Abstract

Recent advancements in nanotechnology and nanofabrication have allowed for the emergence of the division-of-focal-plane (DoFP) polarization imaging sensors. These sensors capture polarization properties of the optical field at every imaging frame. However, the DoFP polarization imaging sensors suffer from large registration error as well as reduced spatial-resolution output. These drawbacks can be improved by applying proper image interpolation methods for the reconstruction of the polarization results. In this paper, we present a new gradient-based interpolation method for DoFP polarimeters. The performance of the proposed interpolation method is evaluated against several previously published interpolation methods by using visual examples and root mean square error (RMSE) comparison. We found that the proposed gradient-based interpolation method can achieve better visual results while maintaining a lower RMSE than other interpolation methods under various dynamic ranges of a scene ranging from dim to bright conditions.

© 2013 OSA

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2012 (5)

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

X. Xu, M. Kulkarni, A. Nehorai, and V. Gruev, “A correlation-based interpolation algorithm for division-of-focal-plane polarization sensors,” Proc. SPIE8364, 83640L, 83640L-8 (2012).
[CrossRef]

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized, ultrathin, broadband circular polarizers,” Nat. Commun. 3(870), (2012).

T. York and V. Gruev, “Characterization of a visible spectrum division-of-focal-plane polarimeter,” Appl. Opt.51(22), 5392–5400 (2012).
[CrossRef] [PubMed]

M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express20(21), 22997–23012 (2012).
[CrossRef] [PubMed]

2011 (7)

J. J. Peltzer, P. D. Flammer, T. E. Furtak, R. T. Collins, and R. E. Hollingsworth, “Ultra-high extinction ratio micropolarizers using plasmonic lenses,” Opt. Express19(19), 18072–18079 (2011).
[CrossRef] [PubMed]

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express19(27), 26161–26173 (2011).
[CrossRef] [PubMed]

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B84(20), 205428 (2011).
[CrossRef]

T. V. T. Krishna, C. D. Creusere, and D. G. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process.20(1), 288–292 (2011).
[CrossRef] [PubMed]

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J.11(8), 1692–1703 (2011).
[CrossRef]

A. Giachetti and N. Asuni, “Real-time artifact-free Image upscaling,” IEEE Trans. Image Process.20(10), 2760–2768 (2011).
[CrossRef] [PubMed]

S. Gao and V. Gruev, “Image interpolation methods evaluation for division of focal plane polarimeters,” Proc. SPIE8012, 80120N, 80120N-10 (2011).
[CrossRef]

2010 (2)

2009 (2)

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc.107(6), 884–890 (2009).
[CrossRef]

B. M. Ratliff, C. F. LaCasse, and J. S. Tyo, “Interpolation strategies for reducing IFOV artifacts in microgrid polarimeter imagery,” Opt. Express17(11), 9112–9125 (2009).
[CrossRef] [PubMed]

2008 (1)

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

2006 (2)

2005 (1)

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng.30(3), 570–587 (2005).
[CrossRef]

1986 (1)

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell.8(6), 679–698 (1986).
[CrossRef] [PubMed]

1981 (1)

R. Keys, “Cubic convolution interpolation for digital image processing,” Acoustics, Speech and Signal Processing, IEEE Transactions on29(6), 1153–1160 (1981).
[CrossRef]

1971 (1)

A. C. Neville and B. M. Luke, “Form optical activity in crustacean cuticle,” J. Insect Physiol.17(3), 519–526 (1971).
[CrossRef]

Achilefua, S.

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

Akersa, W.

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

Alù, A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized, ultrathin, broadband circular polarizers,” Nat. Commun. 3(870), (2012).

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B84(20), 205428 (2011).
[CrossRef]

Anastasiadou, M.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Asuni, N.

A. Giachetti and N. Asuni, “Real-time artifact-free Image upscaling,” IEEE Trans. Image Process.20(10), 2760–2768 (2011).
[CrossRef] [PubMed]

Belkin, M. A.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized, ultrathin, broadband circular polarizers,” Nat. Commun. 3(870), (2012).

Canny, J.

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell.8(6), 679–698 (1986).
[CrossRef] [PubMed]

Chenault, D. B.

Clement, D.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Cohen, H.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Collins, R. T.

Creusere, C. D.

