  The recently introduced Matching by Tone Mapping (MTM) dissimilarity measure
enables template matching under smooth non-linear distortions and also has a
well-established mathematical background. MTM operates by binning the template,
but the ideal binning for a particular problem is an open question. By pointing
out an important analogy between the well known mutual information (MI) and
MTM, we introduce the term "normalized unexplained variance" (nUV) for MTM to
emphasize its relevance and applicability beyond image processing. Then, we
provide theoretical results on the optimal binning technique for the nUV
measure and propose algorithms to find approximate solutions. The theoretical
findings are supported by numerical experiments. Using the proposed techniques
for binning shows 4-13% increase in terms of AUC scores with statistical
significance, enabling us to conclude that the proposed binning techniques have
the potential to improve the performance of the nUV measure in real
applications.
