I want write code to predict CIE XYZ from LED driver R,G,B output value

Question

I am making auto white balance calibration application. I have a chromameter and api. So my application can measure CIExyY and CIEXYZ. And my app can set R,G,B output value of my devices's LED panel.

I set R,G,B value combination and measureed CIEXYZ three times. And then I evaluated follow matrix.

matrix

I thought that once I evaluated the matrix, I could calculate CIEXYZ with R,G,B output value.

But It's not correct value.

R,G,B output value is 0~1023. 0 doesn't mean 0 output. 0~1023 is just level.

Answer 1

Using colour, given the primaries and whitepoint expressed as CIE XYZ tristimulus, you can compute the normalised primary matrix converting from your LED colourspace to CIE XYZ as follows:

import colour
import numpy as np

XYZ_PRIMARIES = np.array(
    [
        [2.12500000, 1.00000000, -0.00000000],
        [0.38405797, 1.00000000, 0.06521739],
        [2.50000000, 1.00000000, 13.16666667],
    ]
)
XYZ_WHITEPOINT = np.array([0.89458689, 1.00000000, 0.95441595])

NPM = colour.normalised_primary_matrix(
    colour.XYZ_to_xy(XYZ_PRIMARIES), colour.XYZ_to_xy(XYZ_WHITEPOINT)
)

print(NPM)
print(np.linalg.inv(NPM))

[[  4.45169812e-01   2.77134409e-01   1.72282669e-01]
 [  2.09491676e-01   7.21595256e-01   6.89130676e-02]
 [ -3.63410128e-17   4.70605593e-02   9.07355391e-01]]
[[ 2.72539405 -1.01800301 -0.4401632 ]
 [-0.79516802  1.68973205  0.02264719]
 [ 0.04124189 -0.08763902  1.10092938]]

You can also create a new RGB colourspace which will allow you to convert to other known colourspaces:

RGB_COLOURSPACE_LED = colour.RGB_Colourspace(
    "LED", colour.XYZ_to_xy(XYZ_PRIMARIES), colour.XYZ_to_xy(XYZ_WHITEPOINT)
)
print(RGB_COLOURSPACE_LED)

print(
    colour.matrix_RGB_to_RGB(RGB_COLOURSPACE_LED, colour.models.RGB_COLOURSPACE_BT2020)
)

[[  7.05392504e-01   2.49107517e-01   4.54999792e-02]
 [  4.04429548e-02   9.47423997e-01   1.21330485e-02]
 [ -5.83382089e-04   2.69551875e-02   9.73628195e-01]]

Note that this assumes that the LED behave linearly which is almost certainly not the case!