T. V. T. Krishna, C. D. Creusere, and D. G. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process.20(1), 288–292 (2011).
[CrossRef] [PubMed]

Cronin, T. W.

Dreyfuss, J.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Flammer, P. D.

Furtak, T. E.

Gao, S.

S. Gao and V. Gruev, “Bilinear and bicubic interpolation methods for division of focal plane polarimeters,” Opt. Express19(27), 26161–26173 (2011).
[CrossRef] [PubMed]

S. Gao and V. Gruev, “Image interpolation methods evaluation for division of focal plane polarimeters,” Proc. SPIE8012, 80120N, 80120N-10 (2011).
[CrossRef]

Giachetti, A.

A. Giachetti and N. Asuni, “Real-time artifact-free Image upscaling,” IEEE Trans. Image Process.20(10), 2760–2768 (2011).
[CrossRef] [PubMed]

Goldstein, D. L.

Greiner, B.

Gruev, V.

Hollingsworth, R. E.

Huynh, B.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Karpel, N.

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng.30(3), 570–587 (2005).
[CrossRef]

Keys, R.

R. Keys, “Cubic convolution interpolation for digital image processing,” Acoustics, Speech and Signal Processing, IEEE Transactions on29(6), 1153–1160 (1981).
[CrossRef]

Krishna, T. V. T.

T. V. T. Krishna, C. D. Creusere, and D. G. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process.20(1), 288–292 (2011).
[CrossRef] [PubMed]

Kulkarni, M.

M. Kulkarni and V. Gruev, “Integrated spectral-polarization imaging sensor with aluminum nanowire polarization filters,” Opt. Express20(21), 22997–23012 (2012).
[CrossRef] [PubMed]

X. Xu, M. Kulkarni, A. Nehorai, and V. Gruev, “A correlation-based interpolation algorithm for division-of-focal-plane polarization sensors,” Proc. SPIE8364, 83640L, 83640L-8 (2012).
[CrossRef]

LaCasse, C. F.

Laude-Boulesteix, B.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Li’ege, F.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Liua, Y.

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

Luke, B. M.

A. C. Neville and B. M. Luke, “Form optical activity in crustacean cuticle,” J. Insect Physiol.17(3), 519–526 (1971).
[CrossRef]

Martino, A. D.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Nazac, A.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Neel, V.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc.107(6), 884–890 (2009).
[CrossRef]

Nehorai, A.

X. Xu, M. Kulkarni, A. Nehorai, and V. Gruev, “A correlation-based interpolation algorithm for division-of-focal-plane polarization sensors,” Proc. SPIE8364, 83640L, 83640L-8 (2012).
[CrossRef]

Neville, A. C.

A. C. Neville and B. M. Luke, “Form optical activity in crustacean cuticle,” J. Insect Physiol.17(3), 519–526 (1971).
[CrossRef]

Peltzer, J. J.

Perkins, R.

Quang, N.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Ratliff, B. M.

Salomatina-Motts, E.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc.107(6), 884–890 (2009).
[CrossRef]

San Segundo Bello, D.

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J.11(8), 1692–1703 (2011).
[CrossRef]

Sarkar, M.

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J.11(8), 1692–1703 (2011).
[CrossRef]

Schechner, Y. Y.

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng.30(3), 570–587 (2005).
[CrossRef]

Schwartz, L.

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Shaw, J. A.

Sudlowa, G.

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

Theuwissen, A.

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J.11(8), 1692–1703 (2011).
[CrossRef]

Tyo, J. S.

van Hoof, C.

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J.11(8), 1692–1703 (2011).
[CrossRef]

Voelz, D. G.

T. V. T. Krishna, C. D. Creusere, and D. G. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process.20(1), 288–292 (2011).
[CrossRef] [PubMed]

Warrant, E. J.

Xu, X.

X. Xu, M. Kulkarni, A. Nehorai, and V. Gruev, “A correlation-based interpolation algorithm for division-of-focal-plane polarization sensors,” Proc. SPIE8364, 83640L, 83640L-8 (2012).
[CrossRef]

Yaroslavskaya, A.

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc.107(6), 884–890 (2009).
[CrossRef]

York, T.

