Fred's ImageMagick Scripts


    Copyright © Fred Weinhaus

    My scripts are available free of charge for non-commercial (non-profit) use, ONLY.

    For use of my scripts in commercial (for-profit) environments or non-free applications, please contact me (Fred Weinhaus) for licensing arrangements. My email address is fmw at alink dot net.

    If you: 1) redistribute, 2) incorporate any of these scripts into other free applications or 3) reprogram them in another scripting language, then you must contact me for permission, especially if the result might be used in a commercial or for-profit environment.

    Usage, whether stated or not in the script, is restricted to the above licensing arrangements. It is also subject, in a subordinate manner, to the ImageMagick license, which can be found at:

    Please read the Pointers For Use on my home page to properly install and customize my scripts.


Performs convolution on an image in the frequency domain.

Download Script

last modified: December 02, 2023

USAGE: fftconvol infile filtfile outfile
USAGE: fftconvol [-h or -help]

No options are required.

PURPOSE: To perform convolution on an image in the frequency domain.

DESCRIPTION: FFTCONVOL performs convolution on an image in the frequency domain using a filter image. Two inputs are required. The image and a grayscale spatial domain convolution filter. Both the image and the grayscale spatial domain filter are transformed to the frequency domain using +fft. Then the Fourier transform of the filter is multiplied with the fft of the image and the product is then returned to the spatial domain using +ift. Any alpha channel on the filter will be removed automatically before processing. If the image has an alpha channel it will not be processed, but simply copied from the input to the output.



The filter image must be appropriately centered and padded with black to the same size as the input image.

REQUIREMENTS: IM version 6.5.4-7 or higher, but compiled with HDRI enabled in any quantum level of Q8, Q16 or Q32. Also requires the FFTW delegate library.

LIMITATIONS: This script works well only with even, square images. Otherwise, the FFT will pad them with black to conform. However, there will be excessive ringing due to the color discontinuity associated with the padding. This even, square limitation is a ramification of the current IM implementation that needs addressing at some future time. It is not a limitation of FFTW.

See Fourier Transform with ImageMagick, for more details.

CAVEAT: No guarantee that this script will work on all platforms, nor that trapping of inconsistent parameters is complete and foolproof. Use At Your Own Risk.


Gaussian Blurring


convert -size 128x128 xc:black -fill white -draw "point 64,64" \
-blur 0x2 -contrast-stretch 0 -alpha off gaussian2.png


Horizontal Motion Blur


convert -size 128x128 xc:black -fill white \
-draw "line 61,64 67,64" -alpha off motion7.png


Lens Defocus


convert -size 128x128 xc:black -fill white \
-draw "circle 64,64 67,64" -alpha off defocus7.png


What the script does is as follows:

  • Computes the real and imaginary components of both the image and the filter
  • Rolls the center of the transformed filter images to the
    upper left corner and stretches it to full dynamic range.
  • Performs complex number multiplication using the four resulting transformed images
  • Converts the real and imaginary products back to the spatial domain

This is equivalent to the following IM commands.

  • width=`identify -ping -format "%w" $infile`
  • height=`identify -ping -format "%h" $infile`
  • cx=`convert xc: -format "%[fx:floor(($width+1)/2)]" info:`
  • cy=`convert xc: -format "%[fx:floor(($height+1)/2)]" info:`
  • gain=`convert $filtfile -format "%[fx:1/mean]" info:`
  • convert \( $filtfile -roll -${cx}-${cy} +fft -evaluate multiply $gain \) \
    \( $infile -alpha off +fft \) \
    \( -clone 0 -clone 2 -compose multiply -composite \) \
    \( -clone 1 -clone 3 -compose multiply -composite \) \
    \( -clone 4 -clone 5 +swap -compose minus -composite \) \
    \( -clone 1 -clone 2 -compose multiply -composite \) \
    \( -clone 0 -clone 3 -compose multiply -composite \) \
    \( -clone 7 -clone 8 -compose plus -composite \) \
    -delete 0,1,2,3,4,5,7,8 +ift \
    -crop ${width}x${height}+0+0 +repage $outfile