Determine that a Luv Color is non-imaginary

Question

Suppose I have a triple of coordinates in the Luv color space. What is the best way to determine that these correspond to a real color?

Answer 1

Assuming your L* is in domain [0, 100], you can construct the boundaries of the Visible Spectrum and then determine if your CIE L*u*v* coordinates are within it.

import colour
import numpy as np


def generate_square_waves(samples):
    square_waves = []
    square_waves_basis = np.tril(np.ones((samples, samples)))[0:-1, :]
    for i in range(samples):
        square_waves.append(np.roll(square_waves_basis, i))
    return np.vstack((np.zeros(samples), np.vstack(square_waves),
                    np.ones(samples)))


def XYZ_outer_surface(samples):
    XYZ = []
    wavelengths = np.linspace(colour.DEFAULT_SPECTRAL_SHAPE.start,
                            colour.DEFAULT_SPECTRAL_SHAPE.end, samples)

    for wave in generate_square_waves(samples):
        spd = colour.SpectralPowerDistribution(
            wave, wavelengths, interpolator=colour.LinearInterpolator).align(
                colour.DEFAULT_SPECTRAL_SHAPE)
        XYZ.append(colour.spectral_to_XYZ(spd))

    return np.array(XYZ).reshape(len(XYZ), -1, 3)

mesh = XYZ_outer_surface(43).reshape((-1, 3))

E = colour.ILLUMINANTS['CIE 1931 2 Degree Standard Observer']['E']

XYZ1 = colour.Luv_to_XYZ([50, 50, 50], E)
print(colour.is_within_mesh_volume(XYZ1, mesh))
# True

XYZ2 = colour.Luv_to_XYZ([50, 250, -250], E)
print(colour.is_within_mesh_volume(XYZ2, mesh))
# False

I would highly recommend caching the mesh as it is quite heavy to compute.

Answer 2

You have Lu'v' coordinates. You may want to check L and limit the allowable value. Often we do not allow L being larger then L of white, but reality (and old television standard) allowed it, just for small period or small surface (else it will become the new white, because of eye adaption).

First step: convert it into XYZ (or any tristimulus coordinates). Wikipedia has one of the formula in https://en.wikipedia.org/wiki/CIELUV#The_reverse_transformation , but care that this is for one specific u and v range and specific gamma correction.

Then you convert it to LMS colour space, according e.g. https://en.wikipedia.org/wiki/LMS_color_space

Finally: check that L, M, and S are positive (L, M, S of LMS colour space: note L is not the same L of LUV, it this case it stands for Long cone type).

If LMS coordinates are positive, the colour is real and visible. On the other case it is impossible to produce such light.

LSM stands for eye cone response of L, M, and S cone types, so it is the definitive answer on visibility of colours. The problem is: it is difficult to measure single eye cone responses. For this reason you see various conversion matrices between XYZ and LMS. On the other hand the results are similar. Note: because of difficulty of direct measurements, the matrices where derived also indirectly (using method similar to Kel answer, but not just for the surface).