T. York and V. Gruev, “Characterization of a visible spectrum division-of-focal-plane polarimeter,” Appl. Opt.51(22), 5392–5400 (2012).
[CrossRef] [PubMed]

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

V. Gruev, R. Perkins, and T. York, “CCD polarization imaging sensor with aluminum nanowire optical filters,” Opt. Express18(18), 19087–19094 (2010).
[CrossRef] [PubMed]

Zhao, Y.

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized, ultrathin, broadband circular polarizers,” Nat. Commun. 3(870), (2012).

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B84(20), 205428 (2011).
[CrossRef]

Acoustics, Speech and Signal Processing, IEEE Transactions on (1)

R. Keys, “Cubic convolution interpolation for digital image processing,” Acoustics, Speech and Signal Processing, IEEE Transactions on29(6), 1153–1160 (1981).
[CrossRef]

Appl. Opt. (3)

IEEE J. Oceanic Eng. (1)

Y. Y. Schechner and N. Karpel, “Recovery of underwater visibility and structure by polarization analysis,” IEEE J. Oceanic Eng.30(3), 570–587 (2005).
[CrossRef]

IEEE Sens. J. (1)

M. Sarkar, D. San Segundo Bello, C. van Hoof, and A. Theuwissen, “Integrated polarization analyzing CMOS image sensor for material classification,” IEEE Sens. J.11(8), 1692–1703 (2011).
[CrossRef]

IEEE Trans. Image Process. (2)

T. V. T. Krishna, C. D. Creusere, and D. G. Voelz, “Passive polarimetric imagery-based material classification robust to illumination source position and viewpoint,” IEEE Trans. Image Process.20(1), 288–292 (2011).
[CrossRef] [PubMed]

A. Giachetti and N. Asuni, “Real-time artifact-free Image upscaling,” IEEE Trans. Image Process.20(10), 2760–2768 (2011).
[CrossRef] [PubMed]

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

J. Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Anal. Mach. Intell.8(6), 679–698 (1986).
[CrossRef] [PubMed]

J. Biomed. Opt. (1)

Y. Liua, T. York, W. Akersa, G. Sudlowa, V. Gruev, and S. Achilefua, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt.17(11), 116001.1–116001.4 (2012)

J. Insect Physiol. (1)

A. C. Neville and B. M. Luke, “Form optical activity in crustacean cuticle,” J. Insect Physiol.17(3), 519–526 (1971).
[CrossRef]

Nat. Commun. (1)

Y. Zhao, M. A. Belkin, and A. Alù, “Twisted optical metamaterials for planarized, ultrathin, broadband circular polarizers,” Nat. Commun. 3(870), (2012).

Opt. Express (6)

Opt. Spectrosc. (1)

E. Salomatina-Motts, V. Neel, and A. Yaroslavskaya, “Multimodal polarization system for imaging skin cancer,” Opt. Spectrosc.107(6), 884–890 (2009).
[CrossRef]

Phys. Rev. B (1)

Y. Zhao and A. Alù, “Manipulating light polarization with ultrathin plasmonic metasurfaces,” Phys. Rev. B84(20), 205428 (2011).
[CrossRef]

Phys. Status Solidi (1)

M. Anastasiadou, A. D. Martino, D. Clement, F. Li’ege, B. Laude-Boulesteix, N. Quang, J. Dreyfuss, B. Huynh, A. Nazac, L. Schwartz, and H. Cohen, “Polarimetric imaging for the diagnosis of cervical cancer,” Phys. Status Solidi5(5), 1423–1426 (2008).
[CrossRef]

Proc. SPIE (2)

S. Gao and V. Gruev, “Image interpolation methods evaluation for division of focal plane polarimeters,” Proc. SPIE8012, 80120N, 80120N-10 (2011).
[CrossRef]

X. Xu, M. Kulkarni, A. Nehorai, and V. Gruev, “A correlation-based interpolation algorithm for division-of-focal-plane polarization sensors,” Proc. SPIE8364, 83640L, 83640L-8 (2012).
[CrossRef]

Other (6)

S. Gao and V. Gruev, “Gradient based interpolation for division of focal plane polarization imaging sensors,” Circuits and Systems (ISCAS), 2012 IEEE International Symposium on, 1855–1858, 20–23 May 2012.

Y. Y. Schechner, S. G. Narasimhan, and S. K. Nayar, “Polarization-based vision through haze,” in ACM SIGGRAPH ASIA 2008 courses, New York, NY, USA, 71:1–71:15 (2008).

