Basically the M1 matrix for linear sRGB [linearR, linearG, linearB, 1] to approximate cone responses:
(I think in this normalization 1 means 250 nits, but not completely sure at this stage of optimizations -- we changed normalizations on this recently.)
The LMS values after cubic root are coded by this matrix M2:
M2 = [[1, -1, 0], [1, 1, 0], [0, 0, 1]]
In practice Y->X and Y->B correlations are decorrelated, so M2 looks more like this:
M2 = [[1+a, -1+a, 0], [1, 1, 0], [b, b, 1]]
after decorrelations a is often around zero and b is around -0.5.
The first dimension in this formulation is X (red-green), second Y (luma), third B (blueness-yellowness).
For quantization, X, Y and B channels are multiplied by constants representing their psychovisual strength. X and B channels (the chromacity channels) are less important when quantization is low, and particularly X channel increases in strength when more quantization is done.
Cube is beautiful in the sense that it allows scaling the intensity without considerations, but it is quite awful in the near black psychovisual performance. That is why sRGB added a linear ramp, and I added biasing (homogeneous transform instead of 3x3).
Regarding: “Cube is beautiful in the sense that it allows scaling the intensity without considerations, but it is quite awful in the near black psychovisual performance.”
Yeah, that is the tradeoff, same for dealing with hdr values. The idea with Oklab is to avoid having to know what luminance the eye is adapted to, by treating all colors as if they are within the normal color vision range basically. Makes it simpler to use and more predictable to use, but makes predictions in the extreme ends worse than it would be taking knowledge of the viewing conditions into account (given that you can do so accurately)
E.g. linear ramp for near black values would not be good if you are in a dark room, only viewing very dark values full screen on a monitor (so there isn’t anything bright around to adapt to)
BTW, just if it didn't become clear from all the proposals I had: I adore your work with Oklab. Humanity would benefit a lot if more scientists and engineers were able to think like you -- from first principles and completely out-of-the-cargo-cult-box. What you propose with Oklab is practical and a huge improvement over the current practice.
Basically the M1 matrix for linear sRGB [linearR, linearG, linearB, 1] to approximate cone responses:
(I think in this normalization 1 means 250 nits, but not completely sure at this stage of optimizations -- we changed normalizations on this recently.)
M1 = [ [0.300, 0.622, 0.078, 0.0038], [0.240, 0.682, 0.078, 0.0038], [0.243, 0.205, 0.552, 0.0038], [0, 0, 0, 1] ]
then non-linearity by cubic root, in decoding cube, see: https://gitlab.com/wg1/jpeg-xl/-/blob/master/lib/jxl/dec_xyb...
The LMS values after cubic root are coded by this matrix M2:
M2 = [[1, -1, 0], [1, 1, 0], [0, 0, 1]]
In practice Y->X and Y->B correlations are decorrelated, so M2 looks more like this:
M2 = [[1+a, -1+a, 0], [1, 1, 0], [b, b, 1]]
after decorrelations a is often around zero and b is around -0.5.
The first dimension in this formulation is X (red-green), second Y (luma), third B (blueness-yellowness).
For quantization, X, Y and B channels are multiplied by constants representing their psychovisual strength. X and B channels (the chromacity channels) are less important when quantization is low, and particularly X channel increases in strength when more quantization is done.
Cube is beautiful in the sense that it allows scaling the intensity without considerations, but it is quite awful in the near black psychovisual performance. That is why sRGB added a linear ramp, and I added biasing (homogeneous transform instead of 3x3).