How do you create a discrete histogram that accurately describes the information in a continuous signal? More specifically, how do you accomplish this task for a pair of two-dimensional (2D) images? One answer to these questions is to apply the methodology of nonparametric (NP) windows.

The goal discussed in this paper is to maximize the amount of shared (mutual) information in an image pair. To do so, appropriate transformation on data from each image must be applied. The authors begin their discussion with a description of a transformation that yields a piece-wise continuous histogram for a single one-dimensional (1D) signal. Next, a transform is presented for a pair of 1D signals. The discussion expands to explain the technique for a pair of 2D signals, the new area of development for the paper. The math behind the technique for the pair of 2D signals is similar to the math of the simpler cases, but describes a solution to the problem in an additional dimension. The pair of 2D signal formulations is simplified by the application of Green’s theorem. The formulation is made even more accurate by building a grid where a cell contains smaller irregular rectangles that capture values from the actual signal. Finally, algorithm efficacy tests demonstrate that the NP windows technique is less biased, and converges more closely to the global mutual information maximum, than any of the other methods considered.

The paper is certainly appropriate for people who outfit magnetic resonance imaging (MRI) or computed axial tomography (CAT) scan equipment with software and/or hardware that builds images from signals. More generally, the paper is of interest to anyone concerned with accurate signal processing.