Abstract

Metamer mismatching (the phenomenon that two objects matching in color under one illuminant may not match under a different illuminant) potentially has important consequences for color perception. Logvinenko et al. [PLoS ONE 10, e0135029 (2015)] show that in theory the extent of metamer mismatching can be very significant. This paper examines metamer mismatching in practice by computing the volumes of the empirical metamer mismatch bodies and comparing them to the volumes of the theoretical mismatch bodies. A set of more than 25 million unique reflectance spectra is assembled using datasets from several sources. For a given color signal (e.g., CIE XYZ) recorded under a given first illuminant, its empirical metamer mismatch body for a change to a second illuminant is computed as follows: the reflectances having the same color signal when lit by the first illuminant (i.e., reflect metameric light) are computationally relit by the second illuminant, and the convex hull of the resulting color signals then defines the empirical metamer mismatch body. The volume of these bodies is shown to vary systematically with Munsell value and chroma. The empirical mismatch bodies are compared to the theoretical mismatch bodies computed using the algorithm of Logvinenko et al. [IEEE Trans. Image Process. 23, 34 (2014)]. There are three key findings: (1) the empirical bodies are found to be substantially smaller than the theoretical ones; (2) the sizes of both the empirical and theoretical bodies show a systematic variation with Munsell value and chroma; and (3) applied to the problem of color-signal prediction, the centroid of the empirical metamer mismatch body is shown to be a better predictor of what a given color signal might become under a specified illuminant than state-of-the-art methods.

© 2016 Optical Society of America

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References

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  1. G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Academic, 1982).
  2. D. H. Foster, K. Amano, S. M. C. Nascimento, and M. J. Foster, “Frequency of metamerism in natural scenes,” J. Opt. Soc. Am. A 23, 2359–2372 (2006).
    [Crossref]
  3. G. Y. Feng and D. H. Foster, “Predicting frequency of metamerism in natural scenes by entropy of colors,” J. Opt. Soc. Am. A 29, A200–A208 (2012).
    [Crossref]
  4. P. Morovic and H. Haneishi, “Quantitative analysis of metamerism for multispectral image capture,” in Proceedings of 9th International Symposium on Multispectral Color Science (Academic, 2007), pp. 88–96.
  5. D. K. Prasad and L. Wenhe, “Metrics and statistics of frequency of occurrence of metamerism in consumer cameras for natural scenes,” J. Opt. Soc. Am. A 32, 1390–1402 (2015).
    [Crossref]
  6. A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
    [Crossref]
  7. A. D. Logvinenko, “Object-color manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
    [Crossref]
  8. X. Zhang, B. Funt, and H. Mirzaei, “Metamer mismatching and its consequences for predicting how colors are affected by the illuminant,” in Proceedings of IEEE International Conference on Computer Vision Workshops (IEEE, 2015).
  9. A. D. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
    [Crossref]
  10. M. D. Fairchild, Color Appearance Models (Academic, 2013).
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  12. H. Mirzaei and B. Funt, “Object-color-signal prediction using wraparound Gaussian metamers,” J. Opt. Soc. Am. A 31, 1680–1687 (2014).
    [Crossref]
  13. F. Yasuma, T. Mitsunaga, D. Iso, and S. K. Nayar, “Generalized assorted pixel camera: post-capture control of resolution, dynamic range and spectrum,” http://www.cs.columbia.edu/CAVE/databases/multispectral/ .
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    [Crossref]
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    [Crossref]
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    [Crossref]
  23. G. Finlayson, M. Drew, and B. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
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  24. H. Chong, S. Gortler, and T. Zickler, “The von Kries hypothesis and a basis for color constancy,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.
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    [Crossref]

2015 (3)

D. K. Prasad and L. Wenhe, “Metrics and statistics of frequency of occurrence of metamerism in consumer cameras for natural scenes,” J. Opt. Soc. Am. A 32, 1390–1402 (2015).
[Crossref]

A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
[Crossref]

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

2014 (3)

C. Li, M. R. Luo, M. R. Pointer, and P. Green, “Comparison of real color gamuts using a new reflectance database,” Color Res Appl. 39, 442–451 (2014).
[Crossref]

A. D. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[Crossref]

H. Mirzaei and B. Funt, “Object-color-signal prediction using wraparound Gaussian metamers,” J. Opt. Soc. Am. A 31, 1680–1687 (2014).
[Crossref]

2013 (2)

A. D. Logvinenko, “Object-color manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
[Crossref]

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

2012 (1)

2009 (1)

A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library,” Version 2.0, Remote Sensing Environ. 113, 711–715 (2009).
[Crossref]

2006 (2)

1994 (1)

1981 (1)

A. Hard and L. Sivik, “NCS–natural color system: a Swedish standard for color notation,” Color Res. Appl. 6, 129–138 (1981).
[Crossref]

Amano, K.

