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Secrets of Photoshop's Colour Blend Mode Revealed (Sort Of)

article by Ben Lincoln

Back when I originally started writing The Mirror's Surface Breaks, I knew that I had to come up with a way to emulate the "Colour" blend mode from Adobe Photoshop®. I'd been extremely happy with some of the false colour images I'd generated by applying e.g. the colour of the RGB variation to the luminance of the near infrared version of the same shot, and if TMSB couldn't handle that for me, I'd be stuck doing a bunch of repetitive, manual work for hours. If I'd known how much trouble it was going to be to implement, I might not have even started, but since I did, hopefully others will benefit from the knowledge I obtained.

First, let's catalogue what the "Colour" blend mode does not do, in the order that my theories were formed and then disproven through testing:

• It does not convert both images to the YUV colourspace, then combine the Y (luminance) channel of one image with the U and V (chrominance) channels of the second.
• It does not involve a similar transformation/combination in the HSL (hue/saturation/lightness), or HSV (hue/saturation/value) colourspaces^[1].
• In fact, it does not involve a simple combination of one channel from one image with the other channels of a second image in any standard colourspace.

If you are very well-read in this area, you may suspect (or even know) that the HSY (hue/saturation/luminance) colourspace is where the work takes place. However, what you probably don't know is that it's still not just a combination of the H and S channels of one image with the Y channel of a second. No, that would be too easy. That method also doesn't bring quite as much of the contrast of the luminance image through to the final result.

After some extensive fiddling around, reading Adobe's PDF specification, and discussing this topic in email (thanks, Andrew!) I can finally describe how to accurately mimic what Photoshop® does when this blend mode is used. You can read about the original method used by TMSB in the Appendix A section near the end of this article.

Adobe's PDF specification (specifically, PDF Blend Modes: Addendum) describes the colour blend mode as a set of three functions, which I've paraphrased here as pseudocode (but not the same pseudocode as in the original document), with pixel being a struct of three floating point values (Red, Green, and Blue).

float Lum(pixel colour)

{

return (colour.Red * 0.3) + (colour.Green * 0.59) + (colour.Blue * 0.11);

}

 

pixel ClipColour(pixel colour)

{

pixel result;

float luminance = Lum(colour);

float cMin = min(colour.Red, colour.Green, colour.Blue);

float cMax = max(colour.Red, colour.Green, colour.Blue);

if (cMin < 0.0)

{

result.Red = luminance + (((colour.Red - luminance) * luminance) / (luminance - cMin));

result.Green = luminance + (((colour.Green - luminance) * luminance) / (luminance - cMin));

result.Blue = luminance + (((colour.Blue - luminance) * luminance) / (luminance - cMin));

}

if (cMax > 1.0)

{

result.Red = luminance + (((colour.Red - luminance) * (1.0 - luminance)) / (cMax - luminance));

result.Green = luminance + (((colour.Green - luminance) * (1.0 - luminance)) / (cMax - luminance));

result.Blue = luminance + (((colour.Blue - luminance) * (1.0 - luminance)) / (cMax - luminance));

}

return result;

}

 

pixel SetLum(pixel colour, float luminance)

{

pixel result;

float diff = luminance - Lum(colour);

result.Red = colour.Red + diff;

result.Green = colour.Green + diff;

result.Blue = colour.Blue + diff;

return ClipColour(colour);

}

These functions together define the colour blend mode (in which the upper layer is passed to SetLum as the first variable, and the lower layer is passed as the second), and the luminance blend mode (with the upper layer passed as the second variable, and the lower layer the first).

It took me awhile to get comfortable enough with the DaVinci script language to write this function in a way that didn't use for loops to iterate through each pixel, which is extremely slow in DaVinci. Once I finally wrapped my head around how to handle this using sets instead of individual values, this was the result, which I've simplified somewhat for presentation here. base represents the image to be used for the luminance, and colour the image to be used for the colour.

For those who are unfamiliar with the DaVinci script language, quirks like defining a variable named "one" are due to the way DaVinci handles mathematical operations involving sets of data^[4].

basey = rgb2hsy(tofloat(base))[0,0,3]

coloury = rgb2hsy(tofloat(colour))[0,0,3]

 

result = colour + (basey - coloury)

 

colourmin = min(result, axis = z)

colourmax = max(result, axis = z)

 

resultmin = threeclone(basey)

resultmax = resultmin

 

resultmin = resultmin + (((result - basey) * basey) / (basey - colourmin))

 

one = basey

one[0,0,0] = 1.0

 

resultmax = resultmax + (((result - basey) * (one - basey)) / (colourmax - basey))

 

minmask = ceil(abs(clipdata(colourmin, min=-1.0, max=0.0, quiet=1)))

maxmask = ceil(clipdata((colourmax - 1.0), min=0.0, max=1.0, quiet=1))

one = maxmask

one[0,0,0] = 1.0

noclipmask = (one - maxmask) - minmask

# in the PDF specification, the max case takes precedence over the min case

minmask = clipdata(minmask - maxmask, min=0.0, max=1.0, quiet=1)

