acfp - calculate the autocorrelation function of an image using padding with zeroes and multiplication in Fourier space.
output = acfp(image, center=True)
- input image (real)
- if set to True (default), the origin of the result is at the center; if set to False, the origin is at (0,0), the option is much faster, but the result is difficult to use
- autocorrelation function of the input image. Real. The origin of the autocorrelation function (term ccf(0,0,0)) is located at (int[n/2], int[n/2], int[n/2]) in 3D, (int[n/2], int[n/2]) in 2D, and at int[n/2] in 1D.
Calculation of the circulant autocorrelation function of an image f is performed first by padding with zeroes to twice the size in real space,
next by calculating Fourier transform of the image, then the modulus squared in Fourier space as `|hat(f)|^2`, then the inverse Fourier transform, and finally the acfp is windowed out using the size of original images.
- In real space, this corresponds to:
`n = -(nx)/2, ..., (nx)/2`
with the assumption that `f(k)=0 fo\r k<0 or kgenx`
Note: acfp is free from "wrap around" artifacts, although coefficients with large lag n have large error (statistical uncertainty).
Pratt, W. K., 1992. Digital image processing. Wiley, New York.
Author / Maintainer
Pawel A. Penczek
- category 1
- category 2
- works for most people, has been tested; test cases/examples available.
None. It is perfect.