Baldridge, A. M.

A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library,” Version 2.0, Remote Sensing Environ. 113, 711–715 (2009).
[Crossref]

Bernard, P.

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

Blahova, J.

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

Chong, H.

H. Chong, S. Gortler, and T. Zickler, “The von Kries hypothesis and a basis for color constancy,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Drew, M.

Fairchild, M. D.

M. D. Fairchild, Color Appearance Models (Academic, 2013).

Feng, G. Y.

Finlayson, G.

G. Finlayson, M. Drew, and B. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[Crossref]

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of Third International Conference on Image and Graphics (Academic, 2004), http://www2.cmp.uea.ac.uk/Research/compvis/MultiSpectralDB.htm .

Finlayson, G. D.

Foster, D. H.

Foster, M. J.

Funt, B.

A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
[Crossref]

A. D. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[Crossref]

H. Mirzaei and B. Funt, “Object-color-signal prediction using wraparound Gaussian metamers,” J. Opt. Soc. Am. A 31, 1680–1687 (2014).
[Crossref]

G. Finlayson, M. Drew, and B. Funt, “Spectral sharpening: sensor transformations for improved color constancy,” J. Opt. Soc. Am. A 11, 1553–1563 (1994).
[Crossref]

X. Zhang, B. Funt, and H. Mirzaei, “Metamer mismatching and its consequences for predicting how colors are affected by the illuminant,” in Proceedings of IEEE International Conference on Computer Vision Workshops (IEEE, 2015).

George, S.

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

Godau, C.

A. D. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[Crossref]

Gortler, S.

H. Chong, S. Gortler, and T. Zickler, “The von Kries hypothesis and a basis for color constancy,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Green, P.

C. Li, M. R. Luo, M. R. Pointer, and P. Green, “Comparison of real color gamuts using a new reflectance database,” Color Res Appl. 39, 442–451 (2014).
[Crossref]

Grove, C. I.

A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library,” Version 2.0, Remote Sensing Environ. 113, 711–715 (2009).
[Crossref]

Haneishi, H.

P. Morovic and H. Haneishi, “Quantitative analysis of metamerism for multispectral image capture,” in Proceedings of 9th International Symposium on Multispectral Color Science (Academic, 2007), pp. 88–96.

Hard, A.

A. Hard and L. Sivik, “NCS–natural color system: a Swedish standard for color notation,” Color Res. Appl. 6, 129–138 (1981).
[Crossref]

Hardeberg, J.

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

Hook, S. J.

A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library,” Version 2.0, Remote Sensing Environ. 113, 711–715 (2009).
[Crossref]

Hordley, S.

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of Third International Conference on Image and Graphics (Academic, 2004), http://www2.cmp.uea.ac.uk/Research/compvis/MultiSpectralDB.htm .

Hordley, S. D.

Jaaskelainen, T.

J. Parkkinen, T. Jaaskelainen, and M. Kuittinen, “Spectral representation of color images,” in Proceedings of IEEE 9th International Conference on Pattern Recognition (IEEE, 1988), pp. 14–17, http://www2.uef.fi/fi/spectral/natural-colors .

Klein, O.

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

Kuittinen, M.

J. Parkkinen, T. Jaaskelainen, and M. Kuittinen, “Spectral representation of color images,” in Proceedings of IEEE 9th International Conference on Pattern Recognition (IEEE, 1988), pp. 14–17, http://www2.uef.fi/fi/spectral/natural-colors .

Ley, C.

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

Leys, C.

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

Li, C.

C. Li, M. R. Luo, M. R. Pointer, and P. Green, “Comparison of real color gamuts using a new reflectance database,” Color Res Appl. 39, 442–451 (2014).
[Crossref]

Licata, L.

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

Logvinenko, A. D.

A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
[Crossref]

A. D. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[Crossref]

A. D. Logvinenko, “Object-color manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
[Crossref]

Luo, M. R.

C. Li, M. R. Luo, M. R. Pointer, and P. Green, “Comparison of real color gamuts using a new reflectance database,” Color Res Appl. 39, 442–451 (2014).
[Crossref]

Mirzaei, H.

A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
[Crossref]

H. Mirzaei and B. Funt, “Object-color-signal prediction using wraparound Gaussian metamers,” J. Opt. Soc. Am. A 31, 1680–1687 (2014).
[Crossref]

X. Zhang, B. Funt, and H. Mirzaei, “Metamer mismatching and its consequences for predicting how colors are affected by the illuminant,” in Proceedings of IEEE International Conference on Computer Vision Workshops (IEEE, 2015).

