Estimating the joint statistics of images using Nonparametric Windows with application to registration using Mutual Information

Recently, Nonparametric (NP) Windows has been proposed to estimate the statistics of real 1D and 2D signals. NP Windows is accurate because it is equivalent to sampling images at a high (infinite) resolution for an assumed interpolation model. This paper extends the proposed approach to consider joint distributions of image pairs. Second, Green's Theorem is used to simplify the previous NP Windows algorithm. Finally, a resolution-aware NP Windows algorithm is proposed to improve robustness to relative scaling between an image pair. Comparative testing of 2D image registration was performed using translation only and affine transformations. Although it is more expensive than other methods, NP Windows frequently demonstrated superior performance for bias (distance between ground truth and global maximum) and frequency of convergence. Unlike other methods, the number of samples and the number of bins have little effect on NP Windows and the prior selection of a kernel is not required.