Abstract

A four-dimensional [4D—three-dimensional (3D) shape varying in time] shape measurement system is described. A single 3D shape of an object is calculated from only one frame. The projected pattern is composed of sinusoidal intensity fringes and one color-encoded stripe, the analysis of which allows us to find the absolute coordinates of the measured object. During measurement, the position of the stripe changes due to the improvement of the quality of spatiotemporal unwrapping. The fringes deformed by the shape of the object are captured by a CCD camera and processed by an adaptive spatial carrier phase-shifting algorithm. The use of an algorithm based on fast Fourier transformation is proposed to approximate the local period of fringes. A new phase-unwrapping routine based on the spatiotemporal information is presented as well. All these features make the 3D shape measurement of an object in motion possible with the additional advantage of using a low-cost system. Experimental results of the developed method together with a preliminary assessment of measurement uncertainty are presented to show the validity of the method.

© 2009 Optical Society of America

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  1. H. G. Nguyen and M. R. Blackburn, “A simple method for range finding via laser triangulation,” Technical document (Naval Research and Development, 1995).
  2. K. Kraus, Photogrammetry (Dümmler, 1993).
  3. R. Sitnik, M. Kujawińska, and J. Woźnicki, “Digital fringe projection system for large volume 360 deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
    [CrossRef]
  4. V. Srinivasan, H. C. Liu, and M. Haliousa, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23, 3105-3108 (1984).
    [CrossRef] [PubMed]
  5. M. Kujawińska and J. Wójciak, “Spatial phase-shifting technique of fringe pattern analysis in photomechanics,” Proc. SPIE 1554B, 503-513 (1991).
  6. G. T. Reid and D. W. Robinson, Interferogram Analysis (Institute of Physics, 1993).
  7. W. Osten, W. Nadeborn, and P. Andrae, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2-13 (1996).
    [CrossRef]
  8. M. Pirga, A. Kozłowska, and M. Kujawińska, “Generalization of the scaling problem for the automatic moire and fringe projection shape measurement systems,”in Fringe '93, Second International Workshop on Automatic Processing of Fringe Patterns (Akademie Verlag, 1993), pp. 188-193.
  9. R. Sitnik, “A fully automatic 3D shape measurement system with data export for engineering and multimedia systems,” Ph.D. dissertation (Warsaw University of Technology, 2002).
  10. L. Zhang, B. Curless, and S. M. Seitz, “Rapid shape acquisition using color structured light and multi-pass dynamic programming,” in Proceedings of 1st International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT) (2002), pp. 24-36.
    [CrossRef] [PubMed]
  11. I. A. Ypsilos, A. Hilton, and S. Rowe, “Video-rate capture of dynamic face shape and appearance,” in Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 2004), pp. 117-122.
    [CrossRef]
  12. M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
    [CrossRef]
  13. T. P. Koninckx and L. Van Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28 (3), 432-445 (2006).
    [CrossRef] [PubMed]
  14. S. Zhang and P. S. Huang, “High-resolution, real-time 3-D shape measurement,” Opt. Eng. 45, 123601 (2006).
    [CrossRef]
  15. M. Pawłowski, “Automated system for absolute shape measurement of 3D time-varying objects,” Ph.D. dissertation (Warsaw University of Technology, 2002).
  16. S. Zhang and S.-T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14 (7), 2644-2649 (2006).
    [CrossRef] [PubMed]
  17. R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37 (3), 390-397 (2001).
    [CrossRef]
  18. J. C. Russ, The Image Processing Handbook (Wiley, 2006).
    [CrossRef]
  19. M. Takeda, “Spatial-carrier fringe pattern analysis and its applications to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79-99 (1990).
    [CrossRef]
  20. M. Pirga and M. Kujawińska, “Two-directional spatial-carrier phase shifting method for analysis of crossed and closed fringe pattern,” Opt. Eng. 34, 2459-2466 (1995).
    [CrossRef]
  21. J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993-4998 (2004).
    [CrossRef] [PubMed]
  22. M. Kujawińska and J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325-339(1991).
    [CrossRef]
  23. J. Zhong and J. Weng, “Dilating Gabor transform for the fringe analysis of 3-D shape measurement,” Opt. Eng. 43, 895-899 (2004).
    [CrossRef]
  24. J. M. Huntley, “Three-dimensional noise-immune phase unwrapping algorithm,” Appl. Opt. 40, 3901-3908 (2001).
    [CrossRef]

