colour.XYZ_to_sd#
- colour.XYZ_to_sd(XYZ: ArrayLike, method: Literal['Gaussian', 'Jakob 2019', 'Mallett 2019', 'Meng 2015', 'Otsu 2018', 'Smits 1999'] | str = 'Meng 2015', **kwargs: Any) SpectralDistribution[source]#
Recover the spectral distribution of the specified CIE XYZ tristimulus values using the specified method.
- Parameters:
XYZ (ArrayLike) – CIE XYZ tristimulus values to recover the spectral distribution from.
method (Literal['Gaussian', 'Jakob 2019', 'Mallett 2019', 'Meng 2015', 'Otsu 2018', 'Smits 1999'] | str) – Computation method.
additional_data – {
colour.recovery.XYZ_to_sd_Jakob2019()}, If True,errorwill be returned alongside the recovered spectral distribution.basis_functions – {
colour.recovery.RGB_to_sd_Mallett2019()}, Basis functions for the method. The default is to use the built-in sRGB basis functions, i.e.,colour.recovery.MSDS_BASIS_FUNCTIONS_sRGB_MALLETT2019.clip – {
colour.recovery.XYZ_to_sd_Otsu2018()}, If True, the default, values below zero and above unity in the recovered spectral distributions will be clipped. This ensures that the returned reflectance is physical and conserves energy, but will cause noticeable colour differences in case of very saturated colours.cmfs – {
colour.recovery.XYZ_to_sd_Meng2015()}, Standard observer colour matching functions.dataset – {
colour.recovery.XYZ_to_sd_Otsu2018()}, Dataset to use for reconstruction. The default is to use the published data.illuminant – {
colour.recovery.XYZ_to_sd_Jakob2019(),colour.recovery.XYZ_to_sd_Meng2015()}, Illuminant spectral distribution, default to CIE Standard Illuminant D65.optimisation_kwargs – {
colour.recovery.XYZ_to_sd_Jakob2019(),colour.recovery.XYZ_to_sd_Meng2015()}, Parameters forscipy.optimize.minimize()andcolour.recovery.find_coefficients_Jakob2019()definitions.kwargs (Any)
- Returns:
Recovered spectral distribution.
- Return type:
Notes
Domain
Scale - Reference
Scale - 1
XYZ1
1
Gaussian and Smits (1999) methods will internally convert specified CIE XYZ tristimulus values to RGB colourspace array assuming sRGB primaries and equal energy illuminant E.
References
[JH19], [MY19], [MSHD15], [OYH18], [Smi99]
Examples
Gaussian reflectance recovery:
>>> import numpy as np >>> from colour import MSDS_CMFS, SDS_ILLUMINANTS, SpectralShape >>> from colour.colorimetry import sd_to_XYZ_integration >>> from colour.utilities import numpy_print_options >>> XYZ = np.array([0.20654008, 0.12197225, 0.05136952]) >>> cmfs = ( ... MSDS_CMFS["CIE 1931 2 Degree Standard Observer"] ... .copy() ... .align(SpectralShape(360, 780, 10)) ... ) >>> illuminant = SDS_ILLUMINANTS["E"].copy().align(cmfs.shape) >>> sd = XYZ_to_sd(XYZ, method="Gaussian").align(SpectralShape(360, 780, 10)) >>> with numpy_print_options(suppress=True): ... sd SpectralDistribution([[360. , 0.04502009], [370. , 0.04501988], [380. , 0.04501914], [390. , 0.0450168 ], [400. , 0.04500998], [410. , 0.04499185], [420. , 0.0449477 ], [430. , 0.0448493 ], [440. , 0.04464874], [450. , 0.04427526], [460. , 0.04364072], [470. , 0.04265916], [480. , 0.04128144], [490. , 0.03953613], [500. , 0.03755869], [510. , 0.03558836], [520. , 0.03392457], [530. , 0.03287194], [540. , 0.03279225], [550. , 0.03461775], [560. , 0.04157706], [570. , 0.06103056], [580. , 0.10398511], [590. , 0.17707942], [600. , 0.26899683], [610. , 0.34699756], [620. , 0.37718472], [630. , 0.37785039], [640. , 0.37824584], [650. , 0.37846014], [660. , 0.37856623], [670. , 0.37861426], [680. , 0.37863415], [690. , 0.3786417 ], [700. , 0.37864431], [710. , 0.37864515], [720. , 0.37864539], [730. , 0.37864545], [740. , 0.37864547], [750. , 0.37864547], [760. , 0.37864547], [770. , 0.37864547], [780. , 0.37864547]], SpragueInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) >>> sd_to_XYZ_integration(sd, cmfs, illuminant) / 100 array([0.19324..., 0.11592..., 0.04332...])
