Fred's ImageMagick Scripts



 

 

FFTCONVOL


Performs convolution on an image in the frequency domain.

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last modified: August 18, 2009



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. Currently useful only for low pass filtering, i.e. blurring.

ARGUMENTS:

None

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.

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.


EXAMPLES


Gaussian Blurring

Input

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

Arguments:
(none)



Horizontal Motion Blur

Input

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

Arguments:
(none)



Lens Defocus

Input

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

Arguments:
(none)



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