How do I subtract pixels from Gaussian, divide by Gaussian, and normalize in imagemagick

Question

I know exactly what I want to do, and could do it with python, scipy, and PIL. I want to use imagemagick, since it is designed specifically for these actions.

T is highest legal intensity (0, of course is lowest)
Input image into temporary MPC named I
Gaussian blur I and store into temporary MPC named G
Subtract and divide D = (I - G) / G
Get maximum M = max (T * abs(D))
Offset, normalize, and scale O = T * (D + M) / (2 * M)
Output O into file name output.png

I can't figure out how to do this from the online documentation. Imagemagick documentation vocabulary seems to be for image manipulation professionals and it is beyond my understanding.

What does the processing achieve? I presume it is single channel grayscale? Do you have sample input and output images? Were you hoping to achieve it on the commandline? What have you tried so far? — Mark Setchell, Jan 18 '18 at 20:55
Do you need to preserve negative values in D=(I-G)/G? If so, you would have to do that in an HDRI compiled Imagemagick. What is your version of Imagemagick and platform? If IM 7, then it it already HDRI compiled. — fmw42, Jan 18 '18 at 21:25

fmw42 · Answer 1 · 2018-01-19T03:07:57.343

I have tried to reproduce your commands in Imagemagick, but I am not sure of the result or about whether T and M should be in range 0 to 1 or 0 to Quantumrange (0 to 65535 for Q16 HDRI IM compile). I tested on the Imagemagick logo: image using Imagemagick 7.0.7.21 Q16 HDRI.

T="65000"
sigma=5
magick logo: I.mpc
magick I.mpc -blur 0x$sigma G.mpc
magick I.mpc G.mpc +swap -compose minus -composite G.mpc +swap -compose divide -composite D.mpc
M=`magick D.mpc D.mpc -compose multiply -composite -evaluate pow 0.5 -evaluate multiply $T -format "%[fx:maxima]" info:`
M2=`magick xc: -format "%[fx:2*$M]" info:`
magick D.mpc -evaluate add $M -evaluate divide $M2 -evaluate multiply $T output.png

Line 1: Set T=65000 (range 0 to 65355)
Line 2: Set gaussian blur sigma to 5
Line 3: Read the input into I.mpc
Line 4: Apply gaussian blur to I.mpc to create G.mpc
Line 5: Create D=(I-G)/G (requires HDRI IM 7 compile to keep negative values)
Line 6: Compute M=T*Max(sqrt(D*D)) as a single number variable in the range 0 to 65535 (Quantumrange for 16-bit IM compile)
Line 7: Compute 2*M as variable M2
Line 8: Compute output O = T * (D + M) / (2 * M)

If this is not correct (does not match your python, etc, approach, then please post and input and output example and then I might be able to correct any false assumptions or mistakes and make it work the same.

If wanting to use Imagemagick 6, then one would have to compile or get a version that is Q16 HDRI compiled. Then in the above commands, just change magick to convert.

Absolutely SPOT ON! I had intended to do this in a single command-line, but you have achieved the precise sequence I intended. Is there any way of giving you extra points for this gem? — jlettvin, Jan 19 '18 at 10:25
It cannot be done in one line due to the need to compute the variables M and M2 prior to their use in IM 6. It likely could be done in IM 7. — fmw42, Jan 19 '18 at 17:51

score 0 · Answer 2 · answered Jan 19 '18 at 11:15

0

Here is a bash script for handling Any 0-255 image file recognized by convert. I tried it on some sample files of my own. It works.

