Abstract

The performance of learning-based spectral estimation is greatly influenced by the set of training samples selected to create the reconstruction model. Training sample selection schemes can be categorized into global and local approaches. Most of the previously proposed global training schemes aim to reduce the number of training samples, or a selection of representative samples, to maintain the generality of the training dataset. This work relates to printed ink reflectance estimation for quality assessment in in-line print inspection. We propose what we believe is a novel global training scheme that models a large population of realistic printable ink reflectances. Based on this dataset, we used a recursive top-down algorithm to reject clusters of training samples that do not enhance the performance of a linear least-square regression (pseudoinverse-based estimation) process. A set of experiments with real camera response data of a 12-channel multispectral camera system illustrate the advantages of this selection scheme over some other state-of-the-art algorithms. For our data, our method of global training sample selection outperforms other methods in terms of estimation quality and, more importantly, can quickly handle large datasets. Furthermore, we show that reflectance modeling is a reasonable, convenient tool to generate large training sets for print inspection applications.

© 2014 Optical Society of America

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2012

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

2010

M. de Lasarte, M. Arjona, M. Vilaseca, and J. Pujol, “Influence of the number of samples of the training set on accuracy of color measurement and spectral reconstruction,” J. Imaging Sci. Technol. 54, 30501–30510 (2010).
[CrossRef]

2008

2006

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
[CrossRef]

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481 (2006).
[CrossRef]

2005

J. Nieves, E. Valero, S. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696–5703 (2005).
[CrossRef]

R. Hersch and F. Crété, “Improving the Yule–Nielsen modified spectral neugebauer model by dot surface coverages depending on the ink superposition conditions,” in Proc. SPIE 5667, 434–445 (2005).
[CrossRef]

2000

1997

J. Romero, A. García-Beltrán, and J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[CrossRef]

D. Lee, S. Baek, and K. Sung, “Modified k-means algorithm for vector quantizer design,” IEEE Signal Process. Lett. 4, 2–4 (1997).
[CrossRef]

1996

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

1993

P. C. Cosman, K. L. Oehler, E. A. Riskin, and R. M. Gray, “Using vector quantization for image processing,” Proc. IEEE 81, 1326–1341 (1993).
[CrossRef]

Arjona, M.

M. de Lasarte, M. Arjona, M. Vilaseca, and J. Pujol, “Influence of the number of samples of the training set on accuracy of color measurement and spectral reconstruction,” J. Imaging Sci. Technol. 54, 30501–30510 (2010).
[CrossRef]

M. Vilaseca, R. Mercadal, J. Pujol, M. Arjona, M. de Lasarte, R. Huertas, M. Melgosa, and F. Imai, “Characterization of the human iris spectral reflectance with a multispectral imaging system,” Appl. Opt. 47, 5622–5630 (2008).
[CrossRef]

Baek, S.

D. Lee, S. Baek, and K. Sung, “Modified k-means algorithm for vector quantizer design,” IEEE Signal Process. Lett. 4, 2–4 (1997).
[CrossRef]

Berns, R.

D. Wyble and R. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4–19 (2000).
[CrossRef]

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “A prototype calibration target for spectral imaging,” in Tenth Congress of the International Colour AssociationGranada, Spain (2005), pp. 387–390.

Briggs, J.

M. Tse, D. Forrest, and J. Briggs, “Automated print quality analysis for digital printing technologies,” in Pan-Pacific Imaging Conference/Japan Hardcopy (Society of Electrophotography of Japan, Tokyo, Japan, 1998).

Cheung, V.

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481 (2006).
[CrossRef]

Cosman, P. C.

P. C. Cosman, K. L. Oehler, E. A. Riskin, and R. M. Gray, “Using vector quantization for image processing,” Proc. IEEE 81, 1326–1341 (1993).
[CrossRef]

Crété, F.

R. Hersch and F. Crété, “Improving the Yule–Nielsen modified spectral neugebauer model by dot surface coverages depending on the ink superposition conditions,” in Proc. SPIE 5667, 434–445 (2005).
[CrossRef]

de Lasarte, M.

