Abstract

Division of focal plane (DoFP) polarization image sensors capture polarization properties of light at every imaging frame. However, these imaging sensors capture only partial polarization information, resulting in reduced spatial resolution output and a varying instantaneous field of overview (IFoV). Interpolation methods are used to reduce the drawbacks and recover the missing polarization information. In this paper, we propose residual interpolation as an alternative to normal interpolation for division of focal plane polarization image sensors, where the residual is the difference between an observed and a tentatively estimated pixel value. Our results validate that our proposed algorithm using residual interpolation can give state-of-the-art performance over several previously published interpolation methods, namely bilinear, bicubic, spline and gradient-based interpolation. Visual image evaluation as well as mean square error analysis is applied to test images. For an outdoor polarized image of a car, residual interpolation has less mean square error and better visual evaluation results.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Gradient-based interpolation method for division-of-focal-plane polarimeters

Shengkui Gao and Viktor Gruev
Opt. Express 21(1) 1137-1151 (2013)

Image interpolation for division of focal plane polarimeters with intensity correlation

Junchao Zhang, Haibo Luo, Bin Hui, and Zheng Chang
Opt. Express 24(18) 20799-20807 (2016)

Bilinear and bicubic interpolation methods for division of focal plane polarimeters

Shengkui Gao and Viktor Gruev
Opt. Express 19(27) 26161-26173 (2011)

References

  • View by:
  • |
  • |
  • |

  1. N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
    [Crossref] [PubMed]
  2. D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
    [Crossref]
  3. H. Zhan and D. G. Voelz, “Modified polarimetric bidirectional reflectance distribution function with diffuse scattering: surface parameter estimation,” Opt. Eng. 55(12), 123103 (2016).
    [Crossref]
  4. V. Thilak, D. G. Voelz, and C. D. Creusere, “Polarization-based index of refraction and reflection angle estimation for remote sensing applications,” Appl. Opt. 46(30), 7527–7536 (2007).
    [Crossref] [PubMed]
  5. B. Shen, P. Wang, R. Polson, and R. Menon, “Ultra-high-efficiency metamaterial polarizer,” Optica 1(5), 356–360 (2014).
    [Crossref]
  6. P. Terrier, V. Devlaminck, and J. M. Charbois, “Segmentation of rough surfaces using a polarization imaging system,” J. Opt. Soc. Am. A 25(2), 423–430 (2008).
    [Crossref] [PubMed]
  7. O. Morel, R. Seulin, and D. Fofi, “Handy method to calibrate division-of-amplitude polarimeters for the first three Stokes parameters,” Opt. Express 24(12), 13634–13646 (2016).
    [Crossref] [PubMed]
  8. M. W. Hyde, J. D. Schmidt, M. J. Havrilla, and S. C. Cain, “Enhanced material classification using turbulence-degraded polarimetric imagery,” Opt. Lett. 35(21), 3601–3603 (2010).
    [Crossref] [PubMed]
  9. S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
    [Crossref] [PubMed]
  10. T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
    [Crossref] [PubMed]
  11. N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
    [Crossref]
  12. J. S. Tyo, D. L. Goldstein, D. B. Chenault, and J. A. Shaw, “Review of passive imaging polarimetry for remote sensing applications,” Appl. Opt. 45(22), 5453–5469 (2006).
    [Crossref] [PubMed]
  13. X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18(17), 17776–17787 (2010).
    [Crossref] [PubMed]
  14. V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19(24), 24361–24369 (2011).
    [Crossref] [PubMed]
  15. V. Gruev and R. E. Cummings, “Implementation of steerable spatiotemporal image filters on the focal plane,” IEEE Trans. Circuits Syst. 49(4), 233–244 (2002).
    [Crossref]
  16. X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin “guest-host” micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19(6), 5565–5573 (2011).
    [Crossref] [PubMed]
  17. V. Gruev, J. Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18(18), 19292–19303 (2010).
    [Crossref] [PubMed]
  18. M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20(21), 22997–23012 (2012).
    [Crossref] [PubMed]
  19. C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41(7), 1291–1296 (2002).
    [Crossref] [PubMed]
  20. V. Gruev and R. E. Cummings, “A pipelined temporal difference imager,” IEEE J. Solid-State Circuits 39(3), 538–543 (2004).
    [Crossref]
  21. Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
    [Crossref] [PubMed]
  22. S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
    [Crossref] [PubMed]
  23. J. Zhang, H. Luo, B. Hui, and Z. Chang, “Image interpolation for division of focal plane polarimeters with intensity correlation,” Opt. Express 24(18), 20799–20807 (2016).
    [Crossref] [PubMed]
  24. R. Perkins and V. Gruev, “Signal-to-noise analysis of Stokes parameters in division of focal plane polarimeters,” Opt. Express 18(25), 25815–25824 (2010).
    [Crossref] [PubMed]
  25. E. Gilboa, J. P. Cunningham, A. Nehorai, and V. Gruev, “Image interpolation and denoising for division of focal plane sensors using Gaussian processes,” Opt. Express 22(12), 15277–15291 (2014).
    [Crossref] [PubMed]
  26. S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
    [Crossref] [PubMed]
  27. B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
    [Crossref] [PubMed]
  28. P. Thévenaz, T. Blu, and M. Unser, “Image interpolation and Resampling” in Handbook of Medical Imaging (SPIE Press, 2000), pp. 393–420.
  29. D. H. Goldstein, Polarized Light, 3rd ed. (CPC Press, 2010).
  30. M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
    [Crossref]
  31. D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Residual interpolation for color image demosaicking,” in 2013 IEEE International Conference on Image Processing, Melbourne, (IEEE, 2013), pp. 2304–2308.
    [Crossref]
  32. Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
    [Crossref]
  33. W. Ye and K. K. Ma, “Color image demosaicing using iterative residual interpolation,” IEEE Trans. Image Process. 24(12), 5879–5891 (2015).
    [Crossref] [PubMed]
  34. D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
    [PubMed]
  35. K. He, J. Sun, and X. Tang, “Guided image filtering,” IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013).
    [Crossref] [PubMed]
  36. G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).