Jakob and Hanika (2019) reflectance recovery:
>>> cmfs = ( ... MSDS_CMFS["CIE 1931 2 Degree Standard Observer"] ... .copy() ... .align(SpectralShape(360, 780, 10)) ... ) >>> illuminant = SDS_ILLUMINANTS["D65"].copy().align(cmfs.shape) >>> sd = XYZ_to_sd(XYZ, method="Jakob 2019", cmfs=cmfs, illuminant=illuminant) >>> with numpy_print_options(suppress=True): ... sd SpectralDistribution([[360. , 0.4893773...], [370. , 0.3258214...], [380. , 0.2147792...], [390. , 0.1482413...], [400. , 0.1086169...], [410. , 0.0841255...], [420. , 0.0683114...], [430. , 0.0577144...], [440. , 0.0504267...], [450. , 0.0453552...], [460. , 0.0418520...], [470. , 0.0395259...], [480. , 0.0381430...], [490. , 0.0375741...], [500. , 0.0377685...], [510. , 0.0387432...], [520. , 0.0405871...], [530. , 0.0434783...], [540. , 0.0477225...], [550. , 0.0538256...], [560. , 0.0626314...], [570. , 0.0755869...], [580. , 0.0952675...], [590. , 0.1264265...], [600. , 0.1779272...], [610. , 0.2649393...], [620. , 0.4039779...], [630. , 0.5832105...], [640. , 0.7445440...], [650. , 0.8499970...], [660. , 0.9094792...], [670. , 0.9425378...], [680. , 0.9616376...], [690. , 0.9732481...], [700. , 0.9806562...], [710. , 0.9855873...], [720. , 0.9889903...], [730. , 0.9914117...], [740. , 0.9931801...], [750. , 0.9945009...], [760. , 0.9955066...], [770. , 0.9962855...], [780. , 0.9968976...]], SpragueInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) >>> sd_to_XYZ_integration(sd, cmfs, illuminant) / 100 array([0.2066217..., 0.1220128..., 0.0513958...])
Mallett and Yuksel (2019) reflectance recovery:
>>> cmfs = ( ... MSDS_CMFS["CIE 1931 2 Degree Standard Observer"] ... .copy() ... .align(SPECTRAL_SHAPE_sRGB_MALLETT2019) ... ) >>> illuminant = SDS_ILLUMINANTS["D65"].copy().align(cmfs.shape) >>> sd = XYZ_to_sd(XYZ, method="Mallett 2019") >>> with numpy_print_options(suppress=True): ... sd SpectralDistribution([[380. , 0.1735531...], [385. , 0.1720357...], [390. , 0.1677721...], [395. , 0.1576605...], [400. , 0.1372829...], [405. , 0.1170849...], [410. , 0.0895694...], [415. , 0.0706232...], [420. , 0.0585765...], [425. , 0.0523959...], [430. , 0.0497598...], [435. , 0.0476057...], [440. , 0.0465079...], [445. , 0.0460337...], [450. , 0.0455839...], [455. , 0.0452872...], [460. , 0.0450981...], [465. , 0.0448895...], [470. , 0.0449257...], [475. , 0.0448987...], [480. , 0.0446834...], [485. , 0.0441372...], [490. , 0.0417137...], [495. , 0.0373832...], [500. , 0.0357657...], [505. , 0.0348263...], [510. , 0.0341953...], [515. , 0.0337683...], [520. , 0.0334979...], [525. , 0.0332991...], [530. , 0.0331909...], [535. , 0.0332181...], [540. , 0.0333387...], [545. , 0.0334970...], [550. , 0.0337381...], [555. , 0.0341847...], [560. , 0.0346447...], [565. , 0.0353993...], [570. , 0.0367367...], [575. , 0.0392007...], [580. , 0.0445902...], [585. , 0.0625633...], [590. , 0.2965381...], [595. , 0.4215576...], [600. , 0.4347139...], [605. , 0.4385134...], [610. , 0.4385184...], [615. , 0.4385249...], [620. , 0.4374694...], [625. , 0.4384672...], [630. , 0.4368251...], [635. , 0.4340867...], [640. , 0.4303219...], [645. , 0.4243257...], [650. , 0.4159482...], [655. , 0.4057443...], [660. , 0.3919874...], [665. , 0.3742784...], [670. , 0.3518421...], [675. , 0.3240127...], [680. , 0.2955145...], [685. , 0.2625658...], [690. , 0.2343423...], [695. , 0.2174830...], [700. , 0.2060461...], [705. , 0.1977437...], [710. , 0.1916846...], [715. , 0.1861020...], [720. , 0.1823908...], [725. , 0.1807923...], [730. , 0.1795571...], [735. , 0.1785623...], [740. , 0.1775758...], [745. , 0.1771614...], [750. , 0.1767431...], [755. , 0.1764319...], [760. , 0.1762597...], [765. , 0.1762209...], [770. , 0.1761803...], [775. , 0.1761195...], [780. , 0.1760763...]], SpragueInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) >>> sd_to_XYZ_integration(sd, cmfs, illuminant) / 100 ... array([0.2065436..., 0.1219996..., 0.0513764...])
