Name

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

Usage

output = scfp(image, center=True)

Input

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

output

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.

Method

• Calculation of the circulant self-correlation 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 in Fourier space as `|hat(f)|`, then the inverse Fourier transform, and finally the scfp 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: scfp is free from "wrap around" artifacts, although coefficients with large lag n have large error (statistical uncertainty).

Reference

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

Author / Maintainer

Pawel A. Penczek

Keywords

category 1

FUNDAMENTALS

category 2

FOURIER

Files

fundamentals.py

Maturity

stable

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

Bugs

None. It is perfect.