![]() Thankfully you don't need to understand any of that to make it work. The direct dot product or pure convolution could likewise be used, but these are much slower. This type of correlation is a very standard statistical analysis tool to ascertain the agreement between two data sets, and Fourier transforms are used here purely for convenience and speed. In addition to this, the normalized cross-correlation used here is essentially a Pearson product moment correlation, where the expected value of the convolution of the data sets is defined as the inverse Fourier transform of the convolution of the two Fourier transforms (The equation below for nXcorr should now look more familiar). There are several ways of understanding this further, a very simple example is that this normalized cross-correlation is not unlike a dot product where the result is the equivalent to the cosine of the angle between the two normalized pixel intensity vectors. Normalized Cross-Correlation (NCC) is by definition the inverse Fourier transform of the convolution of the Fourier transform of two (in this case) images, normalized using the local sums and sigmas (see below).
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