Moan, S.

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

Morovic, P.

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of Third International Conference on Image and Graphics (Academic, 2004), http://www2.cmp.uea.ac.uk/Research/compvis/MultiSpectralDB.htm .

P. Morovic and H. Haneishi, “Quantitative analysis of metamerism for multispectral image capture,” in Proceedings of 9th International Symposium on Multispectral Color Science (Academic, 2007), pp. 88–96.

Nascimento, S. M. C.

Parkkinen, J.

J. Parkkinen, T. Jaaskelainen, and M. Kuittinen, “Spectral representation of color images,” in Proceedings of IEEE 9th International Conference on Pattern Recognition (IEEE, 1988), pp. 14–17, http://www2.uef.fi/fi/spectral/natural-colors .

Pedersen, M.

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

Pointer, M. R.

C. Li, M. R. Luo, M. R. Pointer, and P. Green, “Comparison of real color gamuts using a new reflectance database,” Color Res Appl. 39, 442–451 (2014).
[Crossref]

Prasad, D. K.

Rivera, G.

A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library,” Version 2.0, Remote Sensing Environ. 113, 711–715 (2009).
[Crossref]

Sivik, L.

A. Hard and L. Sivik, “NCS–natural color system: a Swedish standard for color notation,” Color Res. Appl. 6, 129–138 (1981).
[Crossref]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Academic, 1982).

Tokunaga, R.

A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
[Crossref]

Wenhe, L.

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Academic, 1982).

Zhang, X.

X. Zhang, B. Funt, and H. Mirzaei, “Metamer mismatching and its consequences for predicting how colors are affected by the illuminant,” in Proceedings of IEEE International Conference on Computer Vision Workshops (IEEE, 2015).

Zickler, T.

H. Chong, S. Gortler, and T. Zickler, “The von Kries hypothesis and a basis for color constancy,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

Color Res Appl. (1)

C. Li, M. R. Luo, M. R. Pointer, and P. Green, “Comparison of real color gamuts using a new reflectance database,” Color Res Appl. 39, 442–451 (2014).
[Crossref]

Color Res. Appl. (1)

A. Hard and L. Sivik, “NCS–natural color system: a Swedish standard for color notation,” Color Res. Appl. 6, 129–138 (1981).
[Crossref]

IEEE Trans. Image Process. (1)

A. D. Logvinenko, B. Funt, and C. Godau, “Metamer mismatching,” IEEE Trans. Image Process. 23, 34–43 (2014).
[Crossref]

Int. J. Comput. Vis. (1)

A. D. Logvinenko, “Object-color manifold,” Int. J. Comput. Vis. 101, 143–160 (2013).
[Crossref]

J. Exp. Soc. Psychol. (1)

C. Leys, C. Ley, O. Klein, P. Bernard, and L. Licata, “Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median,” J. Exp. Soc. Psychol. 49, 764–766 (2013).
[Crossref]

J. Opt. Soc. Am. A (6)

PLoS ONE (1)

A. D. Logvinenko, B. Funt, H. Mirzaei, and R. Tokunaga, “Rethinking color constancy,” PLoS ONE 10, e0135029 (2015).
[Crossref]

Proc. SPIE (1)

S. Moan, S. George, M. Pedersen, J. Blahova, and J. Hardeberg, “A database for spectral image quality,” Proc. SPIE 9396, 93960P (2015).

Remote Sensing Environ. (1)

A. M. Baldridge, S. J. Hook, C. I. Grove, and G. Rivera, “The ASTER spectral library,” Version 2.0, Remote Sensing Environ. 113, 711–715 (2009).
[Crossref]

Other (12)

J. Parkkinen, T. Jaaskelainen, and M. Kuittinen, “Spectral representation of color images,” in Proceedings of IEEE 9th International Conference on Pattern Recognition (IEEE, 1988), pp. 14–17, http://www2.uef.fi/fi/spectral/natural-colors .

S. Hordley, G. Finlayson, and P. Morovic, “A multi-spectral image database and an application to image rendering across illumination,” in Proceedings of Third International Conference on Image and Graphics (Academic, 2004), http://www2.cmp.uea.ac.uk/Research/compvis/MultiSpectralDB.htm .

Munsell Book of Color—Glossy Edition (X-Rite Corporation, Grand Rapids, Michigan).

