Pattern recognition by graph matching—combinatorial versus continuous optimization

TL;DR: A generalization of subgraph isomorphism for the fault-tolerant interpretation of disturbed line images has been achieved and constrained continuous optimization techniques, such as relaxation labeling and neural network strategies, solve recognition problems within a reasonable time, even in rather complex relational structures where heuristics can fail.

Abstract: A generalization of subgraph isomorphism for the fault-tolerant interpretation of disturbed line images has been achieved. Object recognition is effected by optimal matching of a reference graph to the graph of a distorted image. This optimization is based on the solution of linear and quadratic assignment problems. The efficiency of the procedures developed for this objective has been proved in practical applications. NP-complete problems such as subgraph recognition need exhaustive computation if exact (branch-and-bound) algorithms are used. In contrast to this, heuristics are very fast and sufficiently reliable for less complex relational structures of the kind investigated in the first part of this paper. Constrained continuous optimization techniques, such as relaxation labeling and neural network strategies, solve recognition problems within a reasonable time, even in rather complex relational structures where heuristics can fail. They are also well suited to parallelism. The second part of this paper is devoted exclusively to them.