Abstract

We present a constrained spectral unmixing method to remove highlight from a single spectral image. In the constrained spectral unmixing method, the constraints have been imposed so that all the fractions of diffuse and highlight reflection sum up to 1 and are positive. As a result, the spectra of the diffuse image are always positive. The spectral power distribution (SPD) of the light source has been used as the pure highlight spectrum. The pure diffuse spectrum of the measured spectrum has been chosen from the set of diffuse spectra. The pure diffuse spectrum has a minimum angle among the angles calculated between spectra from a set of diffuse spectra and the measured spectrum projected onto the subspace orthogonal to the SPD of the light source. The set of diffuse spectra has been collected by an automated target generation program from the diffuse part in the image. Constrained energy minimization in a finite impulse response linear filter has been used to detect the highlight and diffuse parts in the image. Results by constrained spectral unmixing have been compared with results by the orthogonal subspace projection (OSP) method [Proceedings of International Conference on Pattern Recognition (2006), pp. 812–815] and probabilistic principal component analysis (PPCA) [Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (2005), paper 15]. Constrained spectral unmixing outperforms OSP and PPCA in the visual assessment of the diffuse results. The highlight removal method by constrained spectral unmixing is suitable for spectral images.

© 2011 Optical Society of America

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References

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  1. S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
    [CrossRef]
  2. R. T. Tan and K. Ikeuchi, “Seperating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 178–193 (2005).
    [CrossRef]
  3. P. Koirala, M. Hauta-Kasari, and J. Parkkinen, “Highlight removal from single image,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Springer, 2009), Vol.  5807, pp. 176–187.
    [CrossRef]
  4. H-C. Lee, “Method for computing the scene illuminant chromaticity from specular highlights,” J. Opt. Soc. Am. A 3, 1694–1699(1986).
    [CrossRef] [PubMed]
  5. P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.
  6. Z. Fu, R. T. Tan, and T. Caelli, “Specular free spectral imaging using orthogonal subspace projection,” in Proceedings of International Conference on Pattern Recognition (IEEE Computer Society, 2006), pp. 812–815.
  7. V. Bochko and J. Parkkinen, “Highlight analysis using a mixture model of probabilistic PCA,” in Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (World Scientific and Engineering Academy and Society, 2005), paper 15.
  8. S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
    [CrossRef]
  9. C.-I. Chang, “Orthogonal subspace projection (OSP) revisited: a comprehensive study and analysis,” IEEE Trans. Geosci. Remote Sens. 43, 502–518 (2005).
    [CrossRef]
  10. J. C. Harsanyi, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785(1994).
    [CrossRef]
  11. N. Keshava, “A survey of spectral unmixing algorithms,” Lincoln Lab. J. 14, 55–78 (2003).
  12. H. Ren and C-I. Chang, “Automatic spectral target recognition in hyper spectral imagery,” IEEE Trans. Aerosp. Electron. Syst. 39, 1232–1248 (2003).
    [CrossRef]
  13. C.-I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 42, 608–619 (2004).
    [CrossRef]
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  15. http://www.hyspex.no/products/hyspex/vnir1600.php (last viewed 03.07.2011).
  16. P. Stigel, K. Miyata, and M. Hauta-Kasari, “Wiener estimation method in estimating of spectral reflectance from RGB images,” Pattern Recogn. Image Anal. 17, 233–242 (2007).
    [CrossRef]
  17. O. L. Frost III, “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE 60, 926–935 (1972).
    [CrossRef]
  18. Q. Du, I. Kopriva, and H. Szu, “Investigation on constrained matrix factorization for hyperspectral image analysis,” in IEEE International Geoscience and Remote Sensing Symposium Proceedings (IEEE International, 2005), pp. 4304–4306.
  19. R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Publication 92-14 (Jet Propulsion Laboratory, 1992), Vol. 1, pp. 147–149.
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2009

P. Koirala, M. Hauta-Kasari, and J. Parkkinen, “Highlight removal from single image,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Springer, 2009), Vol.  5807, pp. 176–187.
[CrossRef]

2007

P. Stigel, K. Miyata, and M. Hauta-Kasari, “Wiener estimation method in estimating of spectral reflectance from RGB images,” Pattern Recogn. Image Anal. 17, 233–242 (2007).
[CrossRef]

2006

Z. Fu, R. T. Tan, and T. Caelli, “Specular free spectral imaging using orthogonal subspace projection,” in Proceedings of International Conference on Pattern Recognition (IEEE Computer Society, 2006), pp. 812–815.

2005

V. Bochko and J. Parkkinen, “Highlight analysis using a mixture model of probabilistic PCA,” in Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (World Scientific and Engineering Academy and Society, 2005), paper 15.