 

result = (result * noclipmask) + (resultmin * minmask) + (resultmax * maxmask)

 

return(result)

For purposes of illustration, here are a series of example images, with the results of blending the colours using the following methods:

• A simple replacement of the lightness channel in the HSL colourspace.
• A simple replacement of the value channel in the HSV colourspace.
• A simple replacement of the luminance channel in the YUV colourspace.
• A simple replacement of the luminance channel in the HSY colourspace.
• A simple replacement of the luminance channel in the IHSL colourspace.
• Photoshop®'s Colour blend mode.
• The original TMSB method.
• The new-and-improved TMSB method based on the PDF specification.

Note: if you wish to do your own comparisons, you must change Photoshop®'s colour settings so that the grey working space is "Gray Gamma 2.2". The default value is "Dot Gain 20%", which boosts the levels of greyscale images, and will throw off the results.

In this first set of example images, you can see the sort of difference in red saturation that I described earlier.

No big surprises in this second set of images, except that the YUV method is beginning to show signs of weakness which will become glaringly obvious shortly.

These next two combinations were the original test cases I used when writing my own colour-blending functionality for TMSB.

YUV provides very little "colour" here. In addition, notice how the HSL version has introduced a couple of artifacts into the image.

Finally, YUV cracks completely under the strain of trying to apply the colour of a green image to a greyscale luminance. Green seems to be one of the more challenging colours for this type of algorithm - possibly because our eyes are so much more sensitive to it than red or blue. You can see that except for the Photoshop® and TMSB methods, every other version has a noticeable problem - a green tint that makes the highly-reflective water appear darker, worse contrast, etc.

Note

There are a few different options available to TMSB users who would prefer to use either a straight luminance channel swap in HSY colourspace or the "classic" TMSB method. Both involve editing dshadow.dvrc (located in the library subdirectory) with a text editor. Look in the blendcolourrgb(), blendcolourhsy(), and blendcolourpdfspec() functions for the lines which are marked "# uncomment the next line", "# uncomment the next two lines", and so forth. Remove the pound signs (#) from the beginning of the lines after that as indicated to switch to the other mechanism.

Appendix A: The Original TMSB Method

Prior to June of 2011, the method used by TMSB was this, which is preserved for historical reasons:

Given two images (A and B), if the "colour" of A is to be applied to the "luminance" of B, the resulting image has:

• The luminance of B.
• The hue of A.
• A saturation which is calculated by:
• Taking the luminance of B.
• Calculating the distance of each pixel's value from the luminance of A.
• For positive differences, dividing them by the inverse of the luminance of A.
• For negative differences, taking the absolute value, then dividing it by the luminance of A.
• Clipping the result to the range of valid values (e.g. 0.0 - 1.0 for floating point, 0-255 for 8-bit, etc.).
• Inverting the resulting value.
• Capping the final result to a maximum of the saturation of A.

This is the script code that is used in DaVinci's Shadow for the original method. DaVinci is heavily optimized for use with set-based operations, so this code does not use for loops.^[3]

y = base[0,0,3]

h = colour[0,0,1]

s = base[0,0,3]

cy = colour[0,0,3]

 

# delta from colour luminance

s = s - cy

spos = s

spos[0,0,1] = 0.0

spos = cat(spos, s, axis=z)

spos = max(spos, axis=z)

 

sneg = s

sneg[0,0,1] = 0.0

sneg = cat(sneg, s, axis=z)

sneg = abs(min(sneg, axis=z))

 

# rescale the delta values

sposceil = cy

sposceil[0,0,1] = 1.0

sposceil = sposceil - cy

spos = spos / sposceil

 

sneg = sneg / cy

 

cy = 0

 

s = cat(spos, sneg, axis=z)

 

spos = 0

sneg = 0

 

s = max(s, axis=z)

 

# clip saturation to a range of 0 - 1

s2 = s

s2[0,0,1] = 1.0

s = cat(s, s2, axis=z)

s = min(s, axis=z)

s2[0,0,1] = 0.0

s = cat(s, s2, axis=z)

s = max(s, axis=z)

# end clip

 

# invert the calculated saturation value

s2 = s

s2[0,0,1] = 1.0

s = s2 - s

s2 = 0

# end inversion

 

# cap the saturation at the value from the colour image

s = cat(s, colour[0,0,2], axis=z)

s = min(s, axis=z)

# end cap

This does not result in an exact match, but it is virtually identical in most cases. The main difference tends to be that this algorithm will sometimes produce slightly higher red saturation than the one used in Photoshop®. However, it preserves the main advantage of the Photoshop® function, which is that both of them provide more constrast in the resulting image than a straight luminance-replacement.

Related Articles:
DaVinci's Shadow
The Mirror's Surface Breaks

Last updated: 04 June 2011

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