M. de Lasarte, M. Arjona, M. Vilaseca, and J. Pujol, “Influence of the number of samples of the training set on accuracy of color measurement and spectral reconstruction,” J. Imaging Sci. Technol. 54, 30501–30510 (2010).
[CrossRef]

M. Vilaseca, R. Mercadal, J. Pujol, M. Arjona, M. de Lasarte, R. Huertas, M. Melgosa, and F. Imai, “Characterization of the human iris spectral reflectance with a multispectral imaging system,” Appl. Opt. 47, 5622–5630 (2008).
[CrossRef]

Eckhard, T.

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Erni, F.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Forrest, D.

M. Tse, D. Forrest, and J. Briggs, “Automated print quality analysis for digital printing technologies,” in Pan-Pacific Imaging Conference/Japan Hardcopy (Society of Electrophotography of Japan, Tokyo, Japan, 1998).

García-Beltrán, A.

Garrote, E.

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

Granahan, J.

J. Granahan and J. Sweet, “An evaluation of atmospheric correction techniques using the spectral similarity scale,” in Geoscience and Remote Sensing Symposium (IGARSS’01) (IEEE, 2001), Vol. 5, pp. 2022–2024.

Gray, R. M.

P. C. Cosman, K. L. Oehler, E. A. Riskin, and R. M. Gray, “Using vector quantization for image processing,” Proc. IEEE 81, 1326–1341 (1993).
[CrossRef]

Haneishi, H.

Hardeberg, J.

J. Hardeberg, “Acquisition and reproduction of color images: colorimetric and multispectral approaches,” Ph.D. thesis (Universal Publishers, 2001).

Hasegawa, T.

Hauta-Kasari, M.

Heikkinen, V.

Hernández-Andrés, J.

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

J. Nieves, E. Valero, S. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696–5703 (2005).
[CrossRef]

J. Romero, A. García-Beltrán, and J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[CrossRef]

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Hersch, R.

R. Hersch and F. Crété, “Improving the Yule–Nielsen modified spectral neugebauer model by dot surface coverages depending on the ink superposition conditions,” in Proc. SPIE 5667, 434–445 (2005).
[CrossRef]

Heuerding, S.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Hosoi, A.

Hu, Y.

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Huertas, R.

Imai, F.

Jääskeläinen, T.

Jetsu, T.

Kang, J.

J. Kang, K. Ryu, and H. Kwon, “Using cluster-based sampling to select initial training set for active learning in text classification,” Advances in Knowledge Discovery and Data Mining, Lecture Notes in Computer Science (Springer, 2004), Vol. 3056, pp. 384–388.

Kohonen, O.

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
[CrossRef]

Koutroumbas, K.

S. Theodoridis and K. Koutroumbas, Pattern Recognition (Academic, 2008).

Kwon, H.

J. Kang, K. Ryu, and H. Kwon, “Using cluster-based sampling to select initial training set for active learning in text classification,” Advances in Knowledge Discovery and Data Mining, Lecture Notes in Computer Science (Springer, 2004), Vol. 3056, pp. 384–388.

Last, I.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Lee, D.

D. Lee, S. Baek, and K. Sung, “Modified k-means algorithm for vector quantizer design,” IEEE Signal Process. Lett. 4, 2–4 (1997).
[CrossRef]

Lenz, R.

Massart, D.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Melgosa, M.

Mercadal, R.

Miyake, Y.

Mohammadi, M.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “A prototype calibration target for spectral imaging,” in Tenth Congress of the International Colour AssociationGranada, Spain (2005), pp. 387–390.

Nascimento, S.

Nezamabadi, M.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “A prototype calibration target for spectral imaging,” in Tenth Congress of the International Colour AssociationGranada, Spain (2005), pp. 387–390.

Nieves, J.

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

J. Nieves, E. Valero, S. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696–5703 (2005).
[CrossRef]

Nieves, J. L.

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Nowack, D.

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Oehler, K. L.

P. C. Cosman, K. L. Oehler, E. A. Riskin, and R. M. Gray, “Using vector quantization for image processing,” Proc. IEEE 81, 1326–1341 (1993).
[CrossRef]

Parkkinen, J.