C.-I. Chang, “Orthogonal subspace projection (OSP) revisited: a comprehensive study and analysis,” IEEE Trans. Geosci. Remote Sens. 43, 502–518 (2005).
[CrossRef]

R. T. Tan and K. Ikeuchi, “Seperating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 178–193 (2005).
[CrossRef]

Q. Du, I. Kopriva, and H. Szu, “Investigation on constrained matrix factorization for hyperspectral image analysis,” in IEEE International Geoscience and Remote Sensing Symposium Proceedings (IEEE International, 2005), pp. 4304–4306.

2004

C.-I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 42, 608–619 (2004).
[CrossRef]

2003

P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.

N. Keshava, “A survey of spectral unmixing algorithms,” Lincoln Lab. J. 14, 55–78 (2003).

H. Ren and C-I. Chang, “Automatic spectral target recognition in hyper spectral imagery,” IEEE Trans. Aerosp. Electron. Syst. 39, 1232–1248 (2003).
[CrossRef]

1997

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

1994

J. C. Harsanyi, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785(1994).
[CrossRef]

1992

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Publication 92-14 (Jet Propulsion Laboratory, 1992), Vol. 1, pp. 147–149.

1986

1985

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

1972

O. L. Frost III, “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE 60, 926–935 (1972).
[CrossRef]

Boardman, J. W.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Publication 92-14 (Jet Propulsion Laboratory, 1992), Vol. 1, pp. 147–149.

Bochko, V.

V. Bochko and J. Parkkinen, “Highlight analysis using a mixture model of probabilistic PCA,” in Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (World Scientific and Engineering Academy and Society, 2005), paper 15.

Boult, T.

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Caelli, T.

Z. Fu, R. T. Tan, and T. Caelli, “Specular free spectral imaging using orthogonal subspace projection,” in Proceedings of International Conference on Pattern Recognition (IEEE Computer Society, 2006), pp. 812–815.

Chang, C.-I.

C.-I. Chang, “Orthogonal subspace projection (OSP) revisited: a comprehensive study and analysis,” IEEE Trans. Geosci. Remote Sens. 43, 502–518 (2005).
[CrossRef]

C.-I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 42, 608–619 (2004).
[CrossRef]

Chang, C-I.

H. Ren and C-I. Chang, “Automatic spectral target recognition in hyper spectral imagery,” IEEE Trans. Aerosp. Electron. Syst. 39, 1232–1248 (2003).
[CrossRef]

Du, Q.

Q. Du, I. Kopriva, and H. Szu, “Investigation on constrained matrix factorization for hyperspectral image analysis,” in IEEE International Geoscience and Remote Sensing Symposium Proceedings (IEEE International, 2005), pp. 4304–4306.

C.-I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 42, 608–619 (2004).
[CrossRef]

Fang, X. S.

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Frost, O. L.

O. L. Frost III, “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE 60, 926–935 (1972).
[CrossRef]

Fu, Z.

Z. Fu, R. T. Tan, and T. Caelli, “Specular free spectral imaging using orthogonal subspace projection,” in Proceedings of International Conference on Pattern Recognition (IEEE Computer Society, 2006), pp. 812–815.

Goetz, A. F. H.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Publication 92-14 (Jet Propulsion Laboratory, 1992), Vol. 1, pp. 147–149.

Harsanyi, J. C.

J. C. Harsanyi, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785(1994).
[CrossRef]

Hauta-Kasari, M.

P. Koirala, M. Hauta-Kasari, and J. Parkkinen, “Highlight removal from single image,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Springer, 2009), Vol.  5807, pp. 176–187.
[CrossRef]

P. Stigel, K. Miyata, and M. Hauta-Kasari, “Wiener estimation method in estimating of spectral reflectance from RGB images,” Pattern Recogn. Image Anal. 17, 233–242 (2007).
[CrossRef]

Ikeuchi, K.

R. T. Tan and K. Ikeuchi, “Seperating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 178–193 (2005).
[CrossRef]

Keshava, N.

N. Keshava, “A survey of spectral unmixing algorithms,” Lincoln Lab. J. 14, 55–78 (2003).

Koirala, P.

P. Koirala, M. Hauta-Kasari, and J. Parkkinen, “Highlight removal from single image,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Springer, 2009), Vol.  5807, pp. 176–187.
[CrossRef]

Kopriva, I.

Q. Du, I. Kopriva, and H. Szu, “Investigation on constrained matrix factorization for hyperspectral image analysis,” in IEEE International Geoscience and Remote Sensing Symposium Proceedings (IEEE International, 2005), pp. 4304–4306.

Lee, H-C.

Lin, S.

P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.

Miyata, K.

