Evaluation of Image Pairs

I and / are intensity values of the image pair, and (x,y) is the image shift. For shift values, when the particle images align with each other, a high correlation value is obtained 

In general, calculation of the correlation function is done in the Fourier space. Each sub-region is transformed into the Fourier space via a Fourier transformation. The subregions are spatially shifted to obtain good correlation between the image pairs. 

The cross correlation of two functions is equivalent to a complex conjugate multiplication of their Fourier transforms, that is, 

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