Second-Order Random Graphs For Modeling Sets Of Attributed Graphs And Their Application To Object Learning And Recognition

The aim of this article is to present a random graph representation, that is based on 2 order relations between graph elements, for modeling sets of attributed graphs (AGs). We refer to these models as second-order random graphs (SORGs). The basic feature of SORGs is that they include both marginal probability functions of graph elements and 2order joint probability functions. This allows a more precise description of both the structural and semantic information contents in a set of AGs and, consequently, an expected improvement in graph matching and object recognition. The article presents a probabilistic formulation of SORGs that includes as particular cases the two previously proposed approaches based on random graphs, namely the first-order random graphs (FORGs) and the function-described graphs (FDGs). We then propose a distance measure derived from the probability of instantiating a SORG into an AG and an incremental procedure to synthesize SORGs from sequences of AGs. Finally, SORGs are shown to improve the performance of FORGs, FDGs and direct AG-to-AG matching in three experimental recognition tasks: one