#!/bin/bash

echo $#
if [ $# -ne 1 ]
then
    echo "Usage: ${0} {imagefilename}"
elif [ -f "$1" ]
then
    T="255"
    sigma=5
    convert ${1} ${1}.I.mpc
    convert ${1}.I.mpc -blur 0x$sigma ${1}.G.mpc
    convert ${1}.I.mpc ${1}.G.mpc +swap -compose minus -composite ${1}.G.mpc +swap -compose divide -composite ${1}.D.mpc
    M=`convert ${1}.D.mpc ${1}.D.mpc -compose multiply -composite -evaluate pow 0.5 -evaluate multiply $T -format "%[fx:maxima]" info:`
    M2=`convert xc: -format "%[fx:2*$M]" info:`
    convert ${1}.D.mpc -evaluate add $M -evaluate divide $M2 -evaluate multiply $T ${1}.mdif.png
else
    echo "Usage: ${0} {imagefilename}\n!exists ${1}"
fi

I had hoped the imagemagick commands would have been easier to read and easier to understand but fmw42 achieved the goal.

answered Jan 19 '18 at 11:15

jlettvin

1,113
7
13

Consider double-quoting all instances of `${1}` so they look like `"${1}"` in your script in case you pass it a file with spaces in its name. – Mark Setchell Jan 19 '18 at 12:00
You should be able to combine the first two commands at least and save some I/O and time. `convert "$1" -write "$1.I.mpc" -blur 0x$sigma "$1.G.mpc"` – Mark Setchell Jan 19 '18 at 12:03
I have not tested this but I think you can replace the first 3 commands with the following and avoid the need for intermediate files by just saving stuff in memory (`MPR`)... `convert "$1" $ +clone -blur 0x$sigma -write MPR:G $ +swap -compose minus -composite MPR:G +swap -compose divide -composite "${1}.D.mpc"` – Mark Setchell Jan 19 '18 at 12:09
Yes, lines 3-5 (computation of D) can be done in one command. In IM 7 probably the whole thing can be done in one command (apart from the input variables). But in IM 6, you need to compute M and M2 in a separate command before using them in the remaining computation. With a little experience Imagemagick command are not that hard. The syntax is read two images, then do the image add, multiply, divide composite as desired. If you need to do another then add a new image to the result and provide the composite for that pair. – fmw42 Jan 19 '18 at 17:54

fmw42 · Answer 3 · 2018-01-20T03:26:55.090

CORRECTION:

I made a mistake in my previous posts. When using HDRI and needing to keep negative values or values outside the range 0 to quantumrange, any composite operations will by default clamp and give results as if HDRI was not enabled. So one needs to add defines before the composite operations to keep from clamping (clipping) to normal non-HDRI dynamic range limits. So the correct code would be as follows:

T="65000"
sigma=5
magick logo: I.mpc
magick I.mpc -blur 0x$sigma G.mpc
magick I.mpc G.mpc +swap -define compose:clamp=off -compose minus -composite G.mpc +swap -define compose:clamp=off -compose divide -composite D.mpc
M=`magick D.mpc D.mpc -define compose:clamp=off -compose multiply -composite -evaluate pow 0.5 -evaluate multiply $T -format "%[fx:maxima]" info:`
M2=`magick xc: -format "%[fx:2*$M]" info:`
magick D.mpc -evaluate add $M -evaluate divide $M2 -evaluate multiply $T output.png

The result is a bit different from my earlier results.

score 0 · Accepted Answer · answered Jan 20 '18 at 03:24

Here is the corrected method as one long command line using Imagemagick 7.0.7.21 Q16 HDRI.

T="65000"
sigma=5
magick \
\( logo: -write mpr:imgI +delete \) \
\( mpr:imgI -blur 0x$sigma -write mpr:imgG +delete \) \
\( mpr:imgI mpr:imgG +swap -define compose:clamp=off -compose minus -composite mpr:imgG +swap -define compose:clamp=off -compose divide -composite -write mpr:imgD +delete \) \
\( mpr:imgD mpr:imgD -define compose:clamp=off -compose multiply -composite -evaluate pow 0.5 -evaluate multiply $T -write mpr:imgT +delete \) \
mpr:imgT -set option:mm "%[fx:maxima]" -set option:nn "%[fx:2*maxima]" +delete mpr:imgD -evaluate add "%[mm]" -evaluate divide "%[nn]" -evaluate multiply $T output3.png

If this answer was of benefit, please consider giving it an up-vote. Note that I have correction answer — fmw42, Feb 14 '18 at 17:37

How do I subtract pixels from Gaussian, divide by Gaussian, and normalize in imagemagick

4 Answers4