Normalized weighted cross correlation for multi-channel image registration

The normalized cross-correlation (NCC) is widely used for image registration due to its simple geometrical interpretation and being feature-agnostic. Here, after reviewing NCC definitions for images with an arbitrary number of dimensions and channels, we propose a generalization in which each pixel value of each channel can be individually weighted using real non-negative numbers. This generalized normalized weighted cross-correlation (NWCC) and its zero-mean equivalent (ZNWCC) can be used, for example, to prioritize pixels based on signal-to-noise ratio. Like a previously defined NWCC with binary weights, the proposed generalizations enable the registration of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling. All NCC definitions discussed here are provided with discrete Fourier transform (DFT) formulations for fast computation. Practical aspects of NCC computational implementation are briefly discussed, and a convenient function to calculate the overlap of uniformly, but not necessarily isotropically, sampled images with irregular boundaries and/or sparse sampling is introduced, together with its DFT formulation. Finally, examples illustrate the benefit of the proposed normalized cross-correlation functions.