Bandpass filter with ImageMagick - image

Question

I've been using Fiji's FFT bandpass filter with great success, but I'd like to do this in the command line with ImageMagick. I see that ImageMagick has FFT filters and they documentation includes low-pass and high-pass filters, but can I perform a bandpass filter?
The bandpass filter settings from Fiji that seem to work well for me:
(With apologies that my filter and FFT knowledge is... really bad, so maybe this is easily accomplished if I knew what to chain together, etc...)

Answer 1

A band pass filter similar to the low pass one you show in your link would be a white ring on a black background for square images. The inner and outer radii of the ring determine the frequencies that would be passed. In ImageMagick you can do that as follows:
Input:
Create ring image:
convert lena-1.png -fill black -colorize 100 \
-fill white -draw "translate 64,64 circle 0,0 0,50" \
-fill black -draw "translate 64,64 circle 0,0 0,20" \
-alpha off -blur 0x1 \
ring.png
Do FFT processing with stretch to full dynamic range:
convert lena-1.png -fft \
\( -clone 0 ring.png -compose multiply -composite \) \
-swap 0 +delete -ift -auto-level \
lena_bp.png
Alternate processing with gain of 10x:
convert lena-1.png -fft \
\( -clone 0 ring.png -compose multiply -composite \) \
-swap 0 +delete -ift -evaluate multiply 10 \
lena_bp.png
As I do not know what they have coded in ImageJ or Fiji and you showed no output, I can only guess that what might be equivalent would be to have inner and outer radii at 3 and 40 pixels from the center. Also I have added again a gain of 10x in dynamic range to make it more visible:
convert lena-1.png -fill black -colorize 100 \
-fill white -draw "translate 64,64 circle 0,0 0,40" \
-fill black -draw "translate 64,64 circle 0,0 0,3" \
-alpha off -blur 0x1 \
ring.png
convert lena-1.png -fft \
\( -clone 0 ring.png -compose multiply -composite \) \
-swap 0 +delete -ift -evaluate multiply 10 \
lena_bp.png
Note that I blurred the ring slightly to reduce "ringing" artifacts. (See https://en.wikipedia.org/wiki/Ringing_artifacts). Many low pass, high pass and band pass filters have stronger/longer tapering similar to increasing the blur. There are specially designed tapers, such as Butterworth. (see https://en.wikipedia.org/wiki/Butterworth_filter)
I have an expanded version of the FFT documentation from ImageMagick at http://www.fmwconcepts.com/imagemagick/fourier_transforms/fourier.html (Note some of the Jinc filtering is a bit outdated. Since I wrote that, Imagemagick implemented the Jinc function within -fx)
Here is a small set of commands to do it all in Unix syntax. Remove the +write ring.png if you do not want it to be created. This code is limited to square images.
ImageMagick 6:
inner=3
outer=40
infile="lena-1.png"
cent=`convert "$infile" -format "%[fx:floor((w-1)/2)]" info:`
inname=`convert "$infile" -format "%t" info:`
suffix=`convert "$infile" -format "%e" info:`
convert "$infile" \
\( +clone -fill black -colorize 100 \
-fill white -draw "translate $cent,$cent circle 0,0 0,$outer" \
-fill black -draw "translate $cent,$cent circle 0,0 0,$inner" \
-alpha off -blur 0x1 +write ring.png \
-write mpr:bpass +delete \) \
-fft \( -clone 0 mpr:bpass -compose multiply -composite \) \
-swap 0 +delete -ift -evaluate multiply 10 \
${inname}_bandpass_${inner}_${outer}.$suffix
ImageMagick 7 (only one command line):
inner=3
outer=40
infile="lena-1.png" \
magick "$infile" \
-set option:cent "%[fx:floor((w-1)/2)]" \
-set filename:fn "%t_bandpass_${inner}_${outer}.%e" \
\( +clone -fill black -colorize 100 \
-fill white -draw "translate "%[cent],%[cent]" circle 0,0 0,$outer" \
-fill black -draw "translate "%[cent],%[cent]" circle 0,0 0,$inner" \
-alpha off -blur 0x1 +write ring.png \
-write mpr:bpass +delete \) \
-fft \( -clone 0 mpr:bpass -compose multiply -composite \) \
-swap 0 +delete -ift -evaluate multiply 10 \
"%[filename:fn]"
If you mean band enhanced (band boost) and not band pass, then you add the result back with the original (-compose plus -composite). In ImageMagick 6, that would be:
inner=3
outer=40
infile="lena-1.png"
cent=`convert "$infile" -format "%[fx:floor((w-1)/2)]" info:`
inname=`convert "$infile" -format "%t" info:`
suffix=`convert "$infile" -format "%e" info:`
convert "$infile" \
\( +clone -fill black -colorize 100 \
-fill white -draw "translate $cent,$cent circle 0,0 0,$outer" \
-fill black -draw "translate $cent,$cent circle 0,0 0,$inner" \
-alpha off -blur 0x1 +write ring.png \
-write mpr:bpass +delete \) \
-fft \( -clone 0 mpr:bpass -compose multiply -composite \) \
-swap 0 +delete -ift "$infile" -compose plus -composite \
${inname}_bandenhance_${inner}_${outer}.$suffix
These are different results from what I get with those settings in ImageJ. Unfortunately, I do not know what they are doing. The ImageJ results look more like low pass filtering to me than what I know as band enhanced/band pass. See https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=12&cad=rja&uact=8&ved=2ahUKEwjJvoWD6L7eAhXJslQKHf1jArgQFjALegQICBAC&url=https%3A%2F%2Fcanvas.instructure.com%2Ffiles%2F6907524%2Fdownload%3Fdownload_frd%3D1&usg=AOvVaw2ws15jPD6C2-yAkfHmHYMH and https://www.scribd.com/doc/51981950/Frequency-Domain-Bandpass-Filtering-for-Image-Processing
In ImageJ, perhaps they are using a Butterworth filter or larger Gaussian blur. Or perhaps they are only processing the intensity channel from say HSI or HSV or LAB.