Approximately Optimal Binning for the Piecewise Constant Approximation of the Normalized Unexplained Variance (nUV) Dissimilarity Measure

TL;DR

This paper introduces an optimal binning method for the nUV dissimilarity measure, enhancing template matching performance by leveraging theoretical insights and algorithms, with significant improvements demonstrated through experiments.

Contribution

It provides the first theoretical analysis and algorithms for optimal binning of the nUV measure, extending its applicability beyond image processing.

Findings

4-13% increase in AUC scores with proposed binning techniques

Theoretical results support the effectiveness of the binning algorithms

Statistically significant performance improvements in experiments

Abstract

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.