Abstract

In the paper, we propose a new edge detection schemes, based on a single-pixel imaging in the frequency domain. In SCHEME-I, special sinusoidal patterns for the x-direction edge and also y-direction edge of the unknown object are first designed. The frequency spectrum for the edge is then obtained using the a four-step phase-shifting technique with the designed sinusoidal patterns in a single-pixel imaging system. In SCHEME-II, the frequency spectrum of the unknown object is first obtained, then the frequency spectrum for the edge is obtained by calculations. The resulting edges are finally obtained by the inverse Fourier transform on their frequency spectrum. We have also verified the proposed schemes by experiments and numerical simulations. The results show that the proposed schemes can produce higher quality edges of character and also image objects. Comparing with SCHEME-II, the application of SCHEME-I to high frequency components has greatly improved signal-to-noise ratio of the received data in the bucket detector, resulting in better experimental results. Comparing with the edge detection scheme by speckle-shifting in ghost imaging systems, the proposed SCHEME-I shows an improvement in the signal-to-noise ratio. Since a single-pixel imaging system is used, the proposed schemes are capable of reconstructing edges from indirect measurements. The number of measurements required can be effectively reduced due to the sparsity of natural images in the Fourier domain and the conjugate symmetry of real-valued signals’ Fourier spectrum.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
    [Crossref] [PubMed]
  2. S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
    [Crossref]
  3. S. M. Zhao, B. Wang, L. Y. Gong, Y. B. Sheng, W. W. Cheng, X. L. Dong, and B. Y. Zheng, “Improving the atmosphere turbulence tolerance in holographic ghost imaging system by channel coding,” J. Lightwave Technol. 31, 2823–2828 (2013).
    [Crossref]
  4. R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 82, 113601 (2002).
    [Crossref]
  5. A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
    [Crossref] [PubMed]
  6. J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
    [Crossref]
  7. C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
    [Crossref]
  8. S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
    [Crossref]
  9. B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
    [Crossref] [PubMed]
  10. Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
    [Crossref] [PubMed]
  11. O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
    [Crossref]
  12. S. M. Zhao and P. Zhuang, “Correspondence normalized ghost imaging on compressive sensing,” Chin. Phys. B 23, 054203 (2014).
    [Crossref]
  13. W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
    [Crossref] [PubMed]
  14. S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
    [Crossref]
  15. W. K. Yu, X. R. Yao, X. F. Liu, L. Z. Li, and G. J. Zhai, “Three-dimensional single-pixel compressive reflectivity imaging based on complementary modulation,” Appl. Opt. 54, 363–367 (2015).
    [Crossref]
  16. Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
    [Crossref] [PubMed]
  17. L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
    [Crossref]
  18. L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh-Hadamard transform,” Photon. Res. 4(6), 240–244 (2016).
    [Crossref]
  19. J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 6, 679–698 (1986).
    [Crossref]
  20. M. Kmieć and A. Glowacz, “Object detection in security applications using dominant edge directions,” Pattern Recognit. Lett. 52, 72–79 (2015).
    [Crossref]
  21. X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
    [Crossref]
  22. L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett. 23, 1771–1784 (2002).
    [Crossref]
  23. S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
    [Crossref] [PubMed]
  24. X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
    [Crossref]
  25. T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).
  26. L. Wang, L. Zou, and S. Zhao, “Edge-detection based on subpixel-speckle-shifting ghost imaging,” Opt. Commun. 407, 181–185 (2018).
    [Crossref]
  27. S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
    [Crossref]
  28. K. Xu and G. Li, “Light-emitting device with monolithic integration on bulk silicon in standard complementary metal oxide semiconductor technology,” J. Nanophoton. 7, 073082 (2013).
    [Crossref]
  29. K. Xu, “Monolithically integrated Si gate-controlled light-emitting device: science and properties,” J. Opt. 20, 024014 (2018)
  30. K. Xu, “Integrated silicon directly modulated light source using p-well in standard CMOS technology,” IEEE Sens. J. 16, 6184–6191 (2016).

2018 (3)

L. Wang, L. Zou, and S. Zhao, “Edge-detection based on subpixel-speckle-shifting ghost imaging,” Opt. Commun. 407, 181–185 (2018).
[Crossref]

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

K. Xu, “Monolithically integrated Si gate-controlled light-emitting device: science and properties,” J. Opt. 20, 024014 (2018)

2017 (1)

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

2016 (4)

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh-Hadamard transform,” Photon. Res. 4(6), 240–244 (2016).
[Crossref]

K. Xu, “Integrated silicon directly modulated light source using p-well in standard CMOS technology,” IEEE Sens. J. 16, 6184–6191 (2016).

