Abstract

The division of Color Space into ten zones, corresponding to the ten Munsell hues, allows a good reconstruction of surface reflectance spectra using just three eigenvectors, obtained by applying principal components analysis to the reflectance spectra of the Munsell Atlas specimens (model group), although the basis vectors obtained are different for each subspace. The use of the tristimulus values from each measured spectrum, calculated with the Illuminant D65 and the Standard Observer CIE64 to obtain the principal components necessary to reconstruct the spectrum, allows a very high degree of metamerism to be attained between the two spectra (measured and reconstructed). Furthermore, this method of calculating the principal components allows reconstruction of the spectra of specimens from other sample sets that differ from the model group used in the PCA. The colorimetric accuracy obtained in the new sample sets is similar to that obtained for the model group.

© 2006 Optical Society of America

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  15. F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. II. White wines and brandies," Am. J. Enol. Vitic. 48, 377-382 (1997).
  16. M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
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    [CrossRef]
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2005 (1)

D. Tzeng and R. S. Berns, "A review of principal component analysis and its applications to color technology," Color Res. Appl. 30, 84-98 (2005).
[CrossRef]

2004 (1)

H. S. Fairman and M. H. Brill, "The principal components of reflectances," Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

2001 (1)

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

1998 (2)

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, "Linear bases for spectral reflectance functions of acrylic paints," Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

1997 (2)

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. I. Red and rosé wines," Am. J. Enol. Vitic. 48, 370-376 (1997).

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. II. White wines and brandies," Am. J. Enol. Vitic. 48, 377-382 (1997).

1995 (1)

C. Salas, A. J. Poza, M. Melgosa, and E. Hita, "Relationship between metamerism indices for achromatic stimuli," Atti Fond Giorgio Ronchi 5, 729-745 (1995).

1994 (1)

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement, deviation and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

1991 (1)

J. Romero, A. García-Beltrán, and L. Jiménez del Barco, "Análisis de un modelo lineal de reflectancia espectral difusa sobre muestras de tono rojo," Opt. Pura Apl. 24, 1-9 (1991).

1989 (1)

1986 (1)

1964 (1)

J. Cohen, "Dependency of the spectral reflectance curves of the Munsell color chips," Psychonomic Sci. 1, 369-370 (1964).

1962 (1)

1943 (1)

Alba, J.

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

Ayala, F.

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. I. Red and rosé wines," Am. J. Enol. Vitic. 48, 370-376 (1997).

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. II. White wines and brandies," Am. J. Enol. Vitic. 48, 377-382 (1997).

A. Lomas, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Método simplificado de medida del color de la miel," in Proceedings of XXV Bienal de la Real Sociedad Española de Física (Real Sociedad Española de Física, 1995), pp. 535-536.

M. P. Renet, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Reconstrucción del espectro de reflectancia de muestras opacas a partir de sus valores triestímulos," in Proceedings of VI Congreso Nacional de Color (Universidad de Sevilla, 2002), pp. 47-48.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucción de los espectros de reflectancia de muestras azules a partir de sus valores triestimulo," in Proceedings of 6th Reunión Nacional de Óptica (Sociedad Española de Óptica, 2000), pp. 297-298.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucctión de espectros de reflectancia a partir de los valores triestimulo obtenidos con un colorímetro," in Proceedings V of Congreso Nacional de Color (Universidad Politécnica de Cataluña, 1999), pp. 233-234.

Berns, R. S.

D. Tzeng and R. S. Berns, "A review of principal component analysis and its applications to color technology," Color Res. Appl. 30, 84-98 (2005).
[CrossRef]

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of The First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

Brill, M. H.

H. S. Fairman and M. H. Brill, "The principal components of reflectances," Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

Cohen, J.

J. Cohen, "Dependency of the spectral reflectance curves of the Munsell color chips," Psychonomic Sci. 1, 369-370 (1964).

Echávarri, J. F.

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. II. White wines and brandies," Am. J. Enol. Vitic. 48, 377-382 (1997).