P. Stigel, K. Miyata, and M. Hauta-Kasari, “Wiener estimation method in estimating of spectral reflectance from RGB images,” Pattern Recogn. Image Anal. 17, 233–242 (2007).
[CrossRef]

Nayar, S. K.

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

Parkkinen, J.

P. Koirala, M. Hauta-Kasari, and J. Parkkinen, “Highlight removal from single image,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Springer, 2009), Vol.  5807, pp. 176–187.
[CrossRef]

V. Bochko and J. Parkkinen, “Highlight analysis using a mixture model of probabilistic PCA,” in Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (World Scientific and Engineering Academy and Society, 2005), paper 15.

Quan, L.

P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.

Ren, H.

H. Ren and C-I. Chang, “Automatic spectral target recognition in hyper spectral imagery,” IEEE Trans. Aerosp. Electron. Syst. 39, 1232–1248 (2003).
[CrossRef]

Shafer, S. A.

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Shum, H-Y.

P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.

Stigel, P.

P. Stigel, K. Miyata, and M. Hauta-Kasari, “Wiener estimation method in estimating of spectral reflectance from RGB images,” Pattern Recogn. Image Anal. 17, 233–242 (2007).
[CrossRef]

Szu, H.

Q. Du, I. Kopriva, and H. Szu, “Investigation on constrained matrix factorization for hyperspectral image analysis,” in IEEE International Geoscience and Remote Sensing Symposium Proceedings (IEEE International, 2005), pp. 4304–4306.

Tan, P.

P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.

Tan, R. T.

Z. Fu, R. T. Tan, and T. Caelli, “Specular free spectral imaging using orthogonal subspace projection,” in Proceedings of International Conference on Pattern Recognition (IEEE Computer Society, 2006), pp. 812–815.

R. T. Tan and K. Ikeuchi, “Seperating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 178–193 (2005).
[CrossRef]

Yuhas, R. H.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Publication 92-14 (Jet Propulsion Laboratory, 1992), Vol. 1, pp. 147–149.

Color Res. Appl.

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst.

H. Ren and C-I. Chang, “Automatic spectral target recognition in hyper spectral imagery,” IEEE Trans. Aerosp. Electron. Syst. 39, 1232–1248 (2003).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

C.-I. Chang and Q. Du, “Estimation of number of spectrally distinct signal sources in hyperspectral imagery,” IEEE Trans. Geosci. Remote Sens. 42, 608–619 (2004).
[CrossRef]

C.-I. Chang, “Orthogonal subspace projection (OSP) revisited: a comprehensive study and analysis,” IEEE Trans. Geosci. Remote Sens. 43, 502–518 (2005).
[CrossRef]

J. C. Harsanyi, “Hyperspectral image classification and dimensionality reduction: an orthogonal subspace projection approach,” IEEE Trans. Geosci. Remote Sens. 32, 779–785(1994).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell.

R. T. Tan and K. Ikeuchi, “Seperating reflection components of textured surfaces using a single image,” IEEE Trans. Pattern Anal. Machine Intell. 27, 178–193 (2005).
[CrossRef]

Int. J. Comput. Vision

S. K. Nayar, X. S. Fang, and T. Boult, “Separation of reflection components using color and polarization,” Int. J. Comput. Vision 21, 163–186 (1997).
[CrossRef]

J. Opt. Soc. Am. A

Lincoln Lab. J.

N. Keshava, “A survey of spectral unmixing algorithms,” Lincoln Lab. J. 14, 55–78 (2003).

Pattern Recogn. Image Anal.

P. Stigel, K. Miyata, and M. Hauta-Kasari, “Wiener estimation method in estimating of spectral reflectance from RGB images,” Pattern Recogn. Image Anal. 17, 233–242 (2007).
[CrossRef]

Proc. IEEE

O. L. Frost III, “An algorithm for linearly constrained adaptive array processing,” Proc. IEEE 60, 926–935 (1972).
[CrossRef]

Other

Q. Du, I. Kopriva, and H. Szu, “Investigation on constrained matrix factorization for hyperspectral image analysis,” in IEEE International Geoscience and Remote Sensing Symposium Proceedings (IEEE International, 2005), pp. 4304–4306.

R. H. Yuhas, A. F. H. Goetz, and J. W. Boardman, “Discrimination among semiarid landscape endmembers using the spectral angle mapper (SAM) algorithm,” in Summaries of the Third Annual JPL Airborne Geoscience Workshop, Publication 92-14 (Jet Propulsion Laboratory, 1992), Vol. 1, pp. 147–149.

http://people.cs.uu.nl/robby/textureSeparation/results.html (last viewed 02.9.2011).

http://www.spectralcameras.com/files/downloads/VariSpec_Technote.pdf (last viewed 24.09.2010).

http://www.hyspex.no/products/hyspex/vnir1600.php (last viewed 03.07.2011).

