rem goto skip call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_hc.miff ^ horseshoe . clamp if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_hc.miff ^ sxs_hc.png
An automated method for squishing xyY image colours into the CIE horseshoe, a triangle of primaries, or any shape.
This script sqshxyY.bat is designed to manipulate colours from a raw camera image before it has been encoded with an RGB profile (such as sRGB, Rec2020, or ACES2065-1). The camera may have apparently captured chromaticities that do not fit within an RGB profile, or even within the locus of observable colours -- the CIE "horseshoe" (aka "tongue"). Manipulating xyY encodings before conversion to RGB may give more satisfactory final results.
This script has a similar purpose to the process module barymap described in Colours as barycentric coordinates, but is more automatic in operation.
This changes chroma only, ie the x and y channels of xyY images. The Y channel is unchanged, and hue is unchanged. The alpha channel, if any, is ignored and unchanged.
Some literature refers to "Yxy" colorspace. This is the same as xyY, with the channels in a different order.
This page originated from the pixls.us discussion Camera gamut outside horseshoe?.
See also references in the source code barymap.c.
The script sqshxyY.bat takes the following parameters:
| Option | Description |
|---|---|
| %1 | Input image in xyY space. |
| %2 | Output image in xyY space. |
| %3 | Shape. One of:
blank or dot. horseshoe named triangle of primaries eg sRGB six numbers eg 0.39,0.41,0.39,0.41,0.39,0.41 Default: sRGB. |
| %4 | White point. One of:
blank or dot. named white point eg D50 two numbers eg 0.39,0.41 |
| %5 | Method. One of:
clamp filmic divide null Default: filmic. |
Lists of named triangle of primaries, and of white points, is available from:
%IM7DEV%magick xc: -process 'barymap list primaries' NULL:
sRGB sRgbD50 Rec709 P3D65 DisplayP3 AdobeRGB Rec2020 ProPhotoRGB ACEScg ACES2065-1 xyY XYZ
%IM7DEV%magick xc: -process 'barymap list illuminants' NULL:
A D50 D60 D65 D65s D75 D100 D200 D300 D400 E Aa D50a D55a D65a D75a Ea D50i
If the shape is horseshoe, the white point will be according to the sRGB standard, which is D50. If the shape is specified by name such as sRGB, this also sets the white point according to that standard. (But beware: there are different standards with slightly different values.)
If parameter %4 is given, this will override the WP set by the shape.
The null method does all the work of converting the (x,y,Y) image to (relative_rho,theta,Y), then doesn't tweak the rho, and converts it back. This can be used to verify parts of the script.
The script also uses these environment variables:
| Variable | Description |
|---|---|
| sqxCLUTDIR | Directory for reading and witing cluts. |
| sqxHiLimit | hiLimit parameter for oogbox. |
| sqxMAXSTAT_FILE | If not blank, write maximum relative chroma to this file. |
| sqxFORCE_MAX | If not blank, assume this maximum relative chroma instead of calculted value. |
Creating the large clut isn't quick, even though the resulting files are small. Hence the script will only create the clut if it doesn't exist in the directory named in %sqxCLUTDIR%. It also writes any created cluts file to that directory. If %sqxCLUTDIR% is blank, the directory named in %ICCPROF% is used.
dir %ICCPROF%\sqx_clut* |findstr sqx_clut
17/01/2019 16:02 16,678 sqx_clut_4096_horseshoe_0_3127_0_329.tiff 16/01/2019 23:08 16,678 sqx_clut_4096_horseshoe_0_31_0_32.tiff 13/12/2018 20:32 16,678 sqx_clut_4096_horseshoe_0_34567_0_3585.tiff 20/12/2018 15:01 16,678 sqx_clut_4096_sRGB_0_3127_0_329.tiff 13/12/2018 20:48 16,678 sqx_clut_4096_sRGB_0_34567_0_3585.tiff 13/12/2018 11:20 2,342 sqx_clut_512_horseshoe_0_34567_0_3585.tiff 13/12/2018 11:28 2,342 sqx_clut_512_sRGB_0_34567_0_3585.tiff
The script calculates the maximum relative chroma, and uses this in the filmic and divide methods. Optionally, it writes this number to the file named in sqxMAXSTAT_FILE. Optionally, it ignores that number and uses sqxFORCE_MAX instead.
We take a raw image from a camera, convert it to XYZ with dcraw, and from there to xyY.
set SRCRAW=%PICTLIB%20171029\AGA_3443.NEF %DCRAW% -v -4 -w -W -o 5 -T -O sxs_src.tiff %SRCRAW% %IM7DEV%magick ^ sxs_src.tiff ^ -set colorspace XYZ ^ -colorspace xyY ^ -depth 32 ^ -define quantum:format=floating-point ^ sxs_xyy.miff
We demonstrate squishing colours into the horseshoe, and into the sRGB triangle. For each, we show the three methods: clamp, filmic and divide.