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. I. Red and rosé wines," Am. J. Enol. Vitic. 48, 370-376 (1997).

A. Lomas, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Método simplificado de medida del color de la miel," in Proceedings of XXV Bienal de la Real Sociedad Española de Física (Real Sociedad Española de Física, 1995), pp. 535-536.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucción de los espectros de reflectancia de muestras azules a partir de sus valores triestimulo," in Proceedings of 6th Reunión Nacional de Óptica (Sociedad Española de Óptica, 2000), pp. 297-298.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucctión de espectros de reflectancia a partir de los valores triestimulo obtenidos con un colorímetro," in Proceedings V of Congreso Nacional de Color (Universidad Politécnica de Cataluña, 1999), pp. 233-234.

M. P. Renet, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Reconstrucción del espectro de reflectancia de muestras opacas a partir de sus valores triestímulos," in Proceedings of VI Congreso Nacional de Color (Universidad de Sevilla, 2002), pp. 47-48.

Fairman, H. S.

H. S. Fairman and M. H. Brill, "The principal components of reflectances," Color Res. Appl. 29, 104-110 (2004).
[CrossRef]

García-Beltrán, A.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, "Linear bases for spectral reflectance functions of acrylic paints," Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

J. Romero, A. García-Beltrán, and L. Jiménez del Barco, "Análisis de un modelo lineal de reflectancia espectral difusa sobre muestras de tono rojo," Opt. Pura Apl. 24, 1-9 (1991).

García-Parrilla, M. C.

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

Gershon, R.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement, deviation and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Gibson, K. S.

Hallikainen, J.

J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, www.it.lut.fi/ip/research/color/database/download.html#munsell-spec-matt/.

Hardeberg, J. Y.

J. Y. Hardeberg, "On the spectral dimensionality of object colours," in Proceedings of The First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 480-485.

Heredia, F. J.

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

Hernández-Andrés, J.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, "Linear bases for spectral reflectance functions of acrylic paints," Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

Hita, E.

C. Salas, A. J. Poza, M. Melgosa, and E. Hita, "Relationship between metamerism indices for achromatic stimuli," Atti Fond Giorgio Ronchi 5, 729-745 (1995).

Imai, F. H.

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of The First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

Iwan, L. S.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement, deviation and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Jaaskelainen, T.

J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, www.it.lut.fi/ip/research/color/database/download.html#munsell-spec-matt/.

Jiménez del Barco, L.

J. Romero, A. García-Beltrán, and L. Jiménez del Barco, "Análisis de un modelo lineal de reflectancia espectral difusa sobre muestras de tono rojo," Opt. Pura Apl. 24, 1-9 (1991).

Kelly, K. L.

Krinov, E. L.

E. L. Krinov, "Spectral reflectance properties of natural formations," technical translation TT-439 (National Research Council of Canada1947).

Lomas, A.

A. Lomas, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Método simplificado de medida del color de la miel," in Proceedings of XXV Bienal de la Real Sociedad Española de Física (Real Sociedad Española de Física, 1995), pp. 535-536.

Maloney, L. T.

Melgosa, M.

C. Salas, A. J. Poza, M. Melgosa, and E. Hita, "Relationship between metamerism indices for achromatic stimuli," Atti Fond Giorgio Ronchi 5, 729-745 (1995).

Moyano, M. J.

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

Negueruela, A. I.

M. J. Moyano, F. Ayala, J. F. Echávarri, J. Alba, A. I. Negueruela, and F. J. Heredia, "Simplified measurement of virgin olive oil color by application of the characteristic vector method," J. Am. Oil Chem. Soc. 78, 1221-1226 (2001).
[CrossRef]

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. I. Red and rosé wines," Am. J. Enol. Vitic. 48, 370-376 (1997).

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. II. White wines and brandies," Am. J. Enol. Vitic. 48, 377-382 (1997).