2016 (5)

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

H. Zhan and D. G. Voelz, “Modified polarimetric bidirectional reflectance distribution function with diffuse scattering: surface parameter estimation,” Opt. Eng. 55(12), 123103 (2016).
[Crossref]

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
[PubMed]

O. Morel, R. Seulin, and D. Fofi, “Handy method to calibrate division-of-amplitude polarimeters for the first three Stokes parameters,” Opt. Express 24(12), 13634–13646 (2016).
[Crossref] [PubMed]

J. Zhang, H. Luo, B. Hui, and Z. Chang, “Image interpolation for division of focal plane polarimeters with intensity correlation,” Opt. Express 24(18), 20799–20807 (2016).
[Crossref] [PubMed]

2015 (3)

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref] [PubMed]

W. Ye and K. K. Ma, “Color image demosaicing using iterative residual interpolation,” IEEE Trans. Image Process. 24(12), 5879–5891 (2015).
[Crossref] [PubMed]

2014 (4)

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

E. Gilboa, J. P. Cunningham, A. Nehorai, and V. Gruev, “Image interpolation and denoising for division of focal plane sensors using Gaussian processes,” Opt. Express 22(12), 15277–15291 (2014).
[Crossref] [PubMed]

B. Shen, P. Wang, R. Polson, and R. Menon, “Ultra-high-efficiency metamaterial polarizer,” Optica 1(5), 356–360 (2014).
[Crossref]

2013 (3)

S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

K. He, J. Sun, and X. Tang, “Guided image filtering,” IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013).
[Crossref] [PubMed]

2012 (1)

2011 (3)

2010 (4)

2009 (2)

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[Crossref]

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
[Crossref] [PubMed]

2008 (1)

2007 (1)

2006 (1)

2004 (1)

V. Gruev and R. E. Cummings, “A pipelined temporal difference imager,” IEEE J. Solid-State Circuits 39(3), 538–543 (2004).
[Crossref]

2002 (2)

V. Gruev and R. E. Cummings, “Implementation of steerable spatiotemporal image filters on the focal plane,” IEEE Trans. Circuits Syst. 49(4), 233–244 (2002).
[Crossref]

C. K. Harnett and H. G. Craighead, “Liquid-crystal micropolarizer array for polarization-difference imaging,” Appl. Opt. 41(7), 1291–1296 (2002).
[Crossref] [PubMed]

Achilefu, S.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Akers, W. J.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Alali, S.

