This paper explores a formulation for attributed graph matching as an inference problem over a hidden Markov Random Field. We approximate the fully connected model with simpler models in which optimal inference is feasible, and contrast them to the well-known probabilistic relaxation method, which can operate over the complete model but does not assure global optimality. The approach is well suited for applications in which there is redundancy in the binary attributes of the graph, such as in the matching of straight line segments. Results demonstrate that, in this application, the proposed models have superior robustness over probabilistic relaxation under additive noise conditions.