Name

cnv - calculate the circulant convolution function between two images using multiplication in Fourier space.

Usage

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

Input

image

input image, can be either real or Fourier

ref

second 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 convolution function between image and ref. Real. The origin of the convolution function (term cnv(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 convolution function between image f and reference image g is performed in Fourier space as `hat(f)hat(g)`

• In real space, this corresponds to:

• `cnv(n)=sum_(k=0)^(n_x-1)f((-k+n+n_x)(mod\n_x))g(k)`

• `n = -(n_x)/2, ..., (n_x)/2`

• Note: for image size nx and object size m, the circulant cnv is valid only within `+//- (n_x-m/2)` pixels from the origin. More distant cnv 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.