Prof. Justin Marshall, Sensory Neurobiology Group, University of Queensland, Brisbane Queensland 4072, Australia, (personal communication, 2012).

B. E. Bayer, “Color imaging array,” U.S. Patent 3,971,065, Jul 20, 1976.

D. Zhou, “An edge-directed bicubic interpolation algorithm,” Image and Signal Processing (CISP), 2010 3rd International Congress on, vol.3, 1186–1189, 16–18 Oct. 2010.

D. Miyazaki, R. Tan, K. Hara, and K. Ikeuchi, “Polarization-based inverse rendering from a single view,” Computer Vision, 2003. Proceedings. Ninth IEEE International Conference on, 2, 982–987 (2003).

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Figures (8)

Fig. 1
Fig. 1

Block diagram of division-of-focal-plane polarization imaging sensor. The array of charge coupled device (CCD) imaging elements is covered with four pixelated linear polarization filters oriented at 0°, 45°, 90° and 135°

Fig. 2
Fig. 2

(a) 135° direction gradient example. (b) 0° direction gradient example. Note: the blue pixels are pixels of known value, the black one is the target pixel, the gray ones are the pixels with same type as the target pixel, and the white ones are pixels of unknown value.

Fig. 3
Fig. 3

The true high-resolution image (a) muse-Intensity, (b) muse-DoLP, (c) muse-AoP, (a) soldier-Intensity, (b) soldier -DoLP, (c) soldier –AoP.

Fig. 4
Fig. 4

Comparison of different interpolation methods on the intensity, DoLP and AoP. (a) True polarization, (b) bilinear interpolation, (c) bicubic spline interpolation, (d) bicubic convolution and (e) gradient-based interpolation.

Fig. 5
Fig. 5

Different CDF threshold selection (a) the normalized AoP RMSE of the toy muse, (b) the normalized AoP RMSE of the toy soldier .

Fig. 6
Fig. 6

The normalized RMSE results (a) Intensity, (b) DoLP, and (c)AoP; The normalized STD of RMSE (d) Intensity, (e) DoLP, (f) AoP, for different interpolation methods by scanning integration time.

Fig. 7
Fig. 7

Image results from the sensor under different integration time. (a) 0.5 msec, (b) 4 msec, (c) 12 msec, (d) 20 msec, (e) 40 msec and (f) 100 msec.

Fig. 8
Fig. 8

Interpolated results of DoFP imager on the intensity, DoLP and AoP. (a) bilinear interpolation, (b) bicubic spline interpolation and (c) gradient-based interpolation.

Tables (1)

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Table 1 The RMSE performance comparison for toy muse

Equations (9)

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Intensity=( 1/2 )·(I( 0 o )+I( 45 o )+I( 90 o )+I( 135 o ))
DoLP= ( I( 0 o )I( 90 o ) ) 2 + ( I( 45 o )I( 135 o ) ) 2 / Intensity
AoP=(1/2 )·arctan( ( I( 45 o )I( 135 o ) ) / ( I( 0 o )I( 90 o ) ) )
I(x,y)= s=1 2 W(s)·f(x+s,y) for=[1,N-1] and y=[1,M]
W(s)={ 3/2· | s | 3 5/2· | s | 2 +1 0<| s |1 1/2· | s | 3 +5/2· | s | 2 4·| s |+2 1<| s |2 0 2<| s |
I(x,y)= [ 1/2 1/4 1/8 1/ 16 ] ·[ 0 2 0 0 1 0 1 0 2 5 4 1 1 3 3 1 ]·[ f(x1,y) f(x,y) f(x+1,y) f(x+2,y) ] x=1N1 y=1M
{ f(0,y)=3f(1,y)3f(2,y)+f(3,y) f(N+1,y)=3f(N,y)3f(N1,y)+f(N2,y)
{ D = 0 o i=2,4,6 j=3,5,7 | I(i,j)I(i,j2) | D = 45 o i=1,3,5 j=3,5,7 | I(i,j)I(i+2,j2) | D 90 o = i=3,5,7 j=2,4,6 | I(i,j)I(i2,j) | D 135 o = i=1,3,5 j=1,3,5 | I(i,j)I(i+2,j+2) |
RMSE= 1 MN 1iM 1jN ( O c (i,j) I c (i,j) ) 2

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