Abstract

The polarization properties of reflected light capture important information about the object’s inherent properties: material composition, i.e. index of refraction and scattering properties, and shape of the object, i.e. surface normal. Polarization information therefore has been used for surface reconstruction using a single-view camera with unpolarized incident light. However, this surface normal reconstruction technique suffers from a zenith angle ambiguity. In this paper, we have utilized circularly polarized light to solve for the zenith ambiguity by developing a detailed model using Mueller matrix formulism and division of focal plane polarization imaging technology. Experiment results validate our model for accurate surface reconstruction.

© 2015 Optical Society of America

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References

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2014 (1)

2013 (2)

2012 (4)

2010 (3)

2009 (3)

E. Puttonen, J. Suomalainen, T. Hakala, and J. Peltoniemi, “Measurement of reflectance properties of asphalt surfaces and their usability as reference targets for aerial photos,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2330–2339 (2009).
[Crossref]

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

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

2007 (2)

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]

G. A. Atkinson and E. R. Hancock, “Shape estimation using polarization and shading from two views,” IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2001–2017 (2007).
[Crossref] [PubMed]

2006 (2)

2005 (2)

M. Olivier, M. Fabrice, S. Christophe, and G. Patrick, “Active Lighting Applied to 3D Reconstruction of Specular Metallic Surfaces by Polarization Imaging,” Appl. Opt. 45, 4062(2005).

O. Morel, F. Meriaudeau, C. Stolz, and P. Gorria, “Polarization imaging applied to 3D reconstruction of specular metallic surfaces,” Proc. SPIE 2005, 178–186 (2005).
[Crossref]

2004 (1)

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, “Transparent surface modeling from a pair of polarization images,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 73–82 (2004).
[Crossref] [PubMed]

2003 (2)

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

A. Sweeney, C. Jiggins, and S. Johnsen, “Insect communication: polarized light as a butterfly mating signal,” Nature 423(6935), 31–32 (2003).
[Crossref] [PubMed]

2002 (1)

2001 (1)

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

2000 (1)

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity in predation on silvery fish,” Vision Res. 40(1), 71–75 (2000).
[Crossref] [PubMed]

1995 (1)

C. Paddock, T. Youngs, E. Eriksen, and R. Boyce, “Validation of wall thickness estimates obtained with polarized light microscopy using multiple fluorochrome labels: correlation with erosion depth estimates obtained by lamellar counting,” Bone 16(3), 381–383 (1995).
[Crossref] [PubMed]

1988 (1)

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439–451 (1988).
[Crossref]

1851 (1)

G. G. Stokes, “On the numerical calculation of a class of definite integrals and infinite series,” Transactions of the Cambridge Philosophical Society. 9, 329(1851).

Achilefu, S.

Y. Liu, T. York, W. Akers, G. Sudlow, V. Gruev, and S. Achilefu, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt. 17(11), 116001 (2012).
[Crossref] [PubMed]

Akers, W.

Y. Liu, T. York, W. Akers, G. Sudlow, V. Gruev, and S. Achilefu, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt. 17(11), 116001 (2012).
[Crossref] [PubMed]

Atkinson, G. A.

G. A. Atkinson and E. R. Hancock, “Shape estimation using polarization and shading from two views,” IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2001–2017 (2007).
[Crossref] [PubMed]

Boal, J. G.

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity in predation on silvery fish,” Vision Res. 40(1), 71–75 (2000).
[Crossref] [PubMed]

Boyce, R.

C. Paddock, T. Youngs, E. Eriksen, and R. Boyce, “Validation of wall thickness estimates obtained with polarized light microscopy using multiple fluorochrome labels: correlation with erosion depth estimates obtained by lamellar counting,” Bone 16(3), 381–383 (1995).
[Crossref] [PubMed]

Brady, P.

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[Crossref] [PubMed]

Bréon, F. M.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Brock, N.

Caldwell, R. L.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

Canterakis, N.

S. Rahmann and N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. I-149.
[Crossref]

Chellappa, R.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439–451 (1988).
[Crossref]

Chenault, D. B.

Cheroske, A. G.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

Chiou, T. H.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

Chipman, R. A.

Christophe, S.

Creusere, C. D.

Cronin, T. W.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

Cummings, M.

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[Crossref] [PubMed]

Cunningham, J. P.

Deuzé, L. J.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Devaux, C.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Eriksen, E.

C. Paddock, T. Youngs, E. Eriksen, and R. Boyce, “Validation of wall thickness estimates obtained with polarized light microscopy using multiple fluorochrome labels: correlation with erosion depth estimates obtained by lamellar counting,” Bone 16(3), 381–383 (1995).
[Crossref] [PubMed]

Fabrice, M.

Ferraton, M.

Frankot, R. T.

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439–451 (1988).
[Crossref]

Gao, S.