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

2015 (8)

M. Kmieć and A. Glowacz, “Object detection in security applications using dominant edge directions,” Pattern Recognit. Lett. 52, 72–79 (2015).
[Crossref]

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref] [PubMed]

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

W. K. Yu, X. R. Yao, X. F. Liu, L. Z. Li, and G. J. Zhai, “Three-dimensional single-pixel compressive reflectivity imaging based on complementary modulation,” Appl. Opt. 54, 363–367 (2015).
[Crossref]

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
[Crossref] [PubMed]

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

2014 (1)

S. M. Zhao and P. Zhuang, “Correspondence normalized ghost imaging on compressive sensing,” Chin. Phys. B 23, 054203 (2014).
[Crossref]

2013 (4)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

S. M. Zhao, B. Wang, L. Y. Gong, Y. B. Sheng, W. W. Cheng, X. L. Dong, and B. Y. Zheng, “Improving the atmosphere turbulence tolerance in holographic ghost imaging system by channel coding,” J. Lightwave Technol. 31, 2823–2828 (2013).
[Crossref]

K. Xu and G. Li, “Light-emitting device with monolithic integration on bulk silicon in standard complementary metal oxide semiconductor technology,” J. Nanophoton. 7, 073082 (2013).
[Crossref]

2010 (1)

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

2009 (2)

S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
[Crossref] [PubMed]

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[Crossref]

2008 (1)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
[Crossref]

2005 (1)

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

2002 (2)

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 82, 113601 (2002).
[Crossref]

L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett. 23, 1771–1784 (2002).
[Crossref]

1995 (1)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 6, 679–698 (1986).
[Crossref]

Bao, P.

L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett. 23, 1771–1784 (2002).
[Crossref]

Bennink, R. S.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 82, 113601 (2002).
[Crossref]

Bentley, S. J.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 82, 113601 (2002).
[Crossref]

Bian, L.

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

Bing, P.

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

Bowman, A.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Bowman, R.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Boyd, R. W.

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 82, 113601 (2002).
[Crossref]

Bromberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[Crossref]

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 6, 679–698 (1986).
[Crossref]

Cao, F.

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

Chen, A. X.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Chen, F.

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

Chen, Q.

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

Cheng, J.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Cheng, W. W.

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

S. M. Zhao, B. Wang, L. Y. Gong, Y. B. Sheng, W. W. Cheng, X. L. Dong, and B. Y. Zheng, “Improving the atmosphere turbulence tolerance in holographic ghost imaging system by channel coding,” J. Lightwave Technol. 31, 2823–2828 (2013).
[Crossref]

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

Cropp, R.

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

D’Angelo, M.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Dai, H.

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

Dai, Q.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

Dale, P.

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

Dong, X. L.

Easley, G. R.

S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
[Crossref] [PubMed]

Edgar, M. P.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Glowacz, A.

M. Kmieć and A. Glowacz, “Object detection in security applications using dominant edge directions,” Pattern Recognit. Lett. 52, 72–79 (2015).
[Crossref]

Gong, L. Y.

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

S. M. Zhao, B. Wang, L. Y. Gong, Y. B. Sheng, W. W. Cheng, X. L. Dong, and B. Y. Zheng, “Improving the atmosphere turbulence tolerance in holographic ghost imaging system by channel coding,” J. Lightwave Technol. 31, 2823–2828 (2013).
[Crossref]

Gong, W. L.

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref] [PubMed]

Gu, G.

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

Han, S. S.

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref] [PubMed]

He, W.

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

Hu, X.

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

Katz, O.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[Crossref]

Klyshko, D. N.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Kmiec, M.

M. Kmieć and A. Glowacz, “Object detection in security applications using dominant edge directions,” Pattern Recognit. Lett. 52, 72–79 (2015).
[Crossref]

Krim, H.

S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
[Crossref] [PubMed]

Labate, D.

S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
[Crossref] [PubMed]

Lan, R. M.

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

Li, G.

K. Xu and G. Li, “Light-emitting device with monolithic integration on bulk silicon in standard complementary metal oxide semiconductor technology,” J. Nanophoton. 7, 073082 (2013).
[Crossref]

Li, L. Z.

Li, X. F.

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

Li, Y. Q.

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

Liang, W. Q.

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

Liu, X.

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

Liu, X. F.

W. K. Yu, X. R. Yao, X. F. Liu, L. Z. Li, and G. J. Zhai, “Three-dimensional single-pixel compressive reflectivity imaging based on complementary modulation,” Appl. Opt. 54, 363–367 (2015).
[Crossref]

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

Liu, Y.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Liu, Z. M.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Luo, C. L.