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref] [PubMed]

Asada, N.

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

Baba, M.

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

Bermak, A.

Boussaid, F.

Cain, S. C.

Caldwell, R. L.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Chang, Z.

Charanya, T.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Charbois, J. M.

Chenault, D. B.

Chigrinov, V. G.

Craighead, H. G.

Creusere, C. D.

Cronin, T. W.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Cummings, R. E.

V. Gruev and R. E. Cummings, “A pipelined temporal difference imager,” IEEE J. Solid-State Circuits 39(3), 538–543 (2004).
[Crossref]

V. Gruev and R. E. Cummings, “Implementation of steerable spatiotemporal image filters on the focal plane,” IEEE Trans. Circuits Syst. 49(4), 233–244 (2002).
[Crossref]

Cunningham, J. P.

de Erausquin, I.

Devlaminck, V.

Edmiston, C.

Engheta, N.

Fofi, D.

Furukawa, R.

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

Gao, S.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
[Crossref] [PubMed]

Garcia, N. M.

Gerhart, G. R.

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[Crossref]

Gilboa, E.

Goldstein, D. L.

Gruev, V.

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

E. Gilboa, J. P. Cunningham, A. Nehorai, and V. Gruev, “Image interpolation and denoising for division of focal plane sensors using Gaussian processes,” Opt. Express 22(12), 15277–15291 (2014).
[Crossref] [PubMed]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20(21), 22997–23012 (2012).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
[Crossref] [PubMed]

V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19(24), 24361–24369 (2011).
[Crossref] [PubMed]

V. Gruev, J. Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18(18), 19292–19303 (2010).
[Crossref] [PubMed]

R. Perkins and V. Gruev, “Signal-to-noise analysis of Stokes parameters in division of focal plane polarimeters,” Opt. Express 18(25), 25815–25824 (2010).
[Crossref] [PubMed]

V. Gruev and R. E. Cummings, “A pipelined temporal difference imager,” IEEE J. Solid-State Circuits 39(3), 538–543 (2004).
[Crossref]

V. Gruev and R. E. Cummings, “Implementation of steerable spatiotemporal image filters on the focal plane,” IEEE Trans. Circuits Syst. 49(4), 233–244 (2002).
[Crossref]

Harnett, C. K.

Havrilla, M. J.

He, K.

K. He, J. Sun, and X. Tang, “Guided image filtering,” IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013).
[Crossref] [PubMed]

Hiura, S.

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

How, M. J.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Hui, B.

Hyde, M. W.

Kahan, L.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Kiku, D.

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
[PubMed]

Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
[Crossref]

Kikuchi, S.

Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
[Crossref]

Kudenov, M. W.

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[Crossref]

Kulkarni, M.

LaCasse, C. F.

Lake, S. P.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Liu, Y.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Luo, H.

Ma, K. K.

W. Ye and K. K. Ma, “Color image demosaicing using iterative residual interpolation,” IEEE Trans. Image Process. 24(12), 5879–5891 (2015).
[Crossref] [PubMed]

Marshall, J.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Marshall, N. J.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Matthews, T.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Menon, R.

Miyazaki, D.

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

Mondal, S.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Monno, Y.

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
[PubMed]

Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
[Crossref]

Morel, O.

Nehorai, A.

Njuguna, R.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Okutomi, M.

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
[PubMed]

Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
[Crossref]

Perkins, R.

Pezzaniti, L. J.

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[Crossref]

Polson, R.

Porter, M. L.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Powell, S. B.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Raman, B.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Ratliff, B. M.

Roberts, N. W.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Saha, D.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Schmidt, J. D.

Seulin, R.

Shaw, J. A.

Shen, B.

Shigetomi, T.

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

Sudlow, G. P.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Sun, J.

K. He, J. Sun, and X. Tang, “Guided image filtering,” IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013).
[Crossref] [PubMed]

Tanaka, M.

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
[PubMed]

Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
[Crossref]

Tang, R.

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

Tang, X.