X. Zhang, B. Funt, and H. Mirzaei, “Metamer mismatching and its consequences for predicting how colors are affected by the illuminant,” in Proceedings of IEEE International Conference on Computer Vision Workshops (IEEE, 2015).

G. Wyszecki and W. S. Stiles, Color Science: Concepts and Methods, Quantitative Data and Formulae (Academic, 1982).

P. Morovic and H. Haneishi, “Quantitative analysis of metamerism for multispectral image capture,” in Proceedings of 9th International Symposium on Multispectral Color Science (Academic, 2007), pp. 88–96.

M. D. Fairchild, Color Appearance Models (Academic, 2013).

“A color appearance model for color management systems: CIECAM02,” (CIE Central Bureau, 2004).

F. Yasuma, T. Mitsunaga, D. Iso, and S. K. Nayar, “Generalized assorted pixel camera: post-capture control of resolution, dynamic range and spectrum,” http://www.cs.columbia.edu/CAVE/databases/multispectral/ .

Joensuu Spectral Image Database, “Spectral color research group,” University of Eastern Finland, http://www.uef.fi/fi/spectral/spectral-database .

H. Chong, S. Gortler, and T. Zickler, “The von Kries hypothesis and a basis for color constancy,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007), pp. 1–8.

“Improvement to industrial color-difference evaluation,” (CIE Central Bureau, 2001).

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Figures (8)

Fig. 1.
Fig. 1. Chromaticities of the reflectances in the various datasets under D65 plotted in the x y -chromaticity diagram. (a) Black dots indicate the samples from the full training dataset; red (gray in grayscale reproduction) dots are the Munsell papers; and green (white) dots indicate the Finland “Natural Colors” reflectances. (b) Black dots as in (a), bright purple (gray) dots indicate the NCS papers, and cyan (white) dots indicate the JPL reflectances.
Fig. 2.
Fig. 2. Relative spectral power distributions of the 11 illuminants used for testing. (a) Illuminants D50, D65, D100, D150, and D200; (b) illuminants F4, F8, F11, LED1, and LED2.
Fig. 3.
Fig. 3. Average volumes of theoretical metamer mismatch bodies obtained for all Munsell hues plotted as a function of Munsell chroma and value for the illuminant conditions D50, D200, A, F4, and LED1, respectively, changing to D65. Red dots indicate the actual data points. The surface is interpolated through the data points to aid in visualization. The plot colors are those provided by Matlab’s “parula” colormap and are provided simply to aid in visualization. They indicate relative magnitude.
Fig. 4.
Fig. 4. Spectral reflectances of the neutral gray Munsell papers N 1/, N 7.5/, and N 9/ of value 1, 7.5, and 9, respectively.
Fig. 5.
Fig. 5. Volumes (averaged across all Munsell hues) of the empirical metamer mismatch bodies as a function of Munsell chroma and value for the illuminant conditions (a) D50→D65, (b) D200→D65, (c) A→D65, (d) F4→D65, and (e) LED1→D65. Red dots indicate the actual data points with the surface interpolated through the data points to aid in visualization. The plot colors are as in Fig. 3.
Fig. 6.
Fig. 6. Comparison across 10 different illumination conditions of the mean of the cube roots of the volumes (i.e., mean of the body “diameters”) of the empirical metamer mismatch bodies as a function of mean of the cube roots of the volumes of the theoretical metamer mismatch bodies for the Munsell samples. The linear fit shown has slope of 0.15 with R-squared of 0.90.
Fig. 7.
Fig. 7. Histogram of the CIEDE2000 prediction errors for the centroid, GM, and CAT02 methods across the combined set of test reflectances and all 10 illuminant pairs. The height of each bar indicates the number of samples falling within the respective interval, [0,1), [1,2), [2,3), [3,4), [4,5), or [5,∞).
Fig. 8.
Fig. 8. Mean prediction error in CIEDE2000 units as a function of the cube root of the volume of the empirical metamer mismatch body (i.e., body “diameter”) for the three prediction methods: (a) centroid method; (b) GM method; (c) CAT02 method.

Tables (3)

Tables Icon

Table 1. Comparison of the Mean Volumes of the Theoretical Metamer Mismatch Bodies for the 1600 Munsell Samples for a Change from Each of the Different Illuminants to D65 a

Tables Icon

Table 2. Comparison of the Mean Empirical Volumes to the Mean Theoretical Volumes for the 10 Illumination Conditions a

Tables Icon

Table 3. Color Signal Prediction Error of the Three Methods Each Applied to the Combined Set of Test Reflectances and Reported in CIEDE2000 (Mean, Median, 95th Percentile, Standard Deviation) for the 10 Illuminant Conditions a

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