Name

filt_gaussl - Gaussian low-pass Fourier filter

Usage

output = filt_gaussl(image, sigma, pad)

Input

image

input image (can be either real or Fourier)

sigma

standard deviation of the Gaussian function in absolute frequency units `f_a`.

pad

logical flag specifying whether before filtering the image should be padded with zeroes in real space to twice the size (this helps avoiding aliasing artifacts). (Default pad = False).

• Note: for sigma = 0.5 (the Nyquist frequency) the value of the filter at the maximum frequency is `G(f_N)=1/sqrt(e)=0.61`.

Output

output

filtered image. Output image is real when input image is real or Fourier when input image is Fourier

Method

Fourier transform of the input image is multiplied by a radially symmetric Gaussian filter:

• `G(f) = exp(-f^2/(2 sigma_f^2))`

In effect, it is same as convolution to a real space symmetric Gaussian model, whose sigma is

• `sigma_r = 1.0/(2*pi*sigma_f)` 

For example: for any image m if you do:

   fm1 = filt_gaussl( m, 0.1 )
   fm2 = rsconvolution( m, model_gauss(1.0/(2*pi*0.1), nx, ny, nz) )
   print  ccc(fm1, fm2)

the ccc between the fm1 and fm2 should be 1.0.

Reference

Gonzalez, R. F., Woods, R. E., 2002. Digital Image Processing. Prentice Hall, Upper Saddle River, NJ.

Author / Maintainer

Pawel A. Penczek

Keywords

category 1

FILTER

category 2

FOURIER

Files

filter.py

Maturity

stable

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

Bugs

None. It is perfect.