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

Ma, X.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
[Crossref] [PubMed]

Mao, T.

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

Padgett, M. J.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Pan, X.

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

Qiao, C.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Scarcelli, G.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Sergienko, A. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Shapiro, J. H.

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
[Crossref]

Sheng, Y. B.

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

S. M. Zhao, B. Wang, L. Y. Gong, Y. B. Sheng, W. W. Cheng, X. L. Dong, and B. Y. Zheng, “Improving the atmosphere turbulence tolerance in holographic ghost imaging system by channel coding,” J. Lightwave Technol. 31, 2823–2828 (2013).
[Crossref]

Shih, Y.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Shih, Y. H.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Silberberg, Y.

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[Crossref]

Situ, G.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Strekalov, D. V.

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

Sun, B.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Suo, J.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

Valencia, A.

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Vittert, L. E.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Wang, B.

Wang, C.

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

Wang, L.

L. Wang, L. Zou, and S. Zhao, “Edge-detection based on subpixel-speckle-shifting ghost imaging,” Opt. Commun. 407, 181–185 (2018).
[Crossref]

L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh-Hadamard transform,” Photon. Res. 4(6), 240–244 (2016).
[Crossref]

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

Wang, Y.

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

Welsh, S.

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

Welsh, S. S.

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

Xiang, D.

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

Xu, K.

K. Xu, “Monolithically integrated Si gate-controlled light-emitting device: science and properties,” J. Opt. 20, 024014 (2018)

K. Xu, “Integrated silicon directly modulated light source using p-well in standard CMOS technology,” IEEE Sens. J. 16, 6184–6191 (2016).

K. Xu and G. Li, “Light-emitting device with monolithic integration on bulk silicon in standard complementary metal oxide semiconductor technology,” J. Nanophoton. 7, 073082 (2013).
[Crossref]

Yang, H.

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

Yao, X. R.

W. K. Yu, X. R. Yao, X. F. Liu, L. Z. Li, and G. J. Zhai, “Three-dimensional single-pixel compressive reflectivity imaging based on complementary modulation,” Appl. Opt. 54, 363–367 (2015).
[Crossref]

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

Yi, S.

S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
[Crossref] [PubMed]

Yu, W. K.

Yuan, S.

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

Zhai, G.

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

Zhai, G. J.

Zhang, L.

L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett. 23, 1771–1784 (2002).
[Crossref]

Zhang, S. Q.

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

Zhang, Z.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
[Crossref] [PubMed]

Zhao, S.

L. Wang, L. Zou, and S. Zhao, “Edge-detection based on subpixel-speckle-shifting ghost imaging,” Opt. Commun. 407, 181–185 (2018).
[Crossref]

Zhao, S. M.

L. Wang and S. M. Zhao, “Fast reconstructed and high-quality ghost imaging with fast Walsh-Hadamard transform,” Photon. Res. 4(6), 240–244 (2016).
[Crossref]

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

S. M. Zhao and P. Zhuang, “Correspondence normalized ghost imaging on compressive sensing,” Chin. Phys. B 23, 054203 (2014).
[Crossref]

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

S. M. Zhao, B. Wang, L. Y. Gong, Y. B. Sheng, W. W. Cheng, X. L. Dong, and B. Y. Zheng, “Improving the atmosphere turbulence tolerance in holographic ghost imaging system by channel coding,” J. Lightwave Technol. 31, 2823–2828 (2013).
[Crossref]

Zheng, B. Y.

Zhong, J.

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
[Crossref] [PubMed]

Zhou, X.

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

Zhuang, P.

S. M. Zhao and P. Zhuang, “Correspondence normalized ghost imaging on compressive sensing,” Chin. Phys. B 23, 054203 (2014).
[Crossref]

Zou, L.

L. Wang, L. Zou, and S. Zhao, “Edge-detection based on subpixel-speckle-shifting ghost imaging,” Opt. Commun. 407, 181–185 (2018).
[Crossref]

Zou, Y.

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

Appl. Opt. (1)

Appl. Phys. Lett. (1)

O. Katz, Y. Bromberg, and Y. Silberberg, “Compressive ghost imaging,” Appl. Phys. Lett. 95, 131110 (2009).
[Crossref]

Chin. Phys. B (1)

S. M. Zhao and P. Zhuang, “Correspondence normalized ghost imaging on compressive sensing,” Chin. Phys. B 23, 054203 (2014).
[Crossref]

IEEE Photonics J. (1)

T. Mao, Q. Chen, W. He, Y. Zou, H. Dai, and G. Gu, “Speckle-shifting ghost imaging,” IEEE Photonics J. 8(4), 1–10 (2016).