K. He, J. Sun, and X. Tang, “Guided image filtering,” IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013).
[Crossref] [PubMed]

Temple, S. E.

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Terrier, P.

Thilak, V.

Tyo, J. S.

Van der Spiegel, J.

Vitkin, A.

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref] [PubMed]

Voelz, D. G.

H. Zhan and D. G. Voelz, “Modified polarimetric bidirectional reflectance distribution function with diffuse scattering: surface parameter estimation,” Opt. Eng. 55(12), 123103 (2016).
[Crossref]

V. Thilak, D. G. Voelz, and C. D. Creusere, “Polarization-based index of refraction and reflection angle estimation for remote sensing applications,” Appl. Opt. 46(30), 7527–7536 (2007).
[Crossref] [PubMed]

Wang, P.

Ye, W.

W. Ye and K. K. Ma, “Color image demosaicing using iterative residual interpolation,” IEEE Trans. Image Process. 24(12), 5879–5891 (2015).
[Crossref] [PubMed]

York, T.

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Zhan, H.

H. Zhan and D. G. Voelz, “Modified polarimetric bidirectional reflectance distribution function with diffuse scattering: surface parameter estimation,” Opt. Eng. 55(12), 123103 (2016).
[Crossref]

Zhang, J.

Zhao, X.

Appl. Opt. (3)

IEEE J. Solid-State Circuits (1)

V. Gruev and R. E. Cummings, “A pipelined temporal difference imager,” IEEE J. Solid-State Circuits 39(3), 538–543 (2004).
[Crossref]

IEEE Trans. Circuits Syst. (1)

V. Gruev and R. E. Cummings, “Implementation of steerable spatiotemporal image filters on the focal plane,” IEEE Trans. Circuits Syst. 49(4), 233–244 (2002).
[Crossref]

IEEE Trans. Image Process. (2)

W. Ye and K. K. Ma, “Color image demosaicing using iterative residual interpolation,” IEEE Trans. Image Process. 24(12), 5879–5891 (2015).
[Crossref] [PubMed]

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Beyond color difference: Residual interpolation for color image demosaicking,” IEEE Trans. Image Process. 25(3), 1288–1300 (2016).
[PubMed]

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

K. He, J. Sun, and X. Tang, “Guided image filtering,” IEEE Trans. Pattern Anal. Mach. Intell. 35(6), 1397–1409 (2013).
[Crossref] [PubMed]

J. Biomed. Opt. (2)

Y. Liu, R. Njuguna, T. Matthews, W. J. Akers, G. P. Sudlow, S. Mondal, R. Tang, V. Gruev, and S. Achilefu, “Near-infrared fluorescence goggle system with complementary metal-oxide-semiconductor imaging sensor and see-through display,” J. Biomed. Opt. 18(10), 101303 (2013).
[Crossref] [PubMed]

S. Alali and A. Vitkin, “Polarized light imaging in biomedicine: emerging Mueller matrix methodologies for bulk tissue assessment,” J. Biomed. Opt. 20(6), 061104 (2015).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (1)

Opt. Eng. (3)

D. Miyazaki, T. Shigetomi, M. Baba, R. Furukawa, S. Hiura, and N. Asada, “Surface normal estimation of black specular objects from multiview polarization images,” Opt. Eng. 56(4), 041303 (2016).
[Crossref]

H. Zhan and D. G. Voelz, “Modified polarimetric bidirectional reflectance distribution function with diffuse scattering: surface parameter estimation,” Opt. Eng. 55(12), 123103 (2016).
[Crossref]

M. W. Kudenov, L. J. Pezzaniti, and G. R. Gerhart, “Microbolometer-infrared imaging Stokes polarimeter,” Opt. Eng. 48(6), 063201 (2009).
[Crossref]

Opt. Express (13)

N. M. Garcia, I. de Erausquin, C. Edmiston, and V. Gruev, “Surface normal reconstruction using circularly polarized light,” Opt. Express 23(11), 14391–14406 (2015).
[Crossref] [PubMed]

O. Morel, R. Seulin, and D. Fofi, “Handy method to calibrate division-of-amplitude polarimeters for the first three Stokes parameters,” Opt. Express 24(12), 13634–13646 (2016).
[Crossref] [PubMed]