Gilboa, E.

Goldstein, D. L.

Goloub, P.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Gorria, P.

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt. 45(17), 4062–4068 (2006).
[Crossref] [PubMed]

O. Morel, F. Meriaudeau, C. Stolz, and P. Gorria, “Polarization imaging applied to 3D reconstruction of specular metallic surfaces,” Proc. SPIE 2005, 178–186 (2005).
[Crossref]

Gruev, V.

Hagan, R.

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity in predation on silvery fish,” Vision Res. 40(1), 71–75 (2000).
[Crossref] [PubMed]

Hakala, T.

E. Puttonen, J. Suomalainen, T. Hakala, and J. Peltoniemi, “Measurement of reflectance properties of asphalt surfaces and their usability as reference targets for aerial photos,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2330–2339 (2009).
[Crossref]

Hancock, E.

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarization images,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1229–1236.

Hancock, E. R.

G. A. Atkinson and E. R. Hancock, “Shape estimation using polarization and shading from two views,” IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2001–2017 (2007).
[Crossref] [PubMed]

Hanlon, R. T.

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity in predation on silvery fish,” Vision Res. 40(1), 71–75 (2000).
[Crossref] [PubMed]

Harker, M.

M. Harker and P. O’Leary, “Least squares surface reconstruction from measured gradient fields,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–7.
[Crossref]

Herman, M.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Hsu, W. L.

Huynh, C. P.

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarization images,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1229–1236.

Ikeuchi, K.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, “Transparent surface modeling from a pair of polarization images,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 73–82 (2004).
[Crossref] [PubMed]

D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19(4), 687–694 (2002).
[Crossref] [PubMed]

Jiggins, C.

A. Sweeney, C. Jiggins, and S. Johnsen, “Insect communication: polarized light as a butterfly mating signal,” Nature 423(6935), 31–32 (2003).
[Crossref] [PubMed]

Johnsen, S.

A. Sweeney, C. Jiggins, and S. Johnsen, “Insect communication: polarized light as a butterfly mating signal,” Nature 423(6935), 31–32 (2003).
[Crossref] [PubMed]

Kagesawa, M.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, “Transparent surface modeling from a pair of polarization images,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 73–82 (2004).
[Crossref] [PubMed]

LaCasse, C.

Lafrance, B.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Liu, Y.

Y. Liu, T. York, W. Akers, G. Sudlow, V. Gruev, and S. Achilefu, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt. 17(11), 116001 (2012).
[Crossref] [PubMed]

Maignan, F.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Marchand, A.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Marshall, J.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

Meriaudeau, F.

Miyazaki, D.

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, “Transparent surface modeling from a pair of polarization images,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 73–82 (2004).
[Crossref] [PubMed]

D. Miyazaki, M. Saito, Y. Sato, and K. Ikeuchi, “Determining surface orientations of transparent objects based on polarization degrees in visible and infrared wavelengths,” J. Opt. Soc. Am. A 19(4), 687–694 (2002).
[Crossref] [PubMed]

Morel, O.

O. Morel, C. Stolz, F. Meriaudeau, and P. Gorria, “Active lighting applied to three-dimensional reconstruction of specular metallic surfaces by polarization imaging,” Appl. Opt. 45(17), 4062–4068 (2006).
[Crossref] [PubMed]

O. Morel, F. Meriaudeau, C. Stolz, and P. Gorria, “Polarization imaging applied to 3D reconstruction of specular metallic surfaces,” Proc. SPIE 2005, 178–186 (2005).
[Crossref]

Myhre, G.

Nadal, F.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Neel, V. A.

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

Nehorai, A.

O’Leary, P.

M. Harker and P. O’Leary, “Least squares surface reconstruction from measured gradient fields,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–7.
[Crossref]

Olivier, M.

Paddock, C.

C. Paddock, T. Youngs, E. Eriksen, and R. Boyce, “Validation of wall thickness estimates obtained with polarized light microscopy using multiple fluorochrome labels: correlation with erosion depth estimates obtained by lamellar counting,” Bone 16(3), 381–383 (1995).
[Crossref] [PubMed]

Patrick, G.

Pau, S.

Peinado, A.

Peltoniemi, J.

E. Puttonen, J. Suomalainen, T. Hakala, and J. Peltoniemi, “Measurement of reflectance properties of asphalt surfaces and their usability as reference targets for aerial photos,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2330–2339 (2009).
[Crossref]

Perkins, R.

Perry, G.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Powell, S. B.

Puttonen, E.

E. Puttonen, J. Suomalainen, T. Hakala, and J. Peltoniemi, “Measurement of reflectance properties of asphalt surfaces and their usability as reference targets for aerial photos,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2330–2339 (2009).
[Crossref]

Rahmann, S.