A. Lomas, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Método simplificado de medida del color de la miel," in Proceedings of XXV Bienal de la Real Sociedad Española de Física (Real Sociedad Española de Física, 1995), pp. 535-536.

M. P. Renet, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Reconstrucción del espectro de reflectancia de muestras opacas a partir de sus valores triestímulos," in Proceedings of VI Congreso Nacional de Color (Universidad de Sevilla, 2002), pp. 47-48.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucctión de espectros de reflectancia a partir de los valores triestimulo obtenidos con un colorímetro," in Proceedings V of Congreso Nacional de Color (Universidad Politécnica de Cataluña, 1999), pp. 233-234.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucción de los espectros de reflectancia de muestras azules a partir de sus valores triestimulo," in Proceedings of 6th Reunión Nacional de Óptica (Sociedad Española de Óptica, 2000), pp. 297-298.

Nickerson, D.

Nieves, J. L.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, "Linear bases for spectral reflectance functions of acrylic paints," Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

Parkkinen, J. P. S.

Parkkinen, P. S.

P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, www.it.lut.fi/ip/research/color/database/download.html#munsell-spec-matt/.

Poza, A. J.

C. Salas, A. J. Poza, M. Melgosa, and E. Hita, "Relationship between metamerism indices for achromatic stimuli," Atti Fond Giorgio Ronchi 5, 729-745 (1995).

Renet, M. P.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucctión de espectros de reflectancia a partir de los valores triestimulo obtenidos con un colorímetro," in Proceedings V of Congreso Nacional de Color (Universidad Politécnica de Cataluña, 1999), pp. 233-234.

J. F. Echávarri, F. Ayala, M. P. Renet, and A. I. Negueruela, "Reconstrucción de los espectros de reflectancia de muestras azules a partir de sus valores triestimulo," in Proceedings of 6th Reunión Nacional de Óptica (Sociedad Española de Óptica, 2000), pp. 297-298.

M. P. Renet, F. Ayala, J. F. Echávarri, and A. I. Negueruela, "Reconstrucción del espectro de reflectancia de muestras opacas a partir de sus valores triestímulos," in Proceedings of VI Congreso Nacional de Color (Universidad de Sevilla, 2002), pp. 47-48.

Renet, P.

P. Renet, "Contribución al estudio de métodos espectrofotométricos abreviados para la determinación del color en modo objeto," Ph.D. thesis (Universidad de Zaragoza, 2003).

Romero, J.

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, "Linear bases for spectral reflectance functions of acrylic paints," Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

J. Romero, A. García-Beltrán, and L. Jiménez del Barco, "Análisis de un modelo lineal de reflectancia espectral difusa sobre muestras de tono rojo," Opt. Pura Apl. 24, 1-9 (1991).

Rosen, M. R.

F. H. Imai, M. R. Rosen, and R. S. Berns, "Comparative study of metrics for spectral match quality," in Proceedings of The First European Conference on Colour in Graphics, Image and Vision (Society for Imaging Science and Technology, 2002), pp. 492-496.

Salas, C.

C. Salas, A. J. Poza, M. Melgosa, and E. Hita, "Relationship between metamerism indices for achromatic stimuli," Atti Fond Giorgio Ronchi 5, 729-745 (1995).

Simonds, J. L.

Troncoso, A. M.

M. C. García-Parrilla, F. Ayala, J. F. Echávarri, A. M. Troncoso, A. I. Negueruela, and F. J. Heredia, "Measurements of wine vinegar's color: application of the characteristic vector method," J. Agric. Food Chem. 46, 4238-4241 (1998).
[CrossRef]

Tzeng, D.

D. Tzeng and R. S. Berns, "A review of principal component analysis and its applications to color technology," Color Res. Appl. 30, 84-98 (2005).
[CrossRef]

Vrhel, M. J.

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement, deviation and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

Am. J. Enol. Vitic. (2)

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. I. Red and rosé wines," Am. J. Enol. Vitic. 48, 370-376 (1997).