J. Zhang, H. Luo, B. Hui, and Z. Chang, “Image interpolation for division of focal plane polarimeters with intensity correlation,” Opt. Express 24(18), 20799–20807 (2016).
[Crossref] [PubMed]

R. Perkins and V. Gruev, “Signal-to-noise analysis of Stokes parameters in division of focal plane polarimeters,” Opt. Express 18(25), 25815–25824 (2010).
[Crossref] [PubMed]

X. Zhao, F. Boussaid, A. Bermak, and V. G. Chigrinov, “High-resolution thin “guest-host” micropolarizer arrays for visible imaging polarimetry,” Opt. Express 19(6), 5565–5573 (2011).
[Crossref] [PubMed]

V. Gruev, “Fabrication of a dual-layer aluminum nanowires polarization filter array,” Opt. Express 19(24), 24361–24369 (2011).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express 19(27), 26161–26173 (2011).
[Crossref] [PubMed]

M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express 20(21), 22997–23012 (2012).
[Crossref] [PubMed]

S. Gao and V. Gruev, “Gradient-based interpolation method for division-of-focal-plane polarimeters,” Opt. Express 21(1), 1137–1151 (2013).
[Crossref] [PubMed]

E. Gilboa, J. P. Cunningham, A. Nehorai, and V. Gruev, “Image interpolation and denoising for division of focal plane sensors using Gaussian processes,” Opt. Express 22(12), 15277–15291 (2014).
[Crossref] [PubMed]

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express 17(11), 9112–9125 (2009).
[Crossref] [PubMed]

X. Zhao, A. Bermak, F. Boussaid, and V. G. Chigrinov, “Liquid-crystal micropolarimeter array for full Stokes polarization imaging in visible spectrum,” Opt. Express 18(17), 17776–17787 (2010).
[Crossref] [PubMed]

V. Gruev, J. Van der Spiegel, and N. Engheta, “Dual-tier thin film polymer polarization imaging sensor,” Opt. Express 18(18), 19292–19303 (2010).
[Crossref] [PubMed]

Opt. Lett. (1)

Optica (1)

Proc IEEE Inst Electr Electron Eng (1)

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, D. Saha, N. W. Roberts, T. W. Cronin, J. Marshall, S. Achilefu, S. P. Lake, B. Raman, and V. Gruev, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications: analysis at the focal plane emulates nature’s method in sensors to image and diagnose with polarized light,” Proc IEEE Inst Electr Electron Eng 102(10), 1450–1469 (2014).
[Crossref] [PubMed]

Proc. IEEE (1)

N. W. Roberts, M. J. How, M. L. Porter, S. E. Temple, R. L. Caldwell, S. B. Powell, V. Gruev, N. J. Marshall, and T. W. Cronin, “Animal polarization imaging and implications for optical processing,” Proc. IEEE 102(10), 1427–1434 (2014).
[Crossref]

Other (5)

P. Thévenaz, T. Blu, and M. Unser, “Image interpolation and Resampling” in Handbook of Medical Imaging (SPIE Press, 2000), pp. 393–420.

D. H. Goldstein, Polarized Light, 3rd ed. (CPC Press, 2010).

D. Kiku, Y. Monno, M. Tanaka, and M. Okutomi, “Residual interpolation for color image demosaicking,” in 2013 IEEE International Conference on Image Processing, Melbourne, (IEEE, 2013), pp. 2304–2308.
[Crossref]

Y. Monno, D. Kiku, S. Kikuchi, M. Tanaka, and M. Okutomi, “Multispectral demosaicking with novel guide image generation and residual interpolation,” in IEEE International Conference on Image Processing (IEEE, 2014), pp. 645–649.
[Crossref]

G. D. Boreman, Modulation Transfer Function in Optical and Electro-Optical Systems (SPIE, 2001).

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (8)