S. Rahmann and N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. I-149.
[Crossref]

Robles-Kelly, A.

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarization images,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1229–1236.

Saito, M.

Salomatina-Motts, E.

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

Sato, Y.

Schechner, Y. Y.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

Shashar, N.

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity in predation on silvery fish,” Vision Res. 40(1), 71–75 (2000).
[Crossref] [PubMed]

Shaw, J. A.

Stokes, G. G.

G. G. Stokes, “On the numerical calculation of a class of definite integrals and infinite series,” Transactions of the Cambridge Philosophical Society. 9, 329(1851).

Stolz, C.

Sudlow, G.

Y. Liu, T. York, W. Akers, G. Sudlow, V. Gruev, and S. Achilefu, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt. 17(11), 116001 (2012).
[Crossref] [PubMed]

Suomalainen, J.

E. Puttonen, J. Suomalainen, T. Hakala, and J. Peltoniemi, “Measurement of reflectance properties of asphalt surfaces and their usability as reference targets for aerial photos,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2330–2339 (2009).
[Crossref]

Sweeney, A.

A. Sweeney, C. Jiggins, and S. Johnsen, “Insect communication: polarized light as a butterfly mating signal,” Nature 423(6935), 31–32 (2003).
[Crossref] [PubMed]

Tanré, D.

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

Thilak, V.

Treibitz, T.

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

Tyo, J. S.

Voelz, D. G.

Yaroslavskaya, A. N.

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

York, T.

Youngs, T.

C. Paddock, T. Youngs, E. Eriksen, and R. Boyce, “Validation of wall thickness estimates obtained with polarized light microscopy using multiple fluorochrome labels: correlation with erosion depth estimates obtained by lamellar counting,” Bone 16(3), 381–383 (1995).
[Crossref] [PubMed]

Am. Nat. (1)

P. Brady and M. Cummings, “Differential response to circularly polarized light by the jewel scarab beetle Chrysina gloriosa,” Am. Nat. 175(5), 614–620 (2010).
[Crossref] [PubMed]

Appl. Opt. (5)

Bone (1)

C. Paddock, T. Youngs, E. Eriksen, and R. Boyce, “Validation of wall thickness estimates obtained with polarized light microscopy using multiple fluorochrome labels: correlation with erosion depth estimates obtained by lamellar counting,” Bone 16(3), 381–383 (1995).
[Crossref] [PubMed]

IEEE Trans. Geosci. Rem. Sens. (1)

E. Puttonen, J. Suomalainen, T. Hakala, and J. Peltoniemi, “Measurement of reflectance properties of asphalt surfaces and their usability as reference targets for aerial photos,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2330–2339 (2009).
[Crossref]

IEEE Trans. Pattern Anal. Mach. Intell. (4)

T. Treibitz and Y. Y. Schechner, “Active polarization descattering,” IEEE Trans. Pattern Anal. Mach. Intell. 31(3), 385–399 (2009).
[Crossref] [PubMed]

D. Miyazaki, M. Kagesawa, and K. Ikeuchi, “Transparent surface modeling from a pair of polarization images,” IEEE Trans. Pattern Anal. Mach. Intell. 26(1), 73–82 (2004).
[Crossref] [PubMed]

G. A. Atkinson and E. R. Hancock, “Shape estimation using polarization and shading from two views,” IEEE Trans. Pattern Anal. Mach. Intell. 29(11), 2001–2017 (2007).
[Crossref] [PubMed]

R. T. Frankot and R. Chellappa, “A method for enforcing integrability in shape from shading algorithms,” IEEE Trans. Pattern Anal. Mach. Intell. 10(4), 439–451 (1988).
[Crossref]

Integr. Comp. Biol. (1)

T. W. Cronin, N. Shashar, R. L. Caldwell, J. Marshall, A. G. Cheroske, and T. H. Chiou, “Polarization vision and its role in biological signaling,” Integr. Comp. Biol. 43(4), 549–558 (2003).
[Crossref] [PubMed]

J. Biomed. Opt. (1)

Y. Liu, T. York, W. Akers, G. Sudlow, V. Gruev, and S. Achilefu, “Complementary fluorescence-polarization microscopy using division-of-focal-plane polarization imaging sensor,” J. Biomed. Opt. 17(11), 116001 (2012).
[Crossref] [PubMed]

J. Geophys. Res., D, Atmospheres (1)

L. J. Deuzé, F. M. Bréon, C. Devaux, P. Goloub, M. Herman, B. Lafrance, F. Maignan, A. Marchand, F. Nadal, G. Perry, and D. Tanré, “Remote sensing of aerosols over land surfaces from POLDER‐ADEOS‐1 polarized measurements,” J. Geophys. Res., D, Atmospheres 106(D5), 4913 (2001).
[Crossref]

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

Nature (1)

