Solve JIGSAW puzzle problems with Co-Normalization

Recently a graphic model method has been developed to reconstruct an image from a bag of square, non-overlapping patches. Markov Random Field (MRF) is used to model this type of jigsaw puzzle problem. In this model, each node represents a spatial position where patches are placed. Belief Propagation (BP) algorithm is used to solve the model. BP naturally fulfills the fact that each node should be assigned a patch with probability one. However, the fact that all patches should be equally used in the reconstructed image with probability one is neglected. As a result, there is little chance for some patches to be used in the reconstructed image. In this paper, we propose a Co-Normalization method to encourage equal treatment toward patches and nodes. Our method naturally yields a new update formula for the exclusivity term introduced by previous work. This term requires each patch to be used only once in the reconstructed image. Experiments show that our method preserves exclusivity term's requirement and adds a new requirement of equal usage of patches. Image reconstruction results show that our method solves the jigsaw puzzle problem much better.