2006

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

T. P. Koninckx and L. Van Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28 (3), 432-445 (2006).
[CrossRef] [PubMed]

S. Zhang and P. S. Huang, “High-resolution, real-time 3-D shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

S. Zhang and S.-T. Yau, “High-resolution, real-time 3D absolute coordinate measurement based on a phase-shifting method,” Opt. Express 14 (7), 2644-2649 (2006).
[CrossRef] [PubMed]

2004

J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993-4998 (2004).
[CrossRef] [PubMed]

J. Zhong and J. Weng, “Dilating Gabor transform for the fringe analysis of 3-D shape measurement,” Opt. Eng. 43, 895-899 (2004).
[CrossRef]

2002

R. Sitnik, M. Kujawińska, and J. Woźnicki, “Digital fringe projection system for large volume 360 deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

2001

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37 (3), 390-397 (2001).
[CrossRef]

J. M. Huntley, “Three-dimensional noise-immune phase unwrapping algorithm,” Appl. Opt. 40, 3901-3908 (2001).
[CrossRef]

1996

W. Osten, W. Nadeborn, and P. Andrae, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

1995

M. Pirga and M. Kujawińska, “Two-directional spatial-carrier phase shifting method for analysis of crossed and closed fringe pattern,” Opt. Eng. 34, 2459-2466 (1995).
[CrossRef]

1991

M. Kujawińska and J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325-339(1991).
[CrossRef]

M. Kujawińska and J. Wójciak, “Spatial phase-shifting technique of fringe pattern analysis in photomechanics,” Proc. SPIE 1554B, 503-513 (1991).

1990

M. Takeda, “Spatial-carrier fringe pattern analysis and its applications to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79-99 (1990).
[CrossRef]

1984

Andrae, P.

W. Osten, W. Nadeborn, and P. Andrae, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Blackburn, M. R.

H. G. Nguyen and M. R. Blackburn, “A simple method for range finding via laser triangulation,” Technical document (Naval Research and Development, 1995).

Curless, B.

L. Zhang, B. Curless, and S. M. Seitz, “Rapid shape acquisition using color structured light and multi-pass dynamic programming,” in Proceedings of 1st International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT) (2002), pp. 24-36.
[CrossRef] [PubMed]

Haex, B.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

Haliousa, M.

Hilton, A.

I. A. Ypsilos, A. Hilton, and S. Rowe, “Video-rate capture of dynamic face shape and appearance,” in Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 2004), pp. 117-122.
[CrossRef]

Huang, P. S.

S. Zhang and P. S. Huang, “High-resolution, real-time 3-D shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

Huntley, J. M.

Koninckx, T. P.

T. P. Koninckx and L. Van Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28 (3), 432-445 (2006).
[CrossRef] [PubMed]

Kowalski, M.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

Kozlowska, A.

M. Pirga, A. Kozłowska, and M. Kujawińska, “Generalization of the scaling problem for the automatic moire and fringe projection shape measurement systems,”in Fringe '93, Second International Workshop on Automatic Processing of Fringe Patterns (Akademie Verlag, 1993), pp. 188-193.

Kraus, K.

