A factor graph evidence combining approach to image defogging

In this paper we introduce an evidence combining inference approach based on factor graphs. The method presented here is quite general in nature and exploits the capability of factor graphs to combine results from multiple algorithms which correspond to different generative models or graphical structures. We do this by using layers across the factor graph to represent each of the algorithms under consideration. For purposes of inference, we convert each of these layers into a simplicial complex using a convex hull algorithm. This allows us to obtain a simplicial spanning tree for each of these simplicial complexes. Making use of this simplicial spanning tree, which corresponds to the reparameterisation of the junction tree of the factor graph, exact inference can be performed using the sum/max-product algorithm. Furthermore, we employ a Procrustean transformation so as to avoid degenerate cases in the inference process. We illustrate how the method can be used for evidence combining in image defogging and compare it against other alternatives elsewhere in literature.