Abstract

Phase unwrapping is a necessary step in fringe-projection profilometry that produces accurate depth maps. However, the original wrapped phase is often corrupted by errors, and thus conventional spatial unwrapping suffers from error propagation, such as scanline-based unwrapping, and high complexity, such as quality-guided methods. In this paper, we propose a fast and robust spatial unwrapping method called multi-anchor scanline unwrapping (MASU). Different from previous work, when unwrapping each pixel, MASU refers to multiple anchors in the scanline, where each anchor has a threshold adapting to its location. In such a manner, a set of fringe order candidates are predicted by the anchors according to phase smoothness assumption, and the one with the highest number of votes is chosen. After that, with the obtained fringe order, the absolute phase and depth are computed. Simulation and experiments have shown that even corrupted by severe phase errors, the proposed MASU can still produce robust unwrapped results. In addition, MASU is thousands of times faster than quality-guided unwrapping with comparative or even superior depth accuracy.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

Full Article  |  PDF Article
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References

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    [Crossref]
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2019 (2)

Y. Yang, Q. Liu, X. He, and Z. Liu, “Cross-view multi-lateral filter for compressed multi-view depth video,” IEEE Trans. on Image Process. 28(1), 302–315 (2019).
[Crossref]

Y. Yang, B. Li, P. Li, and Q. Liu, “A two-stage clustering based 3d visual saliency model for dynamic scenarios,” IEEE Trans. Multimedia 21(4), 809–820 (2019).
[Crossref]

2018 (2)

S. Zhang, “High-speed 3d shape measurement with structured light methods: A review,” Opt. Lasers Eng. 106, 119–131 (2018).
[Crossref]

S. Zhang, “Absolute phase retrieval methods for digital fringe projection profilometry: A review,” Opt. Lasers Eng. 107, 28–37 (2018).
[Crossref]

2017 (5)

S. Xiang, H. Deng, L. Yu, J. Wu, Y. Yang, Q. Liu, and Z. Yuan, “Hybrid profilometry using a single monochromatic multi-frequency pattern,” Opt. Express 25(22), 27195–27209 (2017).
[Crossref]

C. Jiang, B. Li, and Z. Song, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

J. S. Hyun and S. Zhang, “Superfast 3d absolute shape measurement using five binary patterns,” Opt. Lasers Eng. 90, 217–224 (2017).
[Crossref]

C. Jiang and S. Zhang, “Absolute phase unwrapping for dual-camera system without embedding statistical features,” Proc. SPIE 10220, 1022009(2017).
[Crossref]

J. Dai, S. Zhang, and Y. An, “Absolute three-dimensional shape measurement with a known object,” Opt. Express 25(9), 10384 (2017).
[Crossref]

2016 (3)

2015 (2)

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

H. Zhong, J. Tang, and S. Zhang, “Phase quality map based on local multi-unwrapped results for two-dimensional phase unwrapping,” Appl. Opt. 54(4), 739–745 (2015).
[Crossref]

2014 (2)

2013 (1)

2012 (3)

Z. Dai and X. Zha, “An accurate phase unwrapping algorithm based on reliability sorting and residue mask,” IEEE Geosci. Remote Sens. Lett. 9(2), 219–223 (2012).
[Crossref]

Y. Ding, J. Xi, Y. Yu, W. Cheng, S. Wang, and J. F. Chicharo, “Frequency selection in absolute phase maps recovery with two frequency projection fringes,” Opt. Express 20(12), 13238–13251 (2012).
[Crossref]

Z. Dai and X. Zha, “An accurate phase unwrapping algorithm based on reliability sorting and residue mask,” IEEE Geosci. Remote Sens. Lett. 9(2), 219–223 (2012).
[Crossref]

2011 (2)

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8(2), 364–368 (2011).
[Crossref]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref]

2010 (2)

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of fourier transform, windowed fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

K. Liu, Y. Wang, D. L. Lau, Q. Hao, and L. G. Hassebrook, “Dual-frequency pattern scheme for high-speed 3-d shape measurement,” Opt. Express 18(5), 5229–5244 (2010).
[Crossref]

2009 (1)

2007 (2)

Z. Song, L. Xiaolin, and Y. Shing-Tung, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46(1), 50–57 (2007).
[Crossref]