K. Kraus, Photogrammetry (Dümmler, 1993).

Kujawinska, M.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

R. Sitnik, M. Kujawińska, and J. Woźnicki, “Digital fringe projection system for large volume 360 deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

M. Pirga and M. Kujawińska, “Two-directional spatial-carrier phase shifting method for analysis of crossed and closed fringe pattern,” Opt. Eng. 34, 2459-2466 (1995).
[CrossRef]

M. Kujawińska and J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325-339(1991).
[CrossRef]

M. Kujawińska and J. Wójciak, “Spatial phase-shifting technique of fringe pattern analysis in photomechanics,” Proc. SPIE 1554B, 503-513 (1991).

M. Pirga, A. Kozłowska, and M. Kujawińska, “Generalization of the scaling problem for the automatic moire and fringe projection shape measurement systems,”in Fringe '93, Second International Workshop on Automatic Processing of Fringe Patterns (Akademie Verlag, 1993), pp. 188-193.

Lange, R.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37 (3), 390-397 (2001).
[CrossRef]

Liu, H. C.

Mooshake, S.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

Nadeborn, W.

W. Osten, W. Nadeborn, and P. Andrae, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Nguyen, H. G.

H. G. Nguyen and M. R. Blackburn, “A simple method for range finding via laser triangulation,” Technical document (Naval Research and Development, 1995).

Osten, W.

W. Osten, W. Nadeborn, and P. Andrae, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Pawlowski, M.

M. Pawłowski, “Automated system for absolute shape measurement of 3D time-varying objects,” Ph.D. dissertation (Warsaw University of Technology, 2002).

Pirga, M.

M. Pirga and M. Kujawińska, “Two-directional spatial-carrier phase shifting method for analysis of crossed and closed fringe pattern,” Opt. Eng. 34, 2459-2466 (1995).
[CrossRef]

M. Pirga, A. Kozłowska, and M. Kujawińska, “Generalization of the scaling problem for the automatic moire and fringe projection shape measurement systems,”in Fringe '93, Second International Workshop on Automatic Processing of Fringe Patterns (Akademie Verlag, 1993), pp. 188-193.

Rapp, W.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

Reid, G. T.

G. T. Reid and D. W. Robinson, Interferogram Analysis (Institute of Physics, 1993).

Robinson, D. W.

G. T. Reid and D. W. Robinson, Interferogram Analysis (Institute of Physics, 1993).

Rowe, S.

I. A. Ypsilos, A. Hilton, and S. Rowe, “Video-rate capture of dynamic face shape and appearance,” in Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 2004), pp. 117-122.
[CrossRef]

Russ, J. C.

J. C. Russ, The Image Processing Handbook (Wiley, 2006).
[CrossRef]

Seitz, P.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37 (3), 390-397 (2001).
[CrossRef]

Seitz, S. M.

L. Zhang, B. Curless, and S. M. Seitz, “Rapid shape acquisition using color structured light and multi-pass dynamic programming,” in Proceedings of 1st International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT) (2002), pp. 24-36.
[CrossRef] [PubMed]

Sitnik, R.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

R. Sitnik, M. Kujawińska, and J. Woźnicki, “Digital fringe projection system for large volume 360 deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

R. Sitnik, “A fully automatic 3D shape measurement system with data export for engineering and multimedia systems,” Ph.D. dissertation (Warsaw University of Technology, 2002).

Srinivasan, V.

Takeda, M.

M. Takeda, “Spatial-carrier fringe pattern analysis and its applications to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79-99 (1990).
[CrossRef]

Van Gool, L.

T. P. Koninckx and L. Van Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28 (3), 432-445 (2006).
[CrossRef] [PubMed]

Weng, J.

J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993-4998 (2004).
[CrossRef] [PubMed]

J. Zhong and J. Weng, “Dilating Gabor transform for the fringe analysis of 3-D shape measurement,” Opt. Eng. 43, 895-899 (2004).
[CrossRef]

Witkowski, M.

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

Wójciak, J.

M. Kujawińska and J. Wójciak, “Spatial phase-shifting technique of fringe pattern analysis in photomechanics,” Proc. SPIE 1554B, 503-513 (1991).