Fig. 1
Fig. 1 Division of focal plane polarization imaging sensor array with a 4-polarizer filter array (0°, 45°, 90°  135° ) of charge coupled device (CCD) imaging elements.
Fig. 2
Fig. 2 Bilinear interpolation.
Fig. 3
Fig. 3 A 4 X 4 block in a DoFP image sensor.
Fig. 4
Fig. 4 A 4X4 residual interpolated difference and net residual interpolated block.
Fig. 5
Fig. 5 Flow chart for residual interpolation.
Fig. 6
Fig. 6 The MTF of intensity ( S 0 )  for interpolation algorithms: (a) bilinear, (b) bicubic, (c) spline, (d) gradient, (e) residual. (f) The MTF of S 0 along f x = f y
Fig. 7
Fig. 7 The true high-resolution image of a car: (a) car-intensity, (b) car-DoLP and (c) car-AoP.
Fig. 8
Fig. 8 The true high-resolution image and comparison of interpolation methods on the (a) intensity, (b) DoLP, and (c)AoP, showing the effect of interpolation on the artifacts in the patches.

Tables (1)

Tables Icon

Table 1 MSE performance comparison for car image

Equations (21)

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

Intensity ( S 0 )=1/2 ( I 0 + I 90 + I 45 + I 135 ).
S 1 =( I 0 I 90 ).
S 2 =( I 45 I 135 ).
DoLP= ( s 1 2 + s 2 2 ) / s 0 2 .
AoP=1/ 2 tan 1 ( S 2 / S 1 ) .
f( x,y )=f( i,j ).( i+1x ).( j+1y )+f( i,j+1 ).( i+1x ).( yj ) +f( i+1,j+1 ).( xi ).( yj )+f( i+1,j ).( xi ).( j+1y ).
I 45 =1/2( I 45 (1,2)+ I 45 (3,2)).
I 135 =1/2( I 135 (2,1)+ I 45 (2,3)).
I 0 =1/4( I 0 (1,1)+ I 0 (1,3) + 0 (3,1) + 0 (3,3)).
q i0 = a k + b k , w k .
E0( a k , b k )= i w k ( ( a k I 0 + b k I int0 ) 2 +ε a k 2 ).
a k = 1 w i w k I 0 In t 0 μ k Iint0 k σ k 2 +ε .
b k =Iint 0 k a k μ k .
{ qi0 ¯ = 1 | w | i w k ( a k I 0 + b k ) qi45 ¯ = 1 | w | i w k ( a k I 45 + b k ) qi90 ¯ = 1 | w | i w k ( a k I 90 + b k ) qi135 ¯ = 1 | w | i w k ( a k I 135 + b k ) .
{ Δ I 0 (i,j)= i=1:n,j=1:m ( I 0 (i,j) qi0 ¯ (i,j)) Δ I 45 (i,j)= i=1:n,j=1:m ( I 45 (i,j) qi45 ¯ (i,j)) Δ I 90 (i,j)= i=1:n,j=1:m ( I 0 (i,j) qi90 ¯ (i,j)) Δ I 135 (i,j)= i=1:n,j=1:m ( I 0 (i,j) qi135 ¯ (i,j)) .
Δ I int45 =1/2(Δ I 45 (1,2)+Δ I 45 (3,2)).
Δ I int135 =1/2(Δ I 135 (2,1)+Δ I 45 (2,3)).
Δ I int0 =1/2(Δ I 0 (1,1)+Δ I 0 (1,3)+Δ I 0 (3,1)+Δ I 0 (3,3)).
{ RI_ I 0 (i,j)= i=1:n,j=1:m (Δ I int0 (i,j)+ qi0 ¯ (i,j)) RI_ I 45 (i,j)= i=1:n,j=1:m (Δ I int45 (i,j)+ qi45 ¯ (i,j)) RI_ I 90 (i,j)= i=1:n,j=1:m (Δ I int90 (i,j)+ qi90 ¯ (i,j)) RI_ I 135 (i,j)= i=1:n,j=1:m (Δ I int135 (i,j)+ qi135 ¯ (i,j)) .
{ I 0 (x,y)=cos(2π f x x+2π f y y)+1 I 45 (x,y)=2cos(2π f x x+2π f y y)+2 I 90 (x,y)=cos(2π f x x+2π f y y)+1 I 135 (x,y)=0 .
MSE= 1 MN 1iM 1iN ( O img (i,j) i img (i,j)) 2 .

Metrics