Squish into horseshoe with clamp method:
rem goto skip call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_hc.miff ^ horseshoe . clamp if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_hc.miff ^ sxs_hc.png |
|
Squish into horseshoe with filmic method:
call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_hf.miff ^ horseshoe . filmic if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_hf.miff ^ sxs_hf.png |
|
Squish into horseshoe with divide method:
call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_hd.miff ^ horseshoe . divide if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_hd.miff ^ sxs_hd.png |
|
Squish into sRGB triangle with clamp method:
Create a text file for drawing the primaries and WP:
%IM7DEV%magick xc: -process 'barymap v' NULL:
call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_sc.miff ^ sRGB . clamp if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_sc.miff ^ sxs_sc.png call %PICTBAT%drPrimWp ^ sxs_sc.png ^ sxs_sc.png ^ sxs_primwp.lis |
|
Squish into sRGB triangle with filmic method:
call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_sf.miff ^ sRGB . filmic if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_sf.miff ^ sxs_sf.png call %PICTBAT%drPrimWp ^ sxs_sf.png ^ sxs_sf.png ^ sxs_primwp.lis |
|
Squish into sRGB triangle with divide method:
call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ sxs_sd.miff ^ sRGB . divide if ERRORLEVEL 1 exit /B 1 call %PICTBAT%xyyHorse ^ sxs_sd.miff ^ sxs_sd.png call %PICTBAT%drPrimWp ^ sxs_sd.png ^ sxs_sd.png ^ sxs_primwp.lis |
|
We tweak the chroma of colours in an image to put them inside a given shape (a horseshoe, triangle, whatever).
Step 1: In cartesian coordinates (x,y) of xyY space, given a shape and a centre within that shape, we calculate the polar coordinates (rho, theta) of each colour, and normalise rho so it is 1.0*QuantumRange at the edge of the shape. Larger values mean the colour is outside the shape. Smaller values mean the colour is inside the shape.
When the shape is the CIE horseshoe, normalised rho is the excitation purity.
Step 2: Then we tweak values of relative rho to be no greater than 1.0, using one of these methods:
Step 3: Then we invert the rho normalisation, and convert the polar coordinates (rho, theta) back to cartesian coordinates (x,y).
The three steps are detailed below, after some preparation work.
We need a clut image with Nx1 pixels that gives the radius of the shape at any given hue.
We create a square image and draw the horseshoe, or other shape, in white on a black background. Unroll the image, centred on the white point, setting Rmax to the diagonal of the input. ]]Trim it to remove lines that are entirely black from the top, and]] scale to one row. The result is a Nx1 clut file. It represents the radius of the shape at different angles from north, clockwise, as a proportion of the image diagonal. [[The value is 100% at the maximum radius.]]
set HSESHOE=m 426.8 358.8 c-106.3 -106.3 -177.2 -174.2 -222.7 -219.7 -39.2 -39.2 -94 -73.4 -114.3 -73.4 -28.7 0 -39.5 45.1 -39.5 98.5 0 59.3 18.4 227.4 66 306.4 0 0 10.3 15.6 21.7 20 l 288.8 -131.8 z set DR_HSESHOE=translate -47.8,19.2 path '%HSESHOE%' set WPx=0.31 set WPy=0.32 %IM7DEV%magick ^ -size 500x500 xc:Black ^ -fill White -stroke None ^ -draw "scale %%[fx:w/512],%%[fx:h/512] stroke-width %%[fx:512/w] %DR_HSESHOE%" ^ +write sxs_shape.png ^ -rotate 180 ^ -virtual-pixel Black ^ -distort depolar %%[fx:hypot(w,h)/sqrt(2)],0,%%[fx:w-w*%WPx%],%%[fx:h*%WPy%] ^ -scale "x1^!" ^ -flop ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_clut.miff
|
sxs_shape.png |
|
Show a graph of the clut:
call %PICTBAT%graphLineCol ^ sxs_clut.miff . . sxs_clut_glc.png |
|
The script writes cluts with a filename "sqx_clut_*.tiff". The filename is specific to the clut size, the shape, and the white point.
[Putting OOH into the box: from an image in xyY, we can express chromaticity as (rho,theta) roughly (chroma,hue) where rho is normalised to be 1.0 at the horseshoe. We can also do the inverse.
This readily gives the maximum rho, hence a divisor for barymap gain. Better, a scheme such as oogbox.htm, a "filmic" curve.]
From the xyY image: subtract the xy of the white point, convert the cartesian coordinates (x and y) channels to polar (rho and theta), and save the three channels.
rho ranges from 0.0 to 100% of Quantum, increasing anti-clockwise, at zero and 100% where x=WPx and y<WPy, ie the line "south" of the WP on the conventional diagram.
FIXME: also check image has embedded XYZ profile.
%IM7DEV%magick ^
sxs_xyy.miff ^
-set colorspace sRGB ^
-strip ^
+profile "*" ^
-define quantum:format=floating-point ^
-depth 32 ^
-process 'rhotheta offset %WPx%,%WPy%' ^
-channel RGB -separate +channel ^
( -clone 0 ^
-write sxs_rho.miff ^
+delete ) ^
-delete 0 ^
( -clone 0 ^
-write sxs_theta.miff ^
-negate ^
+delete ) ^
-delete 0 ^
sxs_Y.miff
Find the radius of the shape at every hue:
%IM7DEV%magick ^ sxs_theta.miff ^ sxs_clut.miff ^ -clut ^ -colorspace Gray ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_rho0.miff
sxs_rho0.miff has the radius of the shape at that hue. [[A value of 1.0*QuantumRange is the largest radius.]]
Find the relative rho. That is, at each pixel, rho divided by the radius of the shape at that hue.