Prebble, K.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Pujol, J.

M. de Lasarte, M. Arjona, M. Vilaseca, and J. Pujol, “Influence of the number of samples of the training set on accuracy of color measurement and spectral reconstruction,” J. Imaging Sci. Technol. 54, 30501–30510 (2010).
[CrossRef]

M. Vilaseca, R. Mercadal, J. Pujol, M. Arjona, M. de Lasarte, R. Huertas, M. Melgosa, and F. Imai, “Characterization of the human iris spectral reflectance with a multispectral imaging system,” Appl. Opt. 47, 5622–5630 (2008).
[CrossRef]

Riskin, E. A.

P. C. Cosman, K. L. Oehler, E. A. Riskin, and R. M. Gray, “Using vector quantization for image processing,” Proc. IEEE 81, 1326–1341 (1993).
[CrossRef]

Rodriguez, A.

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

Romero, J.

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

J. Nieves, E. Valero, S. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696–5703 (2005).
[CrossRef]

J. Romero, A. García-Beltrán, and J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[CrossRef]

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Ryu, K.

J. Kang, K. Ryu, and H. Kwon, “Using cluster-based sampling to select initial training set for active learning in text classification,” Advances in Knowledge Discovery and Data Mining, Lecture Notes in Computer Science (Springer, 2004), Vol. 3056, pp. 384–388.

Schnitzlein, M.

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Shao, S.

Shen, H.

Sung, K.

D. Lee, S. Baek, and K. Sung, “Modified k-means algorithm for vector quantizer design,” IEEE Signal Process. Lett. 4, 2–4 (1997).
[CrossRef]

Sweet, J.

J. Granahan and J. Sweet, “An evaluation of atmospheric correction techniques using the spectral similarity scale,” in Geoscience and Remote Sensing Symposium (IGARSS’01) (IEEE, 2001), Vol. 5, pp. 2022–2024.

Taplin, L.

M. Mohammadi, M. Nezamabadi, R. Berns, and L. Taplin, “A prototype calibration target for spectral imaging,” in Tenth Congress of the International Colour AssociationGranada, Spain (2005), pp. 387–390.

Theodoridis, S.

S. Theodoridis and K. Koutroumbas, Pattern Recognition (Academic, 2008).

Tse, M.

M. Tse, D. Forrest, and J. Briggs, “Automated print quality analysis for digital printing technologies,” in Pan-Pacific Imaging Conference/Japan Hardcopy (Society of Electrophotography of Japan, Tokyo, Japan, 1998).

Tsumura, N.

Valero, E.

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

J. Nieves, E. Valero, S. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696–5703 (2005).
[CrossRef]

Valero, E. M.

E. M. Valero, Y. Hu, J. Hernández-Andrés, T. Eckhard, J. L. Nieves, J. Romero, M. Schnitzlein, and D. Nowack, “Comparative performance analysis of spectral estimation algorithms and computational optimization of a multispectral imaging system for print inspection,” in Color Research & Application (Wiley, 2014), pp. 16–27.

Viggiano, J.

J. Viggiano, “Metrics for evaluating spectral matches: a quantitative comparison,” in Proceedings of the 2nd European Conference on Colour Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2004), pp. 286–291.

Vilaseca, M.

M. de Lasarte, M. Arjona, M. Vilaseca, and J. Pujol, “Influence of the number of samples of the training set on accuracy of color measurement and spectral reconstruction,” J. Imaging Sci. Technol. 54, 30501–30510 (2010).
[CrossRef]

M. Vilaseca, R. Mercadal, J. Pujol, M. Arjona, M. de Lasarte, R. Huertas, M. Melgosa, and F. Imai, “Characterization of the human iris spectral reflectance with a multispectral imaging system,” Appl. Opt. 47, 5622–5630 (2008).
[CrossRef]

Walczak, B.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Westland, S.

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481 (2006).
[CrossRef]

Wu, W.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Wyble, D.

D. Wyble and R. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4–19 (2000).
[CrossRef]

Xin, J.

Yokoyama, Y.

Zhang, H.

Appl. Opt.