P. Tan, S. Lin, L. Quan, and H-Y. Shum, “Highlight removal by illumination-constrained inpainting,” in Proceedings of the 9th IEEE International Conference on Computer Vision (IEEE Computer Society, 2003), pp. 164–169.

Z. Fu, R. T. Tan, and T. Caelli, “Specular free spectral imaging using orthogonal subspace projection,” in Proceedings of International Conference on Pattern Recognition (IEEE Computer Society, 2006), pp. 812–815.

V. Bochko and J. Parkkinen, “Highlight analysis using a mixture model of probabilistic PCA,” in Proceedings of the 4th WSEAS International Conference on Signal Processing, Robotics and Automation (World Scientific and Engineering Academy and Society, 2005), paper 15.

P. Koirala, M. Hauta-Kasari, and J. Parkkinen, “Highlight removal from single image,” in Proceedings of Advanced Concepts for Intelligent Vision Systems (Springer, 2009), Vol.  5807, pp. 176–187.
[CrossRef]

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Figures (7)

Fig. 1
Fig. 1

Highlight detection in spectral image. (a) and (b) Spectral images rendered in three bands (420, 550, and 700 nm ). (c) and (d) Highlight detected results. Images in (c) and (d) were obtained by applying the K-means algorithm in the fraction image obtained by CEM.

Fig. 2
Fig. 2

Constrained spectral unmixing method compared to OSP method. (a) Original spectral image. (b) Highlight- removed image obtained by constrained spectral unmixing. (c) Highlight-removed image obtained by OSP. All images are rendered in three bands (420, 550, and 700 nm ).

Fig. 3
Fig. 3

Constrained spectral unmixing compared to PPCA. (a) Original spectral image. (b) Highlight-removed image obtained by constrained spectral unmixing. (c) Highlight-removed image obtained by PPCA. All images are rendered in three bands (420, 550, and 700 nm ).

Fig. 4
Fig. 4

Constrained spectral unmixing compared to the polarizer method and OSP. (a) Original spectral image (the radiance spectra of the selected part are shown in Fig. 5). (b) Highlight-removed image obtained by the polarizer method. (c) Highlight-removed image obtained by constrained spectral unmixing. (d) Highlight-removed image obtained by OSP. All images are rendered in three bands (420, 550, and 700 nm ).

Fig. 5
Fig. 5

Comparison of radiance spectra obtained by the polarizer method, constrained spectral unmixing, and OSP. (a) Radiance spectra from the original image. (b) Radiance spectra from a highlight-removed image obtained by the polarizer method. (c) Radiance spectra from a highlight-removed image obtained by constrained spectral unmixing. (d) Radiance spectra from a highlight-removed image obtained by OSP. The radiance spectra are from the selected parts of the images shown in Fig. 4.

Fig. 6
Fig. 6

Target signatures of the highlight and diffuse components. Target signatures of the diffuse components are collected from the image in Fig. 4a. (a) Power distribution of the light source; it is used as the target signature or endmember of the highlight component of the image. (b) Candidate target signatures or endmembers of the diffuse components collected by using ATGP. Out of these candidate target signatures, the best target signature is selected pixelwise.

Fig. 7
Fig. 7

Original spectral image and highlight-removed spectral image obtained by constrained spectral unmixing in different bands: (a)–(d) Images with highlight. (e)–(h) Highlight-removed images obtained by constrained spectral unmixing.

Equations (16)

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

R ( x , λ ) = d ( x ) R d ( λ , x ) S ( λ ) q ( λ ) + s ( x ) S ( λ ) q ( λ ) + e ( x ) ,
R = d D + s S + e ,
R m = i = 1 L d i D i + i = 1 L s i S i + e .
R m = D m d m + S m s m + e .
R r = d D r + s I + e ˜ ,
f i = j = 1 n W j R j i = W T R i = ( R i ) T W .
1 N i = 1 N ( f i ) T f i = 1 N [ i = 1 N ( ( R i ) T W ) T ( R i ) T W ] = W T [ 1 N i = 1 N R i ( R i ) T ] W = W T K W ,
minimize W     W T K W subject to     D T W = W T D = 1.
W T = ( K 1 D D T K 1 D ) T .
P = I S S # ,
P R = P D d + P S s + P e .
P R = P D d + P e .
R ( x ) = i = 1 p a i ( x ) e i ,
R = e a ,
a i ( x ) 0 for all     1 i p , i = 1 p a i ( x ) = 1.
θ = cos 1 λ = 1 n R 1 R 2 λ = 1 n R 1 2 λ = 1 n R 2 2 .

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