Meng (2015) reflectance recovery:
>>> cmfs = ( ... MSDS_CMFS["CIE 1931 2 Degree Standard Observer"] ... .copy() ... .align(SpectralShape(360, 780, 10)) ... ) >>> illuminant = SDS_ILLUMINANTS["D65"].copy().align(cmfs.shape) >>> sd = XYZ_to_sd(XYZ, method="Meng 2015", cmfs=cmfs, illuminant=illuminant) >>> with numpy_print_options(suppress=True): ... sd SpectralDistribution([[ 360. , 0.0762005...], [ 370. , 0.0761792...], [ 380. , 0.0761363...], [ 390. , 0.0761194...], [ 400. , 0.0762539...], [ 410. , 0.0761671...], [ 420. , 0.0754649...], [ 430. , 0.0731519...], [ 440. , 0.0676701...], [ 450. , 0.0577800...], [ 460. , 0.0441993...], [ 470. , 0.0285064...], [ 480. , 0.0138728...], [ 490. , 0.0033585...], [ 500. , 0. ...], [ 510. , 0. ...], [ 520. , 0. ...], [ 530. , 0. ...], [ 540. , 0.0055767...], [ 550. , 0.0317581...], [ 560. , 0.0754491...], [ 570. , 0.1314115...], [ 580. , 0.1937649...], [ 590. , 0.2559311...], [ 600. , 0.3123173...], [ 610. , 0.3584966...], [ 620. , 0.3927335...], [ 630. , 0.4159458...], [ 640. , 0.4306660...], [ 650. , 0.4391040...], [ 660. , 0.4439497...], [ 670. , 0.4463618...], [ 680. , 0.4474625...], [ 690. , 0.4479868...], [ 700. , 0.4482116...], [ 710. , 0.4482800...], [ 720. , 0.4483472...], [ 730. , 0.4484251...], [ 740. , 0.4484633...], [ 750. , 0.4485071...], [ 760. , 0.4484969...], [ 770. , 0.4484853...], [ 780. , 0.4485134...]], SpragueInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) >>> sd_to_XYZ_integration(sd, cmfs, illuminant) / 100 array([0.2065400..., 0.1219722..., 0.0513695...])
Otsu, Yamamoto and Hachisuka (2018) reflectance recovery:
>>> cmfs = ( ... MSDS_CMFS["CIE 1931 2 Degree Standard Observer"] ... .copy() ... .align(SPECTRAL_SHAPE_OTSU2018) ... ) >>> illuminant = SDS_ILLUMINANTS["D65"].copy().align(cmfs.shape) >>> sd = XYZ_to_sd(XYZ, method="Otsu 2018", cmfs=cmfs, illuminant=illuminant) >>> with numpy_print_options(suppress=True): ... sd SpectralDistribution([[380. , 0.0601939...], [390. , 0.0568063...], [400. , 0.0517429...], [410. , 0.0495841...], [420. , 0.0502007...], [430. , 0.0506489...], [440. , 0.0510020...], [450. , 0.0493782...], [460. , 0.0468046...], [470. , 0.0437132...], [480. , 0.0416957...], [490. , 0.0403783...], [500. , 0.0405197...], [510. , 0.0406031...], [520. , 0.0416912...], [530. , 0.0430956...], [540. , 0.0444474...], [550. , 0.0459336...], [560. , 0.0507631...], [570. , 0.0628967...], [580. , 0.0844661...], [590. , 0.1334277...], [600. , 0.2262428...], [610. , 0.3599330...], [620. , 0.4885571...], [630. , 0.5752546...], [640. , 0.6193023...], [650. , 0.6450744...], [660. , 0.6610548...], [670. , 0.6688673...], [680. , 0.6795426...], [690. , 0.6887933...], [700. , 0.7003469...], [710. , 0.7084128...], [720. , 0.7154674...], [730. , 0.7234334...]], SpragueInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) >>> sd_to_XYZ_integration(sd, cmfs, illuminant) / 100 array([0.2065494..., 0.1219712..., 0.0514002...])
Smits (1999) reflectance recovery:
>>> cmfs = ( ... MSDS_CMFS["CIE 1931 2 Degree Standard Observer"] ... .copy() ... .align(SpectralShape(360, 780, 10)) ... ) >>> illuminant = SDS_ILLUMINANTS["E"].copy().align(cmfs.shape) >>> sd = XYZ_to_sd(XYZ, method="Smits 1999") >>> with numpy_print_options(suppress=True): ... sd SpectralDistribution([[380. , 0.0787830...], [417.7778 , 0.0622018...], [455.5556 , 0.0446206...], [493.3333 , 0.0352220...], [531.1111 , 0.0324149...], [568.8889 , 0.0330105...], [606.6667 , 0.3207115...], [644.4444 , 0.3836164...], [682.2222 , 0.3836164...], [720. , 0.3835649...]], LinearInterpolator, {}, Extrapolator, {'method': 'Constant', 'left': None, 'right': None}) >>> sd_to_XYZ_integration(sd, cmfs, illuminant) / 100 array([0.1894770..., 0.1126470..., 0.0474420...])