IEEE Sens. J. (1)

K. Xu, “Integrated silicon directly modulated light source using p-well in standard CMOS technology,” IEEE Sens. J. 16, 6184–6191 (2016).

IEEE Trans. Image Process. (1)

S. Yi, D. Labate, G. R. Easley, and H. Krim, “A Shearlet approach to edge analysis and detection,” IEEE Trans. Image Process. 18(5), 929–941 (2009).
[Crossref] [PubMed]

IEEE Trans. Pattern Anal. Machine Intell. (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Machine Intell. 6, 679–698 (1986).
[Crossref]

Int. J. Remote Sensing (1)

X. F. Li, S. Q. Zhang, X. Pan, P. Dale, and R. Cropp, “Straight road edge detection from high-resolution remote sensing images based on the ridgelet transform with the revised parallel-beam Radon transform,” Int. J. Remote Sensing 31, 5041–5059 (2010).
[Crossref]

J. Lightwave Technol. (1)

J. Nanophoton. (1)

K. Xu and G. Li, “Light-emitting device with monolithic integration on bulk silicon in standard complementary metal oxide semiconductor technology,” J. Nanophoton. 7, 073082 (2013).
[Crossref]

J. Opt. (3)

K. Xu, “Monolithically integrated Si gate-controlled light-emitting device: science and properties,” J. Opt. 20, 024014 (2018)

S. S. Welsh, M. P. Edgar, R. Bowman, B. Sun, and M. J. Padgett, “Near video-rate linear Stokes imaging with single-pixel detectors,” J. Opt. 17, 025705 (2015).
[Crossref]

L. Bian, J. Suo, X. Hu, F. Chen, and Q. Dai, “Efficient single pixel imaging in Fourier space,” J. Opt. 18, 085704 (2016).
[Crossref]

Nat. Commun. (1)

Z. Zhang, X. Ma, and J. Zhong, “Single-pixel imaging by means of Fourier spectrum acquisition,” Nat. Commun. 6, 6225–6230 (2015).
[Crossref] [PubMed]

Opt. Commun. (5)

S. M. Zhao, L. Wang, W. Q. Liang, W. W. Cheng, and L. Y. Gong, “High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique,” Opt. Commun. 353, 90–95 (2015).
[Crossref]

C. L. Luo, J. Cheng, A. X. Chen, and Z. M. Liu, “Computational ghost imaging with higher-order cosh-Gaussian modulated incoherent sources in atmospheric turbulence,” Opt. Commun. 352, 155–160 (2015).
[Crossref]

S. M. Zhao, H. Yang, Y. Q. Li, F. Cao, Y. B. Sheng, W. W. Cheng, and L. Y. Gong, “The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: simulation and experimental studies,” Opt. Commun. 294, 223–228 (2013).
[Crossref]

L. Wang, L. Zou, and S. Zhao, “Edge-detection based on subpixel-speckle-shifting ghost imaging,” Opt. Commun. 407, 181–185 (2018).
[Crossref]

S. Yuan, D. Xiang, X. Liu, X. Zhou, and P. Bing, “Edge detection based on computational ghost imaging with structured illuminations,” Opt. Commun. 410, 350–355 (2018).
[Crossref]

Opt. Exp. (1)

X. F. Liu, X. R. Yao, R. M. Lan, C. Wang, and G. Zhai, “Edge detection based on gradient ghost imaging,” Opt. Exp. 23(26), 33802–33811 (2015).
[Crossref]

Pattern Recognit. Lett. (2)

L. Zhang and P. Bao, “Edge detection by scale multiplication in wavelet domain,” Pattern Recognit. Lett. 23, 1771–1784 (2002).
[Crossref]

M. Kmieć and A. Glowacz, “Object detection in security applications using dominant edge directions,” Pattern Recognit. Lett. 52, 72–79 (2015).
[Crossref]

Photon. Res. (1)

Phys. Rev. A (1)

J. H. Shapiro, “Computational ghost imaging,” Phys. Rev. A 78, 061802(R) (2008).
[Crossref]

Phys. Rev. Lett. (3)

D. V. Strekalov, A. V. Sergienko, D. N. Klyshko, and Y. H. Shih, “Observation of two-photon “ghost” interference and diffraction,” Phys. Rev. Lett. 74, 3600–3603 (1995).
[Crossref] [PubMed]