F. Ayala, J. F. Echávarri, and A. I. Negueruela, "New simplified method for measuring the color of wines. II. White wines and brandies," Am. J. Enol. Vitic. 48, 377-382 (1997).

Atti Fond Giorgio Ronchi (1)

C. Salas, A. J. Poza, M. Melgosa, and E. Hita, "Relationship between metamerism indices for achromatic stimuli," Atti Fond Giorgio Ronchi 5, 729-745 (1995).

Color Res. Appl. (4)

M. J. Vrhel, R. Gershon, and L. S. Iwan, "Measurement, deviation and analysis of object reflectance spectra," Color Res. Appl. 19, 4-9 (1994).

A. García-Beltrán, J. L. Nieves, J. Hernández-Andrés, and J. Romero, "Linear bases for spectral reflectance functions of acrylic paints," Color Res. Appl. 23, 39-45 (1998).
[CrossRef]

D. Tzeng and R. S. Berns, "A review of principal component analysis and its applications to color technology," Color Res. Appl. 30, 84-98 (2005).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Munsell spectra reconstructed with the principal components, M i , given directly by the PCA method. (a) Values of the GFC and RMSE metrics, (b) color differences (llluminant D65 and Observer CIE64) between reconstructed and experimental spectra versus the corresponding RMSE values.

Fig. 2
Fig. 2

Examples of reconstruction for three Munsell samples.

Tables (5)

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Table 1 Percentage of Variance Accounted for by a Linear Model with 1–4 Eigenvectors for the Ten Munsell Hue Zones

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Table 2 Statistics of Color Differences (in CIELAB Units) between Colors Obtained from Experimental Spectra and Spectra Reconstructed Directly from PCA for Each Specimen of the Munsell Atlas ( N = 1485 Specimens)

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Table 3 Statistics of Color Differences (in CIELAB Units) between Colors Obtained from Experimental and Reconstructed Spectra for Each Specimen of the Three Atlases: Munsell ( N = 1485 Specimens), NCS ( N = 1675 Specimens) and Munsell Measured by Parkkinen and Colleagues ( N = 1269 Specimens)

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Table 4 Statistics of Color Differences, Δ E * (in CIELAB Units) between Colors Obtained from Experimental and Reconstructed Spectra for Each Specimen, Calculated with the CIE64 Observer and CIE Illuminant A or Illuminant F11 a

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Table 5 Correlations among the Color Differences Obtained with Different CIE Standard IIluminants

Equations (15)

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det ( S L I ) = 0 ,
ρ λ = ρ λ ¯ + M 1 V 1 λ + M 2 V 2 λ + .... + M p V p λ , p r ,
X = k λ ρ λ S λ x ¯ λ Δ λ , Y = k λ ρ λ S λ y ¯ λ Δ λ ,
Z = k λ ρ λ S λ z ¯ λ Δ λ ,
X = k λ ( ρ ¯ λ + M 1 V 1 λ + M 2 V 2 λ + .... + M p V p λ ) S λ x ¯ λ Δ λ ,
X = k λ ρ ¯ λ S λ x ¯ λ Δ λ + M 1 k λ V 1 λ S λ x ¯ λ Δ λ + .... + M p k λ V p λ S λ x ¯ λ Δ λ
X i = k λ V i λ S λ x ¯ λ Δ λ ,
X = X 0 + M 1 X 1 + M 2 X 2 + .... + M p X p ,
Y = Y 0 + M 1 Y 1 + M 2 Y 2 + .... + M p Y p ,
Z = Z 0 + M 1 Z 1 + M 2 Z 2 + .... + M p Z p .
M 1 = M 1 ( X , Y , Z ) ,
M 2 = M 2 ( X , Y , Z ) ,
M 3 = M 3 ( X , Y , Z ) ,
ρ λ = ρ λ ¯ + M 1 V 1 λ + M 2 V 2 λ + M 3 V 3 λ .
Δ E a b * = ( L 1 * L 2 * ) 2 + ( a 1 * a 2 * ) 2 + ( b 1 * b 2 * ) 2 .

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