Name

acf - calculate the circulant autocorrelation function of an image using multiplication in Fourier space.

Usage

output = acf(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 autocorrelation function of the input image. Real. The origin of the autocorrelation function (term acf(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 autocorrelation function of an image f is performed in Fourier space as `|hat(f)|^2`

• In real space, this corresponds to:

• `acf(n)=sum_(k=0)^(nx-1)f((k+n+nx)mod\nx)f(k)`

• `n = -(nx)/2, ..., (nx)/2`

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

Reference

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

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.