A new attributed relational graph matching algorithm using the nested structure of earth mover's distance

In general, object features can be represented as the nodes in attributed relational graph (ARG) with the connecting edges implying their relations. Therefore, the ARG matching plays a significant role in object recognition. Actually, the ARG matching can be implemented as a 2-step procedure, composed of constructing a distance matrix and establishing the correspondence based on the distance matrix, which seems to be similar to the point matching procedure. In this paper, we present a new ARG matching algorithm using the nested structure of earth mover's distance (EMD). More specifically, the nested structure of the EMD consists of inner EMD and outer EMD: The inner EMD reflects the difference of both nodes and edges between a pair of nodes in two ARG's in a perceptual manner, and the outer EMD establishes the correspondence between nodes in the two ARG's in a natural way. In order to demonstrate the robustness of the proposed algorithm against noise, we have conducted synthetic experiments for fully connected and undirected ARG's.