M. Kujawińska and J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325-339(1991).
[CrossRef]

Woznicki, J.

R. Sitnik, M. Kujawińska, and J. Woźnicki, “Digital fringe projection system for large volume 360 deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

Yau, S.-T.

Ypsilos, I. A.

I. A. Ypsilos, A. Hilton, and S. Rowe, “Video-rate capture of dynamic face shape and appearance,” in Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 2004), pp. 117-122.
[CrossRef]

Zhang, L.

L. Zhang, B. Curless, and S. M. Seitz, “Rapid shape acquisition using color structured light and multi-pass dynamic programming,” in Proceedings of 1st International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT) (2002), pp. 24-36.
[CrossRef] [PubMed]

Zhang, S.

Zhong, J.

J. Zhong and J. Weng, “Spatial carrier-fringe pattern analysis by means of wavelet transform: wavelet transform profilometry,” Appl. Opt. 43, 4993-4998 (2004).
[CrossRef] [PubMed]

J. Zhong and J. Weng, “Dilating Gabor transform for the fringe analysis of 3-D shape measurement,” Opt. Eng. 43, 895-899 (2004).
[CrossRef]

Appl. Opt.

IEEE J. Quantum Electron.

R. Lange and P. Seitz, “Solid-state time-of-flight range camera,” IEEE J. Quantum Electron. 37 (3), 390-397 (2001).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

T. P. Koninckx and L. Van Gool, “Real-time range acquisition by adaptive structured light,” IEEE Trans. Pattern Anal. Mach. Intell. 28 (3), 432-445 (2006).
[CrossRef] [PubMed]

Ind. Metrol.

M. Takeda, “Spatial-carrier fringe pattern analysis and its applications to precision interferometry and profilometry: an overview,” Ind. Metrol. 1, 79-99 (1990).
[CrossRef]

Opt. Eng.

M. Pirga and M. Kujawińska, “Two-directional spatial-carrier phase shifting method for analysis of crossed and closed fringe pattern,” Opt. Eng. 34, 2459-2466 (1995).
[CrossRef]

S. Zhang and P. S. Huang, “High-resolution, real-time 3-D shape measurement,” Opt. Eng. 45, 123601 (2006).
[CrossRef]

R. Sitnik, M. Kujawińska, and J. Woźnicki, “Digital fringe projection system for large volume 360 deg shape measurement,” Opt. Eng. 41, 443-449 (2002).
[CrossRef]

J. Zhong and J. Weng, “Dilating Gabor transform for the fringe analysis of 3-D shape measurement,” Opt. Eng. 43, 895-899 (2004).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

M. Kujawińska and J. Wójciak, “High accuracy Fourier transform fringe pattern analysis,” Opt. Lasers Eng. 14, 325-339(1991).
[CrossRef]

Proc. SPIE

M. Witkowski, R. Sitnik, M. Kujawinska, W. Rapp, M. Kowalski, B. Haex, and S. Mooshake, “4D measurement system for automatic location of anatomical structures,” Proc. SPIE 6191H (2006).
[CrossRef]

M. Kujawińska and J. Wójciak, “Spatial phase-shifting technique of fringe pattern analysis in photomechanics,” Proc. SPIE 1554B, 503-513 (1991).

W. Osten, W. Nadeborn, and P. Andrae, “General hierarchical approach in absolute phase measurement,” Proc. SPIE 2860, 2-13 (1996).
[CrossRef]

Other

M. Pirga, A. Kozłowska, and M. Kujawińska, “Generalization of the scaling problem for the automatic moire and fringe projection shape measurement systems,”in Fringe '93, Second International Workshop on Automatic Processing of Fringe Patterns (Akademie Verlag, 1993), pp. 188-193.

R. Sitnik, “A fully automatic 3D shape measurement system with data export for engineering and multimedia systems,” Ph.D. dissertation (Warsaw University of Technology, 2002).