S. Liu and L. X. Yang, “Regional phase unwrapping method based on fringe estimation and phase map segmentation,” Opt. Eng. 46(5), 051012 (2007).
[Crossref]

2006 (2)

2005 (1)

2004 (1)

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37(4), 827–849 (2004).
[Crossref]

2001 (2)

X. Su and W. Chen, “Fourier transform profilometry:: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

X. Su, W. Chen, Q. Zhang, and Y. Chao, “Dynamic 3-d shape measurement method based on ftp,” Opt. Lasers Eng. 36(1), 49–64 (2001).
[Crossref]

1998 (1)

1983 (1)

Ai, C.

Y. Xu and C. Ai, “Simple and effective phase unwrapping technique,” in Interferometry VI: Techniques and Analysis, vol. 2003 (International Society for Optics and Photonics, 1993), pp. 254–263.

An, Y.

Arieli, Y.

B. Freedman, A. Shpunt, M. Machline, and Y. Arieli, “Depth mapping using projected patterns,” (2012). US Patent 8,150,142.

Asundi, A.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of fourier transform, windowed fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref]

A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37(23), 5416–5420 (1998).
[Crossref]

Batlle, J.

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37(4), 827–849 (2004).
[Crossref]

Boticario, J. G.

Budianto, B.

Burton, D. R.

Chao, Y.

X. Su, W. Chen, Q. Zhang, and Y. Chao, “Dynamic 3-d shape measurement method based on ftp,” Opt. Lasers Eng. 36(1), 49–64 (2001).
[Crossref]

Chen, M.

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8(2), 364–368 (2011).
[Crossref]

Chen, Q.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

Chen, W.

X. Su and W. Chen, “Fourier transform profilometry:: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

X. Su, W. Chen, Q. Zhang, and Y. Chao, “Dynamic 3-d shape measurement method based on ftp,” Opt. Lasers Eng. 36(1), 49–64 (2001).
[Crossref]

Cheng, W.

Chicharo, J. F.

Cong, P.

P. Cong, Z. Xiong, Y. Zhang, S. Zhao, and F. Wu, “Accurate dynamic 3d sensing with fourier-assisted phase shifting,” IEEE J. Sel. Top. Signal Process. 9(3), 396–408 (2015).
[Crossref]

Dai, J.

Dai, Z.

Z. Dai and X. Zha, “An accurate phase unwrapping algorithm based on reliability sorting and residue mask,” IEEE Geosci. Remote Sens. Lett. 9(2), 219–223 (2012).
[Crossref]

Z. Dai and X. Zha, “An accurate phase unwrapping algorithm based on reliability sorting and residue mask,” IEEE Geosci. Remote Sens. Lett. 9(2), 219–223 (2012).
[Crossref]

Dardikman, G.

G. Dardikman and N. T. Shaked, “Phase unwrapping using residual neural networks,” in Imaging and Applied Optics (Optical Society of America, 2018), p. CW3B.5.
[Crossref]

Deng, H.

Ding, Y.

Freedman, B.

B. Freedman, A. Shpunt, M. Machline, and Y. Arieli, “Depth mapping using projected patterns,” (2012). US Patent 8,150,142.

Groves, R. M.

Hao, Q.

Hassebrook, L. G.

He, X.

Y. Yang, Q. Liu, X. He, and Z. Liu, “Cross-view multi-lateral filter for compressed multi-view depth video,” IEEE Trans. on Image Process. 28(1), 302–315 (2019).
[Crossref]

Herráez, M. A.

Hsung, T.-C.

Huang, L.

C. Zuo, L. Huang, M. Zhang, Q. Chen, and A. Asundi, “Temporal phase unwrapping algorithms for fringe projection profilometry: A comparative review,” Opt. Lasers Eng. 85, 84–103 (2016).
[Crossref]

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref]

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of fourier transform, windowed fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref]

Huang, P. S.

Hyun, J. S.

J. S. Hyun and S. Zhang, “Superfast 3d absolute shape measurement using five binary patterns,” Opt. Lasers Eng. 90, 217–224 (2017).
[Crossref]

Y. An, J. S. Hyun, and S. Zhang, “Pixel-wise absolute phase unwrapping using geometric constraints of structured light system,” Opt. Express 24(16), 18445–18459 (2016).
[Crossref]

Jiang, C.

