# Name

scf - calculate the circulant self-correlation function of an image using multiplication in Fourier space.

# Usage

output = scf(image, center=True)

## Input

- image
- input image, can be either real or Fourier
- 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
- circulant self-correlation function of the input image. Real. The origin of the self-correlation function (term scf(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 in Fourier space as``|hat(f)|``

- This expression does not have any corresponding expression in real space - it can be considered to be adaptive filtration.
Note: for image size

*nx*and object size*m*, the circulant*scf*is valid only within``+//- (nx-m/2)``pixels from the origin. More distant*scf*values are corrupted by the "wrap around" artifacts.

# 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.