R. S. Bennink, S. J. Bentley, and R. W. Boyd, “‘Two-photon’ coincidence imaging with a classical source,” Phys. Rev. Lett. 82, 113601 (2002).
[Crossref]

A. Valencia, G. Scarcelli, M. D’Angelo, and Y. Shih, “Two-photon imaging with thermal light,” Phys. Rev. Lett. 94, 063601 (2005).
[Crossref] [PubMed]

Sci. Rep. (2)

Y. Wang, Y. Liu, J. Suo, G. Situ, C. Qiao, and Q. Dai, “High speed computational ghost imaging via spatial sweeping,” Sci. Rep. 7, 45325 (2017).
[Crossref] [PubMed]

W. L. Gong and S. S. Han, “High-resolution far-field ghost imaging via sparsity constraint,” Sci. Rep. 5, 9280 (2015).
[Crossref] [PubMed]

Science (1)

B. Sun, M. P. Edgar, R. Bowman, L. E. Vittert, S. Welsh, A. Bowman, and M. J. Padgett, “3D computational imaging with single-pixel detectors,” Science 340, 844–847 (2013).
[Crossref] [PubMed]

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Figures (4)

Fig. 1
Fig. 1 The experimental setup for the proposed edge detection schemes based on single-pixel imaging in frequency domain. DLP: digital light projector.
Fig. 2
Fig. 2 The experimental and simulation results of the proposed edge detection schemes, where the original edges are obtained by Sobel operators on the original images.
Fig. 3
Fig. 3 The comparison of the performance for different edge detection schemes. The results with the proposed scheme SCHEME-I, the SSGI scheme and original edge image, where the original edges are obtained by Sobel operators on the original images, and original edge images are achieved by Sobel operators on the reconstruction of the object using the single-pixel imaging.
Fig. 4
Fig. 4 The reduction of the central line by using a filter.

Equations (17)

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

Sobel = ( f ( x , y ) x ) 2 + ( f ( x , y ) y ) 2
f ( x , y ) = R C ( f x , f y ) e j 2 π ( f x . x + f y . y ) d f x d f y ,
f x = x ( R C ( f x , f y ) e j 2 π ( f x . x + f y . y ) d f x d f y ) = R C ( f x , f y ) j 2 π f x e j 2 π ( f x * x + f y * y ) d f x d f y ,
f x = R { C ( f x , f y ) j 2 π f x } e j 2 π ( f x * x + f y * y ) d f x d f y = F 1 [ j 2 π f x C ( f x , f y ) ] ,
f y = F 1 [ j 2 π f y C ( f x , f y ) ] .
P ϕ ( x , y ; f x , f y ) = a + b * 2 π f x * cos ( 2 π f x * x + 2 π f y * y + ϕ ) ,
I ϕ ( f x , f y ) = Ω f ( x , y ) P ϕ ( x , y ; f x , f y ) d x d y ,
I ϕ ( f x , f y ) = I en + k * I ϕ ( f x , f y ) ,
I ϕ ( f x , f y ) = I en + k a Ω f ( x , y ) d x d y + k b * 2 π f x Ω f ( x , y ) c o s ( 2 π f x * x + 2 π f y * y + ϕ ) d x d y .
( I 3 π / 2 I π / 2 ) + j ( I 0 I π ) = 2 k b Ω f ( x , y ) j 2 π f x e j 2 π ( f x * x + f y * y ) d x d y = 2 k b * j 2 π f x C ( f x , f y ) .
f x = F 1 { 1 2 k b [ ( I 3 π / 2 I π / 2 ) + j ( I 0 I π ) ] } F 1 { ( I 3 π / 2 I π / 2 ) + j ( I 0 I π ) } .
Q ϕ ( x , y ; f x , f y ) = a + b * 2 π f y * c o s ( 2 π f x * x + 2 π f y * y + ϕ ) .
E = ( F 1 { ( I 3 π / 2 I π / 2 ) + j ( I 0 I π ) } ) 2 + ( F 1 { ( I 3 π / 2 I π / 2 ) + j ( I 0 I π ) } ) 2 , Edge E .
S ϕ ( x , y ; f x , f y ) = a + b * c o s ( 2 π f x * x + 2 π f y * y + ϕ ) ,
C ( f x , f y ) = Ω f ( x , y ) e j 2 π ( f x * x + f y * y ) d x d y = 1 2 k b { ( I 0 I π ) + j ( I π / 2 I 3 π / 2 ) } .
f x = F 1 [ j 2 π f x × C ( f x , f y ) ] , f y = F 1 [ j 2 π f y × C ( f x , f y ) ] .
SNR = mean ( I edge ) mean ( I background ) Var ( I background ) ,

Metrics