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Correlation Functions

 

Autocorrelation Function

For an M x N image, the autocorrelation function, S(x,y), takes the form as shown below:

 

AutoCorrelation Function for Image

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To reduce the calculation time SPIP will typically be using Fourier algorithm for the calculation of correlation functions.

 

 

For two images I and J of size M x N pixels, the cross correlation function, Sx(x,y), can be expressed as shown below:

 

 

Cross-correlation Function

The cross-correlation function is used for detecting certain patterns and used internally in SPIP for correlation averaging and linearity analysis

 

Cross-correlation function for Image

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