What Is the Algorithm Behind Photoshop's "Black and White" Adjustment Layer?

Question

Can someone explain the algorithm behind the "Black and White" adjustment layer in photoshop?

I have to reproduce it using C++ for an application that emphasizes non-red/magenta(ish) pixels from an image (with a percent-like configurable tolerance), and this resource showed the behavior I'm expecting.

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Update: Still couldn't reproduce it, but I found a clue:

Each pixel is defined by up to two controls, one additive (RGB) and one subtractive (CMY).

Answer 1

I replicated the algorithm perfectly in MATLAB (Based on @Ivan Kuckir answer):

function [ mO ] = ApplyBlackWhiteFilter( mI, vCoeffValues )

FALSE   = 0;
TRUE    = 1;

OFF = 0;
ON  = 1;

numRows = size(mI, 1);
numCols = size(mI, 2);
dataClass = class(mI);

numCoeff    = size(vCoeffValues, 1);
hueRadius   = 1 / numCoeff;
vHueVal     = [0:(numCoeff - 1)] * hueRadius;

mHsl = ConvertRgbToHsl(mI);
mO = zeros(numRows, numCols, dataClass);

vCoeffValues = numCoeff * vCoeffValues;

for jj = 1:numCols
    for ii = 1:numRows
        hueVal = mHsl(ii, jj, 1);
        lumCoeff = 0;
        
        % For kk = 1 we're dealing with circular distance
        diffVal     = min(abs(vHueVal(1) - hueVal), abs(1 - hueVal));
        lumCoeff    = lumCoeff + (vCoeffValues(1) * max(0, hueRadius - diffVal));
        for kk = 2:numCoeff
            lumCoeff = lumCoeff + (vCoeffValues(kk) * max(0, hueRadius - abs(vHueVal(kk) - hueVal)));
        end
        
        mO(ii, jj) = mHsl(ii, jj, 3) * (1 + lumCoeff);
    end
end


end

Pay attention that the conversion from vPhotoshopValues to vCoeffValues should be done as vCoeffValues = (vPhotoshopValues - 50) ./ 50.
As Photoshop values are in [-200, 300] and should be linearly mapped into [-5, 5] with 50 -> 0.

Here is a comparison to Photoshop:

The maximum error is less than 1 in [0, 255] range.

The MATLAB code is available at my StackExchange Signal Processing Q29041 GitHub Repository (Look at the SignalProcessing\Q688 folder).

Answer 2

Each (color) image is composed of RGB components. when you add (or reduce) a constant value to all pixels only in RED components you will see the effect equivalent to moving the RED tab towards the right, and same way reducing the RED component by a constant will have the reverse effect.

Like wise you can increment/decrement each component by a fixed value as described. If you increase/decrease ALL RGB components by a same value this will be equivalent to change in brightness (basically you are adding/removing WHITE color).

The Cyan, Blue, Magenta - corresponds to such transformation in CMYK color space. (But i guess, Blue in this color space corresponds to mix of Cyan and Yellow. So that's a bit tricky. The transformation is essentially same for all.

The last element Tint: { Hue and Saturation } corresponds to same operations but here, the images is first transformed in HSV model and then HUE and Saturation is added/subtracted independently.

I don't know about the exact relationships of markers of the dial to the corresponding numbers but that you can figure out by trying out practical values.