Cross Correlation Function (XCF)/Coefficient between Two Images
- Practical Electron Microscopy and Database -
- An Online Book -  




The cross correlation between two images can be evaluated by cross-correlation function (XCF) or cross-correlation coefficient (XCC).

The Cross Correlation Function (XCF) between any two images Cx(r) and Cy(r)  can be defined in terms of their Fourier transforms, given by,

          Cross Correlation Function (XCF) between Two Images --------------------- [3717a]

The Cross Correlation Coefficient between the two images can be defined as,
          Cross Correlation Function (XCF) between Two Images --------------------- [3717b]
          Cross Correlation Function (XCF)/Coefficient and Cross Correlation Function (XCF)/Coefficient -- The mean values of the image IA and IB, respectively.
          x and y -- The coordinates in the two images (e.g. the coordinates of a pixel if the images are in digital format).

From Equation 3717b, we can know the coefficient XCC(A,B) is equal to 1 if the two images are absolutely identical. In the case of which Gatan DM is used, XCC(A,B) based on Equation 3717b can be computed by scripts.