%IM7DEV%magick ^ sxs_rho.miff ^ sxs_rho0.miff ^ -define compose:clamp=off ^ -compose DivideSrc -composite ^ -colorspace Gray ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_rho_rel.miff
call %PICTBAT%rhoStats sxs_rho_rel.miff
MIN=6.85305e-08 MEAN=0.179919 MAX=1.13878 PROPOUT=2.42229e-06
%IM7DEV%magick ^ sxs_rho_rel.miff ^ -process 'oogbox h 0.7 channel 0 v' ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_rho_rel2.miff %IM7DEV%magick ^ sxs_rho_rel.miff ^ -clamp ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_rho_rel2.miff %IM7DEV%magick ^ sxs_rho_rel.miff ^ -evaluate Divide %%[fx:maxima] ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_rho_rel2.miff
This is the inverse of step 1.
Multiply the [adjusted] relative rho by the rho at that hue to get the absolute rho. Combine this with the unchanged theta and Y to get a (rho,theta,Y) image. The inverse rhotheta module converts this to xyY, and adds the origin xy.
%IM7DEV%magick ^ sxs_rho_rel2.miff ^ sxs_rho0.miff ^ -define compose:clamp=off ^ -compose Multiply -composite ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_theta.miff ^ sxs_Y.miff ^ -combine ^ -set colorspace xyY ^ -process 'rhotheta offset %WPx%,%WPy% inverse' ^ sxs_xyy_new.miff
Show the xy chart and a JPG sRGB version:
call %PICTBAT%xyyHorse ^ sxs_xyy_new.miff sxs_xyy_new_out.png |
|
Show a sRGB version:
%IM7DEV%magick ^ sxs_xyy_new.miff ^ -set colorspace xyY -colorspace XYZ ^ -profile sRGB.icc ^ -resize 600x600 ^ sxs_srgb.jpg |
|
A hald clut might transform:
The filmic and divide methods automatically use the maximum relative chroma of the image. To create a hald clut that does the same processing, we need to find the maximum that was used, and force it to be used when creating the hald.
:skip set sqxMAXSTAT_FILE=sxs_max_stat.lis call %PICTBAT%sqshxyY ^ sxs_xyy.miff ^ NULL: ^ sRGB . filmic if ERRORLEVEL 1 exit /B 1 for /F %%A in (%sqxMAXSTAT_FILE%) do set maxChroma=%%A echo maxChroma=%maxChroma%
maxChroma=2.14044
We make an identity hald clut in xyY colorspace:
%IM7DEV%magick ^ hald:16 ^ -set colorspace xyY ^ -define quantum:format=floating-point ^ -depth 32 ^ sxs_hald.miff
call %PICTBAT%xyyHorse ^ sxs_hald.miff sxs_hald.png |
|
We squish values:
set sqxFORCE_MAX=%maxChroma% call %PICTBAT%sqshxyY ^ sxs_hald.miff ^ sxs_hald2.miff ^ sRGB . filmic if ERRORLEVEL 1 exit /B 1 set sqxFORCE_MAX=
call %PICTBAT%xyyHorse ^ sxs_hald2.miff sxs_hald2.png |
|
We could use this result, sxs_hald2.miff, to convert xyY images to squished xyY images. However, we might use it on an image with relative chroma greater than %maxChroma%, so we should ensure the hald will gracefully clamp those colours.
call %PICTBAT%sqshxyY ^ sxs_hald2.miff ^ sxs_hald3.miff ^ sRGB . clamp
call %PICTBAT%xyyHorse ^ sxs_hald3.miff sxs_hald3.png |
|
[Why is the XYZ triangle not an exact triangle?]
Now the hald contains only chromaticities that are within the sRGB triangle.
%IM7DEV%magick ^ sxs_xyy.miff ^ sxs_hald3.miff ^ -strip ^ -hald-clut ^ -alpha off ^ -set colorspace xyY ^ +write sxs_s_xyy.miff ^ -colorspace sRGB ^ sxs_s.miff
[Do we still have the XYZ profile?]
%IM7DEV%magick ^ sxs_s_xyy.miff ^ -verbose ^ info:
Image: sxs_s_xyy.miff
Format: MIFF (Magick Image File Format)
Class: DirectClass
Geometry: 4924x7378+0+0
Resolution: 300x300
Print size: 16.4133x24.5933
Units: PixelsPerInch
Colorspace: xyY
Type: TrueColor
Endianess: Undefined
Depth: 32-bit
Channel depth:
Channel 0: 32-bit
Channel 1: 32-bit
Channel 2: 32-bit
Channel statistics:
Pixels: 36329272
Channel 0:
min: 7.48537e+08 (0.174282)
max: 2.41355e+09 (0.561948)
mean: 1.33357e+09 (0.310496)
standard deviation: 1.41579e+08 (0.0329639)
kurtosis: 1.01152
skewness: -0.666185
entropy: 0.911231
Channel 1:
min: 4.20375e+08 (0.0978763)
max: 2.48519e+09 (0.578628)
mean: 1.49697e+09 (0.34854)
standard deviation: 2.25636e+08 (0.052535)
kurtosis: 0.758821
skewness: 0.27168
entropy: 0.923141
Channel 2:
min: 4.45652e+06 (0.00103761)
max: 4.29497e+09 (1)
mean: 4.42186e+08 (0.102954)
standard deviation: 8.97874e+08 (0.209053)
kurtosis: 10.1702
skewness: 3.34113
entropy: 0.808902
Image statistics:
Overall:
min: 4.45652e+06 (0.00103761)
max: 4.29497e+09 (1)
