# Name

ccfp - calculate the cross-correlation function between two images using padding with zeroes and multiplication in Fourier space.

# Usage

output = ccfp(image, ref, center=True)

## Input

image
input image (real)
ref
second input image (real) (in the alignment problems, it should be the reference image).
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
cross-correlation function between image and ref. Real. The origin of the cross-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 cross-correlation function between image f and reference image g is performed first by padding with zeroes to twice the size in real space, next by calculating Fourier transforms of both images, then the product in Fourier space as `hat(f)hat(g)^**`, then the inverse Fourier transform, and finally the c_p is windowed out using the size of original images.

• In real space, this corresponds to:
• `\c_p(n)=sum_(k=0)^(nx-1)f(k+n)g(k)`

• `n = -(nx)/2, ..., (nx)/2`

• with the assumption that `g(k)=0 fo\r k<0 or kgenx`

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

# Reference

Pratt, W. K., 1992. Digital image processing. Wiley, New York.

Pawel A. Penczek

category 1
FUNDAMENTALS
category 2
FOURIER

fundamentals.py

# Maturity

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

# Bugs

None. It is perfect.

ccfp (last edited 2013-07-01 13:13:03 by localhost)