colour.colorimetry.multi_sds_to_XYZ_integration

colour.colorimetry.multi_sds_to_XYZ_integration(msd, shape, cmfs=XYZ_ColourMatchingFunctions(name='CIE 1931 2 Degree Standard Observer', ...), illuminant=SpectralDistribution(name='1 Constant', ...), k=None)

Converts given multi-spectral distribution array \(msd\) with given spectral shape to CIE XYZ tristimulus values using given colour matching functions and illuminant.

Parameters:

• msa (array_like) – Multi-spectral distribution array \(msd\), the wavelengths are expected to be in the last axis, e.g. for a 512x384 multi-spectral image with 77 bins, msd shape should be (384, 512, 77).
• shape (SpectralShape, optional) – Spectral shape of the multi-spectral distribution array \(msd\), cmfs and illuminant will be aligned with it.
• cmfs (XYZ_ColourMatchingFunctions) – Standard observer colour matching functions.
• illuminant (SpectralDistribution, optional) – Illuminant spectral distribution.
• k (numeric, optional) – Normalisation constant \(k\). For reflecting or transmitting object colours, \(k\) is chosen so that \(Y = 100\) for objects for which the spectral reflectance factor \(R(\lambda)\) of the object colour or the spectral transmittance factor \(\tau(\lambda)\) of the object is equal to unity for all wavelengths. For self-luminous objects and illuminants, the constants \(k\) is usually chosen on the grounds of convenience. If, however, in the CIE 1931 standard colorimetric system, the \(Y\) value is required to be numerically equal to the absolute value of a photometric quantity, the constant, \(k\), must be put equal to the numerical value of \(K_m\), the maximum spectral luminous efficacy (which is equal to 683 \(lm\cdot W^{-1}\)) and \(\Phi_\lambda(\lambda)\) must be the spectral concentration of the radiometric quantity corresponding to the photometric quantity required.

Returns:

CIE XYZ tristimulus values, for a 512x384 multi-spectral image with 77 bins, the output shape will be (384, 512, 3).

Return type:

array_like

Notes

Range	Scale - Reference	Scale - 1
XYZ	[0, 100]	[0, 1]

References

[WS00f]

Examples

>>> from colour import ILLUMINANTS_SDS
>>> msd = np.array([
...     [
...         [0.0137, 0.0913, 0.0152, 0.0281, 0.1918, 0.0430],
...         [0.0159, 0.3145, 0.0842, 0.0907, 0.7103, 0.0437],
...         [0.0096, 0.2582, 0.4139, 0.2228, 0.0041, 0.3744],
...         [0.0111, 0.0709, 0.0220, 0.1249, 0.1817, 0.0020],
...         [0.0179, 0.2971, 0.5630, 0.2375, 0.0024, 0.5819],
...         [0.1057, 0.4620, 0.1918, 0.5625, 0.4209, 0.0027],
...     ],
...     [
...         [0.0433, 0.2683, 0.2373, 0.0518, 0.0118, 0.0823],
...         [0.0258, 0.0831, 0.0430, 0.3230, 0.2302, 0.0081],
...         [0.0248, 0.1203, 0.0054, 0.0065, 0.1860, 0.3625],
...         [0.0186, 0.1292, 0.0079, 0.4006, 0.9404, 0.3213],
...         [0.0310, 0.1682, 0.3719, 0.0861, 0.0041, 0.7849],
...         [0.0473, 0.3221, 0.2268, 0.3161, 0.1124, 0.0024],
...     ],
... ])
>>> D65 = ILLUMINANTS_SDS['D65']
>>> multi_sds_to_XYZ(
... msd, SpectralShape(400, 700, 60), illuminant=D65)
... # doctest: +ELLIPSIS
array([[[  7.1958378...,   3.8605390...,  10.1016398...],
        [ 25.5738615...,  14.7200581...,  34.8440007...],
        [ 17.5854414...,  28.5668344...,  30.1806687...],
        [ 11.3271912...,   8.4598177...,   7.9015758...],
        [ 19.6581831...,  35.5918480...,  35.1430220...],
        [ 45.8212491...,  39.2600939...,  51.7907710...]],
<BLANKLINE>
       [[  8.8287837...,  13.3870357...,  30.5702050...],
        [ 22.3324362...,  18.9560919...,   9.3952305...],
        [  6.6887212...,   2.5728891...,  13.2618778...],
        [ 41.8166227...,  27.1191979...,  14.2627944...],
        [  9.2414098...,  20.2056200...,  20.1992502...],
        [ 24.7830551...,  26.2221584...,  36.4430633...]]])