mean: 1.09091e+09 (0.253997)
standard deviation: 4.21696e+08 (0.0981838)
kurtosis: 2.95854
skewness: 0.678704
entropy: 0.881091
Rendering intent: Perceptual
Gamma: 1
Chromaticity:
red primary: (0.64,0.33)
green primary: (0.3,0.6)
blue primary: (0.15,0.06)
white point: (0.3127,0.329)
Matte color: grey74
Background color: white
Border color: srgb(223,223,223)
Transparent color: none
Interlace: None
Intensity: Undefined
Compose: Over
Page geometry: 4924x7378+0+0
Dispose: Undefined
Iterations: 0
Compression: None
Orientation: TopLeft
Properties:
date:create: 2019-03-13T13:00:48+00:00
date:modify: 2019-03-13T13:00:48+00:00
exif:ExposureTime: 0.033333
exif:FNumber: 8
exif:FocalLength: 20
exif:ISOSpeedRatings: 400
icc:copyright: auto-generated by dcraw
icc:description: XYZ
icc:manufacturer: XYZ
icc:model: XYZ
signature: 1c36db2692fec936d023dc1795fb097f4e5d350a0f56e165a06dd582d307dc4d
tiff:alpha: unspecified
tiff:artist: Alan Gibson
tiff:endian: lsb
tiff:make: Nikon
tiff:model: D800
tiff:photometric: RGB
tiff:rows-per-strip: 1
tiff:software: dcraw v9.27
tiff:timestamp: 2017:10:29 15:03:38
Tainted: False
Filesize: 415.756MiB
Number pixels: 36.3293M
Pixels per second: 6.55172MB
User time: 4.954u
Elapsed time: 0:06.545
Version: ImageMagick 7.0.7-28 Q32 x86_64 2018-12-09 http://www.imagemagick.org
%IM7DEV%magick ^ sxs_s.miff ^ -verbose ^ info:
Image: sxs_s.miff
Format: MIFF (Magick Image File Format)
Class: DirectClass
Geometry: 4924x7378+0+0
Resolution: 300x300
Print size: 16.4133x24.5933
Units: PixelsPerInch
Colorspace: sRGB
Type: TrueColor
Endianess: Undefined
Depth: 32-bit
Channel depth:
Red: 32-bit
Green: 32-bit
Blue: 32-bit
Channel statistics:
Pixels: 36329272
Red:
min: 123168 (2.86773e-05)
max: 5.00797e+09 (1.16601)
mean: 1.05118e+09 (0.244747)
standard deviation: 8.55543e+08 (0.199197)
kurtosis: 7.36047
skewness: 2.72601
entropy: 0.89222
Green:
min: 6.82383e+07 (0.015888)
max: 4.34779e+09 (1.0123)
mean: 1.17491e+09 (0.273555)
standard deviation: 8.6788e+08 (0.202069)
kurtosis: 5.01274
skewness: 2.33188
entropy: 0.906312
Blue:
min: 3.40549e+06 (0.000792903)
max: 4.32106e+09 (1.00608)
mean: 1.11752e+09 (0.260192)
standard deviation: 9.86508e+08 (0.229689)
kurtosis: 3.582
skewness: 2.14339
entropy: 0.901631
Image statistics:
Overall:
min: 123168 (2.86773e-05)
max: 5.00797e+09 (1.16601)
mean: 1.11454e+09 (0.259498)
standard deviation: 9.0331e+08 (0.210318)
kurtosis: 5.0532
skewness: 2.36834
entropy: 0.900054
Rendering intent: Perceptual
Gamma: 0.454545
Chromaticity:
red primary: (0.64,0.33)
green primary: (0.3,0.6)
blue primary: (0.15,0.06)
white point: (0.3127,0.329)
Matte color: grey74
Background color: white
Border color: srgb(223,223,223)
Transparent color: none
Interlace: None
Intensity: Undefined
Compose: Over
Page geometry: 4924x7378+0+0
Dispose: Undefined
Iterations: 0
Compression: None
Orientation: TopLeft
Properties:
date:create: 2019-03-13T13:00:54+00:00
date:modify: 2019-03-13T13:00:54+00:00
exif:ExposureTime: 0.033333
exif:FNumber: 8
exif:FocalLength: 20
exif:ISOSpeedRatings: 400
icc:copyright: auto-generated by dcraw
icc:description: XYZ
icc:manufacturer: XYZ
icc:model: XYZ
signature: 7d4b4f15be19c06d5939285147113c47f4ccb2d7a99cac28496c92224b29d46b
tiff:alpha: unspecified
tiff:artist: Alan Gibson
tiff:endian: lsb
tiff:make: Nikon
tiff:model: D800
tiff:photometric: RGB
tiff:rows-per-strip: 1
tiff:software: dcraw v9.27
tiff:timestamp: 2017:10:29 15:03:38
Tainted: False
Filesize: 415.756MiB
Number pixels: 36.3293M
Pixels per second: 7.42323MB
User time: 4.875u
Elapsed time: 0:05.893
Version: ImageMagick 7.0.7-28 Q32 x86_64 2018-12-09 http://www.imagemagick.org
We may as well incorporate the next stage, which is converting the xyY encoding to an RGB encoding.
As I use dcraw to make XYZ images, and dcraw embeds an XYZ ICC profile, I will convert to XYZ then assign that profile to the hald, then convert the hald to sRGB.
%IM7DEV%magick ^ sxs_hald3.miff ^ -strip ^ -colorspace XYZ ^ -set profile "%ICCPROFFWD%/dcrXYZ.icc" ^ -profile "%ICCPROFFWD%/sRGB-elle-V4-srgbtrc.icc" ^ sxs_hald4.miff
%IM7DEV%magick ^ sxs_hald3.miff ^ -strip ^ -set colorspace xyY ^ -colorspace sRGB ^ sxs_hald4a.miff
[BUG: hald4 has negative values.]