C. Jiang and S. Zhang, “Absolute phase unwrapping for dual-camera system without embedding statistical features,” Proc. SPIE 10220, 1022009(2017).
[Crossref]

C. Jiang, B. Li, and Z. Song, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

Kemao, Q.

Lalor, M. J.

Lanari, R.

C. Ojha, M. Manunta, A. Pepe, L. Paglia, and R. Lanari, “An innovative region growing algorithm based on minimum cost flow approach for phase unwrapping of full-resolution differential interferograms,” in IEEE Intl. Geos. Remo. Sens. Symp., (IEEE, 2012), pp. 5582–5585.

Lau, D. L.

Li, B.

Y. Yang, B. Li, P. Li, and Q. Liu, “A two-stage clustering based 3d visual saliency model for dynamic scenarios,” IEEE Trans. Multimedia 21(4), 809–820 (2019).
[Crossref]

C. Jiang, B. Li, and Z. Song, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

B. Li, Z. Liu, and S. Zhang, “Motion-induced error reduction by combining fourier transform profilometry with phase-shifting profilometry,” Opt. Express 24(20), 23289 (2016).
[Crossref]

Li, P.

Y. Yang, B. Li, P. Li, and Q. Liu, “A two-stage clustering based 3d visual saliency model for dynamic scenarios,” IEEE Trans. Multimedia 21(4), 809–820 (2019).
[Crossref]

Liu, H.

Liu, K.

Liu, Q.

Y. Yang, B. Li, P. Li, and Q. Liu, “A two-stage clustering based 3d visual saliency model for dynamic scenarios,” IEEE Trans. Multimedia 21(4), 809–820 (2019).
[Crossref]

Y. Yang, Q. Liu, X. He, and Z. Liu, “Cross-view multi-lateral filter for compressed multi-view depth video,” IEEE Trans. on Image Process. 28(1), 302–315 (2019).
[Crossref]

S. Xiang, H. Deng, L. Yu, J. Wu, Y. Yang, Q. Liu, and Z. Yuan, “Hybrid profilometry using a single monochromatic multi-frequency pattern,” Opt. Express 25(22), 27195–27209 (2017).
[Crossref]

Liu, S.

S. Liu and L. X. Yang, “Regional phase unwrapping method based on fringe estimation and phase map segmentation,” Opt. Eng. 46(5), 051012 (2007).
[Crossref]

Liu, Z.

Y. Yang, Q. Liu, X. He, and Z. Liu, “Cross-view multi-lateral filter for compressed multi-view depth video,” IEEE Trans. on Image Process. 28(1), 302–315 (2019).
[Crossref]

B. Li, Z. Liu, and S. Zhang, “Motion-induced error reduction by combining fourier transform profilometry with phase-shifting profilometry,” Opt. Express 24(20), 23289 (2016).
[Crossref]

Lun, P.

Machline, M.

B. Freedman, A. Shpunt, M. Machline, and Y. Arieli, “Depth mapping using projected patterns,” (2012). US Patent 8,150,142.

Manunta, M.

C. Ojha, M. Manunta, A. Pepe, L. Paglia, and R. Lanari, “An innovative region growing algorithm based on minimum cost flow approach for phase unwrapping of full-resolution differential interferograms,” in IEEE Intl. Geos. Remo. Sens. Symp., (IEEE, 2012), pp. 5582–5585.

Mutoh, K.

Ojha, C.

C. Ojha, M. Manunta, A. Pepe, L. Paglia, and R. Lanari, “An innovative region growing algorithm based on minimum cost flow approach for phase unwrapping of full-resolution differential interferograms,” in IEEE Intl. Geos. Remo. Sens. Symp., (IEEE, 2012), pp. 5582–5585.

Pages, J.

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37(4), 827–849 (2004).
[Crossref]

Paglia, L.

C. Ojha, M. Manunta, A. Pepe, L. Paglia, and R. Lanari, “An innovative region growing algorithm based on minimum cost flow approach for phase unwrapping of full-resolution differential interferograms,” in IEEE Intl. Geos. Remo. Sens. Symp., (IEEE, 2012), pp. 5582–5585.

