Specification of deformation congruence models using combinatorial iterative DIA testing procedure

Abstract

Deformation congruence models form the basis for conventional deformation analysis (CDA). In geometrical sense, these models connect an epochal object states—represented by its characteristic points—at stable/congruent points to disclose possible deformations. To this day, the deformation congruence models are usually specified using the global congruence test (GCT) procedure which, however, has a weakness in the case of multiple displacements. More precisely, the GCT procedure is based on consecutive point-by-point specification which may suffer from so-called displacement smearing. To overcome the above weakness, a revolutionary—in the context of GCT—concept (two methods) involving combinatorial possibilities was suggested in recent years. Admittedly, this concept avoids the problem of consecutive point-by-point specification. Nevertheless, it generates another weakness, namely the problem of the comparison of different-dimensional models. This paper makes a step forward in this new combinatorial field and discusses a more sophisticated combinatorial procedure, denoted as CIDIA. It was shown that, thanks to an appropriately used the possibilities of combinatorics and generalized likelihood ratio tests performed in the detection–identification–adaptation (DIA) iterative steps, the above weaknesses can be overcome. In the context of GCT, the suggested procedure has rather evolutionary—than revolutionary—character and the general concepts of both procedures have similar heuristic substantiation. To demonstrate the efficacy of CIDIA against GCT and the two existing combinatorial methods, various deformation scenarios were being randomized independently many times with the use of comprehensive computer simulations and then processed. Generally, the obtained results confirmed the statement that the suggested CIDIA procedure—unlike the existing combinatorial methods—can be substantially more resistant to displacement smearing than the GCT procedure, at no significant costs. The efficacy of CIDIA—unlike the ones of the two existing combinatorial methods—turned out always higher (on average by several percentages) than the one of GCT for all considered deformation scenarios. At the same time, the CIDIA procedure turned out substantially less time-consuming than the other combinatorial methods.