%IM7DEV%magick ^ sxs_xyy.miff ^ sxs_hald4a.miff ^ -hald-clut ^ -alpha off ^ -strip ^ -set colorspace sRGB ^ sxs_x4a.miff
Now we can convert xyY images to sRGB with that hald, and assign the sRGB profile:
%IM7DEV%magick ^ sxs_xyy.miff ^ sxs_hald4.miff ^ -hald-clut ^ -alpha off ^ -strip ^ -set colorspace sRGB ^ -set profile %ICCPROFFWD%/sRGB-elle-V4-srgbtrc.icc ^ sxs_srgb.miff
%IM7DEV%magick ^ sxs_src.tiff ^ sxs_hald4.miff ^ -hald-clut ^ -alpha off ^ -strip ^ -set colorspace sRGB ^ -set profile %ICCPROFFWD%/sRGB-elle-V4-srgbtrc.icc ^ sxs_srgb2.miff
As a check, all pixel values should be in the range 0 to 100%.
%IM7DEV%magick ^ sxs_srgb.miff ^ -verbose ^ info:
Image: sxs_srgb.miff
Format: MIFF (Magick Image File Format)
Class: DirectClass
Geometry: 4924x7378+0+0
Resolution: 300x300
Print size: 16.4133x24.5933
Units: PixelsPerInch
Colorspace: sRGB
Type: TrueColor
Endianess: Undefined
Depth: 32-bit
Channel depth:
Red: 32-bit
Green: 32-bit
Blue: 32-bit
Channel statistics:
Pixels: 36329272
Red:
min: -7.04145e+09 (-1.63947)
max: 2.72204e+09 (0.633775)
mean: 8.81828e+07 (0.0205317)
standard deviation: 5.57613e+08 (0.129829)
kurtosis: 14.5165
skewness: 0.978066
entropy: 0.619863
Green:
min: -1.31329e+09 (-0.305775)
max: 2.45743e+09 (0.572164)
mean: 2.09088e+08 (0.0486821)
standard deviation: 5.24037e+08 (0.122012)
kurtosis: 9.33306
skewness: 3.22879
entropy: 0.744437
Blue:
min: -6.27556e+07 (-0.0146114)
max: 2.39936e+09 (0.558644)
mean: 2.37565e+08 (0.0553124)
standard deviation: 5.95204e+08 (0.138582)
kurtosis: 6.3409
skewness: 2.78778
entropy: 0.70688
Image statistics:
Overall:
min: -7.04145e+09 (-1.63947)
max: 2.72204e+09 (0.633775)
mean: 1.78279e+08 (0.0415087)
standard deviation: 5.58951e+08 (0.130141)
kurtosis: 10.083
skewness: 2.28453
entropy: 0.690393
Rendering intent: Perceptual
Gamma: 0.454545
Chromaticity:
red primary: (0.64,0.33)
green primary: (0.3,0.6)
blue primary: (0.15,0.06)
white point: (0.3127,0.329)
Matte color: grey74
Background color: white
Border color: srgb(223,223,223)
Transparent color: none
Interlace: None
Intensity: Undefined
Compose: Over
Page geometry: 4924x7378+0+0
Dispose: Undefined
Iterations: 0
Compression: None
Orientation: TopLeft
Properties:
date:create: 2019-03-13T13:03:31+00:00
date:modify: 2019-03-13T13:03:31+00:00
exif:ExposureTime: 0.033333
exif:FNumber: 8
exif:FocalLength: 20
exif:ISOSpeedRatings: 400
icc:copyright: Copyright 2016, Elle Stone (http://ninedegreesbelow.com/), CC-BY-SA 3.0 Unported (https://creativecommons.org/licenses/by-sa/3.0/legalcode).
