Why Does Mutual-Information Work for Image Registration? A Deterministic Explanation

This paper proposes a deterministic explanation for mutual-information-based image registration (MI registration). The explanation is that MI registration works because it aligns certain image partitions. This notion of aligning partitions is new, and is shown to be related to Schur- and quasi-convexity. The partition-alignment theory of this paper goes beyond explaining mutual-information. It suggests other objective functions for registering images. Some of these newer objective functions are not entropy-based. Simulations with noisy images show that the newer objective functions work well for registration, lending support to the theory. The theory proposed in this paper opens a number of directions for further research in image registration. These directions are also discussed.