbolic relations; there is a single exponential associated with each potential relational mapping. These exponential functions naturally soften the symbolic constraints represented by the relational mappings. This compound exponential structure also bestows a number of tangible benefits over the use of quadratic alternatives. In the first instance, it both renders the method more robust to errors and allows it to operate effectively in a large space of relational mappings. Moreover, this robustness to inconsistency means that the method may be operated without the need for an explicit null matching process. Unmatchable entities are identified by a constraint filtering operation once the relaxation scheme has converged. The utility of the method is illustrated on the matching of hedge structures in SAR images against their cartographic representation in a digital map.