icc:description: sRGB-elle-V4-srgbtrc.icc
icc:manufacturer: sRGB chromaticities from A Standard Default Color Space for the Internet - sRGB, http://www.w3.org/Graphics/Color/sRGB; also see http://www.color.org/specification/ICC1v43_2010-12.pdf
icc:model: sRGB chromaticities from A Standard Default Color Space for the Internet - sRGB, http://www.w3.org/Graphics/Color/sRGB; also see http://www.color.org/specification/ICC1v43_2010-12.pdf
signature: 956e4724a8ec0f61c1c2fbf4fe9fba9fc1daf956238225e5be568189d55a2a5b
tiff:alpha: unspecified
tiff:artist: Alan Gibson
tiff:endian: lsb
tiff:make: Nikon
tiff:model: D800
tiff:photometric: RGB
tiff:rows-per-strip: 1
tiff:software: dcraw v9.27
tiff:timestamp: 2017:10:29 15:03:38
Profiles:
Profile-icc: 1256 bytes
Tainted: False
Filesize: 415.758MiB
Number pixels: 36.3293M
Pixels per second: 7.02694MB
User time: 4.921u
Elapsed time: 0:06.170
Version: ImageMagick 7.0.7-28 Q32 x86_64 2018-12-09 http://www.imagemagick.org
%IM7DEV%magick ^ sxs_srgb2.miff ^ -verbose ^ info:
Image: sxs_srgb2.miff
Format: MIFF (Magick Image File Format)
Class: DirectClass
Geometry: 4924x7378+0+0
Resolution: 300x300
Print size: 16.4133x24.5933
Units: PixelsPerInch
Colorspace: sRGB
Type: TrueColor
Endianess: Undefined
Depth: 16/32-bit
Channel depth:
Red: 32-bit
Green: 32-bit
Blue: 32-bit
Channel statistics:
Pixels: 36329272
Red:
min: -719349 (-10.9766)
max: 54687.2 (0.834473)
mean: -858.775 (-0.0131041)
standard deviation: 18714.1 (0.285559)
kurtosis: 41.7296
skewness: -3.61668
entropy: 0.0855916
Green:
min: -1437.98 (-0.0219421)
max: 42399.4 (0.646973)
mean: 3994.78 (0.0609565)
standard deviation: 9380.81 (0.143142)
kurtosis: 6.04868
skewness: 2.7225
entropy: 0.858323
Blue:
min: -32767.5 (-0.5)
max: 105278 (1.60645)
mean: 2917.11 (0.0445122)
standard deviation: 11105.7 (0.169462)
kurtosis: 5.65067
skewness: 0.107391
entropy: 0.932668
Image statistics:
Overall:
min: -719349 (-10.9766)
max: 105278 (1.60645)
mean: 2017.7 (0.0307882)
standard deviation: 13066.9 (0.199388)
kurtosis: 51.5195
skewness: -2.95456
entropy: 0.625528
Rendering intent: Perceptual
Gamma: 0.454545
Chromaticity:
red primary: (0.64,0.33)
green primary: (0.3,0.6)
blue primary: (0.15,0.06)
white point: (0.3127,0.329)
Matte color: grey74
Background color: white
Border color: srgb(223,223,223)
Transparent color: none
Interlace: None
Intensity: Undefined
Compose: Over
Page geometry: 4924x7378+0+0
Dispose: Undefined
Iterations: 0
Compression: None
Orientation: TopLeft
Properties:
date:create: 2019-03-13T13:08:54+00:00
date:modify: 2019-03-13T13:08:54+00:00
exif:ExposureTime: 0.033333
exif:FNumber: 8
exif:FocalLength: 20
exif:ISOSpeedRatings: 400
icc:copyright: Copyright 2016, Elle Stone (http://ninedegreesbelow.com/), CC-BY-SA 3.0 Unported (https://creativecommons.org/licenses/by-sa/3.0/legalcode).
icc:description: sRGB-elle-V4-srgbtrc.icc
icc:manufacturer: sRGB chromaticities from A Standard Default Color Space for the Internet - sRGB, http://www.w3.org/Graphics/Color/sRGB; also see http://www.color.org/specification/ICC1v43_2010-12.pdf
icc:model: sRGB chromaticities from A Standard Default Color Space for the Internet - sRGB, http://www.w3.org/Graphics/Color/sRGB; also see http://www.color.org/specification/ICC1v43_2010-12.pdf
signature: 9cf2353df9606bd5516b9cfec245d423996a0fbef22ba294b933c499dc183e64
tiff:alpha: unspecified
tiff:artist: Alan Gibson
tiff:endian: lsb
tiff:make: Nikon
tiff:model: D800
tiff:photometric: RGB
tiff:rows-per-strip: 1
tiff:software: dcraw v9.27
tiff:timestamp: 2017:10:29 15:03:38
Profiles:
Profile-icc: 1256 bytes
Tainted: False
Filesize: 207.88MiB
Number pixels: 36.3293M
Pixels per second: 10.5701MB
User time: 3.423u
Elapsed time: 0:04.436
Version: ImageMagick 7.0.7-28 Q32 x86_64 2018-12-09 http://www.imagemagick.org
There is scope for squishing that is adaptive to hue. For example, this image has higher chroma in green and blue than in red, so an adaptive mechanism might reduce chroma less for red colours.
For video and similar work, the script is too automatic. We could take an aggregate xyY of all the frames, calculate the required squishing, and apply the same squishing to all frames.
The process isn't fast. For practical use, it may be better to use it to make HALD cluts to cover some typical situations, and automatically choose the best of these based on image statistics.
For convenience, .bat scripts are also available in a single zip file. See Zipped BAT files.
rem %1 input image in xyY space
rem %2 output image in xyY space
rem %3 Primaries and WP: "horseshoe", "sRGB", etc.
rem %4 white point
rem %5 method: clamp, filmic, divide or null
@rem
@rem Also uses:
@rem sqxCLUTDIR Directory for cluts. [%ICCPROF%]
@rem sqxHiLimit hiLimit for oogbox [0.7]
@rem sqxMAXSTAT_FILE name for maximum statistic [none]
@rem sqxFORCE_MAX assume this maximum instead of statistic [no force]
@rem
@rem FIXME: also check image has embedded XY profile.
