More accurate ICtCp matrices

[facelessuser]

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[facelessuser]

It occurred to me today how to fix the rough conversion in ICtCp.

Simply using the rational matrix and applying a matrix multiply of the Rec2020 XYZ to RGB matrix creates a much more accurate conversion. This is directly inferred from the Dolby paper. https://professional.dolby.com/siteassets/pdfs/ictcp_dolbywhitepaper_v071.pdf

Matrix Calculations

"""
Calculate ICtCp matrices.

https://professional.dolby.com/siteassets/pdfs/ictcp_dolbywhitepaper_v071.pdf
"""
import numpy as np

np.set_printoptions(precision=16, sign='-', floatmode='fixed')

# Matrix is directly from Color.js Rec2020
XYZ_TO_RGB = [
    [  1.716651187971268,  -0.355670783776392, -0.253366281373660  ],
    [ -0.666684351832489,   1.616481236634939,  0.0157685458139111 ],
    [  0.017639857445311,  -0.042770613257809,  0.942103121235474  ]
]

# Use rational values and apply Rec. 2020 matrix to get a precise XYZ to LMS matrix
m1 = [
    [1688, 2146, 262],
    [683, 2951, 462],
    [99, 309, 3688]
]
m1 = np.matmul(np.divide(m1, 4096), XYZ_TO_RGB)

# LMS to ICtCp
m2 = [
    [2048, 2048, 0],
    [6610, -13613, 7003],
    [17933, -17390, -543]
]
m2 = np.divide(m2, 4096)

if __name__ == "__main__":
    print('===== XYZ to LMS =====')
    print(m1)
    print('===== LMS to XYZ =====')
    print(np.linalg.inv(m1))
    print('===== PQ LMS to ICtCp =====')
    print(m2)
    print('===== ICtCp to PQ LMS =====')
    print(np.linalg.inv(m2))

The results are much, much better, especially around the achromatic regions.

> new Color('rec2100pq', [1, 1, 1]).to('ictcp').coords
[ 1, 0, 0 ]
> new Color('white').to('ictcp').coords
[ 0.5806888810416109, 1.1102230246251565e-16, 2.914335439641036e-16 ]