L. Zhang, B. Curless, and S. M. Seitz, “Rapid shape acquisition using color structured light and multi-pass dynamic programming,” in Proceedings of 1st International Symposium on 3D Data Processing, Visualization and Transmission (3DPVT) (2002), pp. 24-36.
[CrossRef] [PubMed]

I. A. Ypsilos, A. Hilton, and S. Rowe, “Video-rate capture of dynamic face shape and appearance,” in Proceedings of the Sixth IEEE International Conference on Automatic Face and Gesture Recognition (IEEE, 2004), pp. 117-122.
[CrossRef]

G. T. Reid and D. W. Robinson, Interferogram Analysis (Institute of Physics, 1993).

H. G. Nguyen and M. R. Blackburn, “A simple method for range finding via laser triangulation,” Technical document (Naval Research and Development, 1995).

K. Kraus, Photogrammetry (Dümmler, 1993).

M. Pawłowski, “Automated system for absolute shape measurement of 3D time-varying objects,” Ph.D. dissertation (Warsaw University of Technology, 2002).

J. C. Russ, The Image Processing Handbook (Wiley, 2006).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

Classification of optical full-field shape measurement techniques.

Fig. 2
Fig. 2

Measurement processing scheme.

Fig. 3
Fig. 3

Sine image cross section (height represents pixels color intensities).

Fig. 4
Fig. 4

Visualization of color stripe recognition: (a) image with stripes captured by a detector and (b) detected stripe position.

Fig. 5
Fig. 5

Image division for local period approximation by FFT (S—input data size for period approximation).

Fig. 6
Fig. 6

Visualization of local period approximation: (a) input image, (b)–(d) frequency spectra calculated for S 1 in different image areas.

Fig. 7
Fig. 7

Visualization of modulo- 2 π phase map: (a) image with fringes, (b) modulo- 2 π phase map.

Fig. 8
Fig. 8

(a) Wrapped phase map and (b) phase jumps.

Fig. 9
Fig. 9

(a) Image of object and (b) phase jumps with split points.

Fig. 10
Fig. 10

Visualization of grouping process: (a) phase jumps and split points and (b) unwrapped groups.

Fig. 11
Fig. 11

Visualization of uncertainty map.

Fig. 12
Fig. 12

Exemplary calculation of temporal unwrapping uncertainty for three frames with central color-encoded stripe on first frame: (a) spatial and (b) temporal uncertainty for first frame—forearm group has been chosen for next color-encoded stripe position; (c) spatial and (d) temporal uncertainty for second frame—three medium fingers have been chosen for next stripe position; (e) spatial and (f) temporal uncertainty for third frame—smallest finger has been chosen for next stripe position.

Fig. 13
Fig. 13

Experimental setup.

Fig. 14
Fig. 14

Experimental results: (a) single frame cloud of points; (b), (c) face at different time moments; (d), (e) hand at different time moments.

Fig. 15
Fig. 15

Error distribution on the surface of the measured ball.

Tables (1)

Tables Icon

Table 1 Measurement Results of Testing Ball

Equations (14)

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

Ph CS = N CS * 2 π .
I i ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) + δ i ) ,
I 1 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) 2 Π 3 ) ,
I 2 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) ) ,
I 3 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) + 2 Π 3 ) .
Φ ( x , y ) = arctan ( 3 ( I 1 I 3 ) 2 I 2 I 1 I 3 ) .
I 1 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) Π ) ,
I 2 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) Π 2 ) ,
I 3 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) ) ,
I 4 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) + Π 2 ) ,
I 5 ( x , y ) = a ( x , y ) b ( x , y ) cos ( Φ ( x , y ) + Π ) ,
Φ ( x , y ) = arctan ( 2 ( I 4 I 2 ) 2 I 3 I 1 I 5 ) .
U = t = 0 - M C w t * u t
w t 1 = w t × 0.7 ,

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