@if "%1"=="" findstr /B "rem @rem" %~f0 & exit /B 1
@setlocal enabledelayedexpansion
@call echoOffSave
call %PICTBAT%setInOut %1 sqx
if not "%2"=="" if not "%2"=="." set OUTFILE=%2
set SHAPE=%~3
if "%SHAPE%"=="." set SHAPE=
if "%SHAPE%"=="" set SHAPE=sRGB
set WhtPnt=%~4
if "%WhtPnt%"=="." set WhtPnt=
set METHOD=%5
if "%METHOD%"=="." set METHOD=
if "%METHOD%"=="" set METHOD=filmic
if /I not %METHOD%==clamp if /I not %METHOD%==divide if /I not %METHOD%==filmic if /I not %METHOD%==null (
echo %0: Bad method [%METHOD%]
exit /B 1
)
if "%sqxCLUTDIR%"=="" set sqxCLUTDIR=%ICCPROF%
if "%sqxHiLimit%"=="" set sqxHiLimit=0.7
set TMPDIR=\temp
set CLUTDIM=4096
rem FIXME: CLUT_NAME also needs WP, including for horseshoe.
set CLUT_NAME=%SHAPE: =_%
set MultiParam=1
if %CLUT_NAME%==%SHAPE% set MultiParam=0
set WPx=0.31
set WPy=0.32
:: But what if horseshoe?
:: How does user declare WP for horseshoe?
if "%SHAPE%"=="horseshoe" (
call :getbary "outPrim sRGB"
if ERRORLEVEL 1 exit /B 1
) else if %MultiParam%==0 (
call :getbary "outPrim %SHAPE%"
if ERRORLEVEL 1 exit /B 1
) else (
call :getbary "%SHAPE%"
if ERRORLEVEL 1 exit /B 1
)
if ERRORLEVEL 1 exit /B 1
if not "%WhtPnt%"=="" (
call :getwp "%WhtPnt%"
)
set CLUT_NAME=%CLUTDIM%_%CLUT_NAME%_%WPx:.=_%_%WPy:.=_%
echo %0: CLUT_NAME=%CLUT_NAME%
set CLUT_FILE=%sqxCLUTDIR%\sqx_clut_%CLUT_NAME%.tiff
echo %0: CLUT_FILE=%CLUT_FILE%
if exist %CLUT_FILE% goto clut_ok
if %MultiParam%==1 goto MultiName
if /I not %SHAPE%==horseshoe goto notHorseshoe
echo %0: Making %CLUT_FILE%
set HSESHOE=m 426.8 358.8 c-106.3 -106.3 -177.2 -174.2 -222.7 -219.7 -39.2 -39.2 -94 -73.4 -114.3 -73.4 -28.7 0 -39.5 45.1 -39.5 98.5 0 59.3 18.4 227.4 66 306.4 0 0 10.3 15.6 21.7 20 l 288.8 -131.8 z
set DR_HSESHOE=translate -47.8,19.2 path '%HSESHOE%'
%IM7DEV%magick ^
-size %CLUTDIM%x%CLUTDIM% xc:Black ^
-fill White -stroke None ^
-draw "scale %%[fx:w/512],%%[fx:h/512] stroke-width %%[fx:512/w] %DR_HSESHOE%" ^
-rotate 180 ^
-virtual-pixel Black ^
-distort depolar %%[fx:hypot(w,h)/sqrt(2)],0,%%[fx:w-w*%WPx%],%%[fx:h*%WPy%] ^
-scale "x1^!" ^
-flop ^
-alpha off ^
-define quantum:format=floating-point ^
-depth 32 ^
%CLUT_FILE%
goto clut_ok
:MultiName
call :drTri "%SHAPE%"
if ERRORLEVEL 1 exit /B 1
goto clut_ok
:notHorseshoe
call :drTri "outPrim %SHAPE%"
if ERRORLEVEL 1 exit /B 1
goto clut_ok
:clut_ok
echo %0: Applying method %METHOD% forwards:
set wrMAXSTAT=
if not "%sqxMAXSTAT_FILE%"=="" (
set wrMAXSTAT=-format %%[fx:maxima] +write info:%sqxMAXSTAT_FILE%
)
set sTWEAK=
if /I %METHOD%==clamp (
set sTWEAK=-clamp
) else if /I %METHOD%==divide (
if "%sqxFORCE_MAX%"=="" (
set sTWEAK=-evaluate Divide %%[fx:maxima]
) else (
set sTWEAK=-evaluate Divide %sqxFORCE_MAX%
)
) else if /I %METHOD%==filmic (
if "%sqxFORCE_MAX%"=="" (
set sTWEAK=-process 'oogbox loLimit 0 hiLimit %sqxHiLimit% channel 0 v'
) else (
set sTWEAK=-process 'oogbox forceMax %sqxFORCE_MAX% loLimit 0 hiLimit %sqxHiLimit% channel 0 v'
)
) else if /I %METHOD%==null (
set sTWEAK=
) else (
echo %0: Bad method [%METHOD%]
exit /B 1
)
%IM7DEV%magick ^
%INFILE% ^
-set colorspace sRGB ^
-strip ^
+profile "*" ^
-define quantum:format=floating-point ^
-depth 32 ^
-process 'rhotheta offset %WPx%,%WPy%' ^
-channel RGB -separate +channel ^
( -clone 1 ^
-write %TMPDIR%\sxs_theta.miff ^
%CLUT_FILE% ^
-clut ^
-colorspace Gray ^
-write %TMPDIR%\sxs_rho0.miff ^
+delete ) ^
-delete 1 ^
( -clone 0 ^
%TMPDIR%\sxs_rho0.miff ^
-define compose:clamp=off ^
-compose DivideSrc -composite ^
-colorspace Gray ^
%wrMAXSTAT% ^
%sTWEAK% ^
-write %TMPDIR%\sxs_rho_rel2.miff ^
+delete ) ^
-delete 0 ^
%TMPDIR%\sxs_Y.miff
echo %0: Reverse:
if /I not %OUTFILE%==NULL: %IM7DEV%magick ^
%TMPDIR%\sxs_rho_rel2.miff ^
%TMPDIR%\sxs_rho0.miff ^
-define compose:clamp=off ^
-compose Multiply -composite ^
-define quantum:format=floating-point ^
-depth 32 ^
%TMPDIR%\sxs_theta.miff ^
%TMPDIR%\sxs_Y.miff ^
-combine ^
-set colorspace xyY ^
-process 'rhotheta offset %WPx%,%WPy% inverse' ^
%OUTFILE%
call echoRestore
@endlocal
@exit /B 0
::---------------------------------------
:: Subroutines
:drTri
call :getbary %1
if ERRORLEVEL 1 exit /B 1
set i=0
for %%A in (%NUMS%) do (
if "!prev!"=="" (
set prev=%%A
) else (
set /A rad=8
echo ow !prev! and %%A !rad!