Pan, B.

L. Huang, Q. Kemao, B. Pan, and A. Asundi, “Comparison of fourier transform, windowed fourier transform, and wavelet transform methods for phase extraction from a single fringe pattern in fringe projection profilometry,” Opt. Lasers Eng. 48(2), 141–148 (2010).
[Crossref]

B. Pan, Q. Kemao, L. Huang, and A. Asundi, “Phase error analysis and compensation for nonsinusoidal waveforms in phase-shifting digital fringe projection profilometry,” Opt. Lett. 34(4), 416–418 (2009).
[Crossref]

Pepe, A.

C. Ojha, M. Manunta, A. Pepe, L. Paglia, and R. Lanari, “An innovative region growing algorithm based on minimum cost flow approach for phase unwrapping of full-resolution differential interferograms,” in IEEE Intl. Geos. Remo. Sens. Symp., (IEEE, 2012), pp. 5582–5585.

Salvi, J.

J. Salvi, J. Pages, and J. Batlle, “Pattern codification strategies in structured light systems,” Pattern Recognit. 37(4), 827–849 (2004).
[Crossref]

Sawaf, F.

Shaked, N. T.

G. Dardikman and N. T. Shaked, “Phase unwrapping using residual neural networks,” in Imaging and Applied Optics (Optical Society of America, 2018), p. CW3B.5.
[Crossref]

Shekatkar, S.

S. Shekatkar, “The sum of the r’th roots of first n natural numbers and new formula for factorial,” arXiv preprint arXiv:1204.0877 (2012).

Shing-Tung, Y.

Shpunt, A.

B. Freedman, A. Shpunt, M. Machline, and Y. Arieli, “Depth mapping using projected patterns,” (2012). US Patent 8,150,142.

Song, Z.

C. Jiang, B. Li, and Z. Song, “Pixel-by-pixel absolute phase retrieval using three phase-shifted fringe patterns without markers,” Opt. Lasers Eng. 91, 232–241 (2017).
[Crossref]

Z. Song, L. Xiaolin, and Y. Shing-Tung, “Multilevel quality-guided phase unwrapping algorithm for real-time three-dimensional shape reconstruction,” Appl. Opt. 46(1), 50–57 (2007).
[Crossref]

Su, W.-H.

Su, X.

M. Zhao, L. Huang, Q. Zhang, X. Su, A. Asundi, and Q. Kemao, “Quality-guided phase unwrapping technique: comparison of quality maps and guiding strategies,” Appl. Opt. 50(33), 6214–6224 (2011).
[Crossref]

X. Su, W. Chen, Q. Zhang, and Y. Chao, “Dynamic 3-d shape measurement method based on ftp,” Opt. Lasers Eng. 36(1), 49–64 (2001).
[Crossref]

X. Su and W. Chen, “Fourier transform profilometry:: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[Crossref]

Takeda, M.

Tang, J.

H. Zhong, J. Tang, and S. Zhang, “Phase quality map based on local multi-unwrapped results for two-dimensional phase unwrapping,” Appl. Opt. 54(4), 739–745 (2015).
[Crossref]

H. Zhong, J. Tang, S. Zhang, and M. Chen, “An improved quality-guided phase-unwrapping algorithm based on priority queue,” IEEE Geosci. Remote Sens. Lett. 8(2), 364–368 (2011).
[Crossref]

Wang, S.

Wang, Y.

Wensen, Z.

Wu, F.

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Figures (12)