Chemom. Intell. Lab. Syst.

W. Wu, B. Walczak, D. Massart, S. Heuerding, F. Erni, I. Last, and K. Prebble, “Artificial neural networks in classification of NIR spectral data: design of the training set,” Chemom. Intell. Lab. Syst. 33, 35–46 (1996).
[CrossRef]

Color Res. Appl.

O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381–390 (2006).
[CrossRef]

D. Wyble and R. Berns, “A critical review of spectral models applied to binary color printing,” Color Res. Appl. 25, 4–19 (2000).
[CrossRef]

IEEE Signal Process. Lett.

D. Lee, S. Baek, and K. Sung, “Modified k-means algorithm for vector quantizer design,” IEEE Signal Process. Lett. 4, 2–4 (1997).
[CrossRef]

J. Imaging Sci. Technol.

M. de Lasarte, M. Arjona, M. Vilaseca, and J. Pujol, “Influence of the number of samples of the training set on accuracy of color measurement and spectral reconstruction,” J. Imaging Sci. Technol. 54, 30501–30510 (2010).
[CrossRef]

V. Cheung and S. Westland, “Methods for optimal color selection,” J. Imaging Sci. Technol. 50, 481 (2006).
[CrossRef]

J. Opt. Soc. Am. A

Proc. IEEE

P. C. Cosman, K. L. Oehler, E. A. Riskin, and R. M. Gray, “Using vector quantization for image processing,” Proc. IEEE 81, 1326–1341 (1993).
[CrossRef]

Proc. SPIE

A. Rodriguez, J. Nieves, E. Valero, E. Garrote, J. Hernández-Andrés, and J. Romero, “Modified fuzzy c-means applied to a Bragg grating-based spectral imager for material clustering,” in Proc. SPIE 8300, 830003 (2012).
[CrossRef]

R. Hersch and F. Crété, “Improving the Yule–Nielsen modified spectral neugebauer model by dot surface coverages depending on the ink superposition conditions,” in Proc. SPIE 5667, 434–445 (2005).
[CrossRef]

Other

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Figures (8)

Fig. 1.
Fig. 1.

Schematic illustration of the working principle of the 12 channel multispectral camera system. The orange line indicates the field of view of all lenses of the camera system. To acquire an image scene (illustrated by the multicolor logo of the Color Imaging Laboratory at the University of Granada), the image is translated horizontally under the camera in the direction indicated by the green arrow.

Fig. 2.
Fig. 2.

Normalized product of responsivities Y and spectral power distribution of the illumination l of the 12-channel multispectral camera system.

Fig. 3.
Fig. 3.

Pseudocode of the RR algorithm proposed in this work.

Fig. 4.
Fig. 4.

CIE-L*a*b* color coordinates of modeled (green), Toyo (red), and CC140 (blue) dataset.

Fig. 5.
Fig. 5.

Mean colorimetric estimation performance (ΔE¯00) over a number of training samples n for RD, SH, CW, and HD method and the small dataset.

Fig. 6.
Fig. 6.

Mean colorimetric estimation performance (ΔE¯00) over number of training samples n for KG, SSV, KS, and MH and the small dataset. For most methods, the optimal number of samples for training approaches the maximal number of samples.

Fig. 7.
Fig. 7.

RR method optimal parameter search: ΔE¯00 error over k and th.

Fig. 8.
Fig. 8.

Mean colorimetric estimation performance (ΔE¯00) over number of training samples n for RD, KG, KS, and MH method and the large dataset. The optimal number of samples nopt is indicated for all methods, including RR with a squared marker.

Tables (2)

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Table 1. Experiment 1 Compares Mean Estimation Error for the Method-Depending Optimal nopt Selected Training Samples and the Small Dataseta

Tables Icon

Table 2. Experiment 2 Compares Mean Estimation Error and Time Performance for the Method-Depending Optimal nopt Selected Training Samples and the Large Dataseta

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

Rte=Rtr×Ptr+×Pte.
RMSE=1m|rr˜|2.
dp=1r,r˜r·r˜.
P=Δλ*Y×diag(l)×R+b,

Metrics