set sDRAW[!i!]=%%[fx:w*!prev!],%%[fx:h-h*%%A]
set prev=
set /A i+=1
)
)
set sDRAW
%IM7DEV%magick ^
-size %CLUTDIM%x%CLUTDIM% xc:Black ^
-fill White -stroke None ^
-draw "polygon %sDRAW[0]%,%sDRAW[1]%,%sDRAW[2]%" ^
-rotate 180 ^
-virtual-pixel Black ^
-distort depolar %%[fx:hypot(w,h)/sqrt(2)],0,%%[fx:w-w*%WPx%],%%[fx:h*%WPy%] ^
-scale "x1^!" ^
-flop ^
-alpha off ^
-define quantum:format=floating-point ^
-depth 32 ^
%CLUT_FILE%
exit /B 0
::---------------------------------------
:getbary
set ARGS=%~1
echo %0: ARGS=%ARGS%
set NUMS=
set WP=
for /F "usebackq tokens=1,2" %%A in (`%IM7DEV%magick ^
xc: ^
-process 'barymap inChannels xyY outChannels xyY %ARGS% f stdout v' ^
NULL: 2^>^&1`) do (
echo %0: [%%A][%%B]
if %%A==outPrim set NUMS=%%B
if %%A==outWP set WP=%%B
)
rem FIXME: no longer outPrim etc.
echo %0: WP=%WP%
if "%NUMS%"=="" (
echo %0: barymap failed ARGS=%ARGS%
exit /B 1
)
for /F "tokens=1,2 delims=," %%A in ("%WP%") do (
set WPx=%%A
set WPy=%%B
)
exit /B 0
::---------------------------------------
:getwp
set ARGS=%~1
echo %0: ARGS=%ARGS%
set NUMS=
set WP=
for /F "usebackq tokens=1,2" %%A in (`%IM7DEV%magick ^
xc: ^
-process 'barymap inChannels xyY outChannels xyY outWP %ARGS% f stdout v' ^
NULL: 2^>^&1`) do (
if %%A==outWP set WP=%%B
)
echo %0: WP=%WP%
if "%WP%"=="" (
echo %0: barymap failed ARGS=%ARGS%
exit /B 1
)
for /F "tokens=1,2 delims=," %%A in ("%WP%") do (
set WPx=%%A
set WPy=%%B
)
exit /B 0
rem %1 input image in xyY space.
rem %2 output black/white histogram with horseshoe.
rem Also creates small sRGB version of input image.
%IM7DEV%magick ^
%1 ^
-strip ^
( +clone ^
-set colorspace xyY ^
-resize 512x512 ^
-colorspace sRGB ^
+write %~n1_sm.jpg ^
+delete ^
) ^
-process 'plotrg dim 512 norm verbose' ^
-flip ^
-fill White +opaque Black ^
-set colorspace sRGB ^
%2
if ERRORLEVEL 1 exit /B 1
call %PICTBAT%cieHorseshoe %2 %2
if ERRORLEVEL 1 exit /B 1
@rem %1 A grayscale file containing rho (chroma) at each pixel.
@%IM7DEV%magick ^
%1 ^
-format "MIN=%%[fx:minima] MEAN=%%[fx:mean] MAX=%%[fx:maxima]\n" ^
+write info: ^
( +clone ^
-clamp ^
) ^
-define compose:clamp=off ^
-compose Difference -composite ^
-fill White +opaque Black ^
-scale "1x1^!" ^
-format PROPOUT=%%[fx:mean] ^
+write info: ^
NULL:
All images on this page were created by the commands shown, using:
%IM%identify -version
Version: ImageMagick 6.9.9-50 Q16 x64 2018-06-02 http://www.imagemagick.org Copyright: Copyright (C) 1999-2015 ImageMagick Studio LLC License: http://www.imagemagick.org/script/license.php Visual C++: 180040629 Features: Cipher DPC Modules OpenMP Delegates (built-in): bzlib cairo flif freetype gslib heic jng jp2 jpeg lcms lqr lzma openexr pangocairo png ps raw rsvg tiff webp xml zlib
To improve internet download speeds, some images may have been automatically converted (by ImageMagick, of course) from PNG to JPG.
Source file for this web page is sqshxyysh.h1. To re-create this web page, execute "procH1 sqshxyysh".
This page, including the images, is my copyright. Anyone is permitted to use or adapt any of the code, scripts or images for any purpose, including commercial use.
Anyone is permitted to re-publish this page, but only for non-commercial use.
Anyone is permitted to link to this page, including for commercial use.
Page version v1.0 17-December-2018.
Page created 13-Mar-2019 13:10:24.
Copyright © 2019 Alan Gibson.