Fig. 1.
Fig. 1. Sketch of a typical SL system. (a) System setup. (b) Mainstream coding strategies.
Fig. 2.
Fig. 2. Principle of the multi-anchor scanline unwrapping. (a)(d) Spatial unwrapping without phase errors. (b)(e) Spatial unwrapping with phase errors. (c)(f) The proposed MASU with phase errors. The upper row represents $\varphi _w$ and the lower row illustrates $m$.
Fig. 3.
Fig. 3. Sketch of invalid region processing. (a) Flowchart of detecting the low modulation region and the reflective region. (b)(c) Modification of MASU in the low illumination region and the reflective region, respectively.
Fig. 4.
Fig. 4. Probability of correct phase unwrapping with one anchor and three anchors.
Fig. 5.
Fig. 5. Noisy patterns (the upper row) and the corresponding wrapped phase maps (the lower row) of dragon. From left to right, the amplitudes of the noise are $\pm$10, $\pm$20, $\pm$30 and $\pm$40. Correspondingly, the PSNR values of the patterns are 32.90dB, 26.88dB, 23.36dB, 20.86dB, respectively.
Fig. 6.
Fig. 6. Resultant depth maps of dragon generated with Fig. 5. From top to bottom, the phase values are unwrapped with CS, QG-PDV, QG-MPG, TF-TPU and the proposed MASU. From left to right are the results generated with the four noisy phase maps in Fig. 5, respectively.
Fig. 7.
Fig. 7. Noisy patterns (the upper row) and corresponding wrapped phase maps (the lower row) of Buddha. From left to right, the amplitudes of the noise are $\pm$10, $\pm$20, $\pm$30 and $\pm$40. Correspondingly, the PSNR values of the patterns are 32.90dB, 26.88dB, 23.36dB, 20.86dB, respectively.
Fig. 8.
Fig. 8. Resultant depth maps of Buddha generated with Fig. 7. From top to bottom, the phase values are unwrapped with CS, QG-PDV, QG-MPG, TF-TPU and the proposed MASU. From left to right are the results generated with the four noisy phase maps in Fig. 7, respectively.
Fig. 9.
Fig. 9. An example of unwrapping detail of CS and the proposed MASU. (a) depth map. (b) Intensity. (c) Wrapped phase. (d) Coefficient $m$ with CS and MASU . (e) Unwrapped phase $\varphi$ with CS and MASU.
Fig. 10.
Fig. 10. Response curve between the projected intensity and the recorded intensity.
Fig. 11.
Fig. 11. Results of boy. (a) The second captured pattern. (b) Map of the wrapped phase. (c)–(g) Results of CS, QG-PDV, QG-MPG, TF-TPU and the proposed MASU, respectively.
Fig. 12.
Fig. 12. Results of cones. (a) The second captured pattern. (b) Map of the wrapped phase. (c)–(g) Results of CS, QG-PDV, QG-MPG, , TF-TPU and the proposed MASU, respectively.

Tables (3)

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Table 1. Relative MAD (%) of the depth maps

Tables Icon

Table 2. MAD (mm) and relative MAD (%) of boy and cones

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Table 3. Average time consumed (seconds) in unwrapping a single pixel

Equations (11)

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φ ( p ) = φ w ( p ) + m ( p ) 2 π
I i ( p ) = A + B c o s ( φ ( p ) + i 2 π N ) , i = 1 , 2 , , N
φ = arctan Σ i = 0 N I i s i n ( i 2 π N ) Σ i = 0 N I i c o s ( i 2 π N )
Z = b f L Z 0 f L b + Δ φ 2 π f Z 0
m ( p ) = { m ( q ) + 1  if  Δ φ w ( p , q ) < T h m ( q ) 1  if  Δ φ w ( p , q ) > T h m ( q )  otherwise 
d i = { 1  if  i = 1 T 2 1 2 ( n + 1 i )  if  1 < i n
m i ( p ) = { m ( q i ) + 1  if  Δ φ w ( p , q i ) < T h i m ( q i ) 1  if  Δ φ w ( p , q i ) > T h i m ( q i ) otherwise 
T h i = π ( 1 2 d i T )
{ I m a x = m a x ( I 1 , I 2 , , I N ) I m i n = m i n ( I 1 , I 2 , , I N )
P 1 A = ξ 1
P 3 A = ξ 1 ξ 2 ξ 3 + ξ 1 ξ 2 ( 1 ξ 3 ) + ξ 1 ( 1 ξ 2 ) ξ 3 + ( 1 ξ 1 ) ξ 2 ξ 3 = ξ 1 ξ 2 + ξ 1 ξ 3 + ξ 2 ξ 3 2 ξ 1 ξ 2 ξ 3 = ξ 1 ( ξ 2 + ξ 3 2 ξ 2 ξ 3 ) + ξ 2 ξ 3 = k 3 A ξ 1 + b 3 A

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