Name

scfnp - calculate the normalized self-correlation function of an image using padding with zeroes and multiplication in Fourier space.

Usage

output = scfnp(image, center=True)

image: input image (real)
center: 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

output: normalized self-correlation function of the input image. Real. The origin of the self-correlation 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 normalized self-correlation function of an image f is performed by first normalization of the image by subtracting its average and by dividing it by its standard deviation. Next, theh image is padded with zeroes to twice the size in real space, Fourier transform is calculated, its modulus in Fourier space calculated as `|hat(f)|`, then the inverse Fourier transform, and finally the scfnp is windowed out using the size of original images.
This expression does not have any corresponding expression in real space - it can be considered to be adaptive filtration.

Note: scfnp is free from "wrap around" artifacts, although coefficients with large lag n have large error (statistical uncertainty).

van Heel, M., Schatz, M., Orlova, E., 1992. Correlation functions revisited. Ultramicroscopy 46, 307-316.

Pawel A. Penczek

fundamentals.py

stable: works for most people, has been tested; test cases/examples available.

None. It is perfect.