A Unifying Framework for Mutual Information Methods for Use in Non-linear Optimisation

  • Nicholas Dowson
  • Richard Bowden
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3951)


Many variants of MI exist in the literature. These vary primarily in how the joint histogram is populated. This paper places the four main variants of MI: Standard sampling, Partial Volume Estimation (PVE), In-Parzen Windowing and Post-Parzen Windowing into a single mathematical framework. Jacobians and Hessians are derived in each case. A particular contribution is that the non-linearities implicit to standard sampling and post-Parzen windowing are explicitly dealt with. These non-linearities are a barrier to their use in optimisation. Side-by-side comparison of the MI variants is made using eight diverse data-sets, considering computational expense and convergence. In the experiments, PVE was generally the best performer, although standard sampling often performed nearly as well (if a higher sample rate was used). The widely used sum of squared differences metric performed as well as MI unless large occlusions and non-linear intensity relationships occurred. The binaries and scripts used for testing are available online.


Mutual Information Image Registration Window Function Warp Function Medical Image Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Nicholas Dowson
    • 1
  • Richard Bowden
    • 1
  1. 1.Centre for Vision Speed and Signal ProcessingUniversity of SurreyGuildfordUK

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