A. Sweeney, C. Jiggins, and S. Johnsen, “Insect communication: polarized light as a butterfly mating signal,” Nature 423(6935), 31–32 (2003).
[Crossref] [PubMed]

Opt. Express (6)

Opt. Lett. (1)

Opt. Spectrosc. (1)

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

Proc. SPIE (1)

O. Morel, F. Meriaudeau, C. Stolz, and P. Gorria, “Polarization imaging applied to 3D reconstruction of specular metallic surfaces,” Proc. SPIE 2005, 178–186 (2005).
[Crossref]

Transactions of the Cambridge Philosophical Society. (1)

G. G. Stokes, “On the numerical calculation of a class of definite integrals and infinite series,” Transactions of the Cambridge Philosophical Society. 9, 329(1851).

Vision Res. (1)

N. Shashar, R. Hagan, J. G. Boal, and R. T. Hanlon, “Cuttlefish use polarization sensitivity in predation on silvery fish,” Vision Res. 40(1), 71–75 (2000).
[Crossref] [PubMed]

Other (7)

G. Horváth and D. Varjú, Polarized Light in Animal Vision: Polarization Patterns in Nature (Springer, 2004).

T. York, S. B. Powell, S. Gao, L. Kahan, T. Charanya, and D. Saha, “Bioinspired polarization imaging sensors: from circuits and optics to signal processing algorithms and biomedical applications,” in Proceedings of IEEE (IEEE, 2014), pp. 1450–1469.

D. Goldstein, Polarized Light (Marcel Dekker, 2003).

C. P. Huynh, A. Robles-Kelly, and E. Hancock, “Shape and refractive index recovery from single-view polarization images,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2010), pp. 1229–1236.

S. Rahmann and N. Canterakis, “Reconstruction of specular surfaces using polarization imaging,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2001), pp. I-149.
[Crossref]

M. Harker and P. O’Leary, “Least squares surface reconstruction from measured gradient fields,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2008), pp. 1–7.
[Crossref]

V. V. Tuchin, L. Wang, and D. A. Zimnyakov, Optical Polarization in Biomedical Applications (Springer, 2006).

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Figures (13)

Fig. 1
Fig. 1 Typical setup of a polarizer rotated α degrees followed by a retarder with a phase shift of ϕ degrees.
Fig. 2
Fig. 2 Light reflection on a specular surface.
Fig. 3
Fig. 3 DoLP and DoCP as a function of the incident angle. The black dotted angle indicates the location of the Brewster angle. If the camera records DoLP of 0.2 then there are two possible incident angles (22.39° and 85.40°). This ambiguity is resolved using DoCP measurement.
Fig. 4
Fig. 4 DoFP CCD polarimeter with an overlaid pixelated polarization filter.
Fig. 5
Fig. 5 (a) Diagram of setup utilized to reconstruct the object surface. (b) Picture of setup utilized to reconstruct the object surface. (a) & (b) Object is inside of a cylinder made of circular polarizer sheets which is inside of a diffusing box. An achromatic QWR is in front of the camera with its fast axis aligned to the x-axis in order to capture S3.
Fig. 6
Fig. 6 Scene showing a PET plastic bottle. (a) Monochromatic picture of the reconstructed scene. (b) AoP in false color. (c) DoLP in false color. (d) DoCP in false color with a black contour plot pointing to the location of the Brewster angle. (b) & (d) Black rectangles pointing to the regions A and B to be reconstructed. (c) & (d) Dotted line showing the location of the profile plot in Fig. 7.
Fig. 7
Fig. 7 (a) DoLP vs zenith angle, θi, cross profile plot of scene shown in Fig. 6. (b) DoCP vs zenith angle, θi, cross profile plot of scene shown in Fig. 6. Dotted black line shows the location of the Brewster angle. Equation (16) was used to compute the zenith angles. Each data point represents the information computed on a single pixel.
Fig. 8
Fig. 8 (a) Azimuth angle map in false color in reconstructed region B. (b) Zenith angle map in false color with a black contour plot pointing to the location of the Brewster angle in reconstructed region B. (c) Orthographic projection of the reconstructed surface in region B.
Fig. 9
Fig. 9 (a) Azimuth angle map in false color in reconstructed region A. (b) Zenith angle map in false color with a black contour plot pointing to the location of the Brewster angle in reconstructed region A. (c) Orthographic projection of the reconstructed surface in region A.
Fig. 10
Fig. 10 Scene created by a HDPE blue sphere. (a) Monochromatic picture of the reconstructed scene. (b) AoP in false color. (c) DoLP in false color. (d) DoCP in false color. (b) & (d) Black rectangles pointing to the regions A and B to be reconstructed.
Fig. 11
Fig. 11 (a) Azimuth angle map in false color in reconstructed region C. (b) Zenith angle map in false color in reconstructed region C. (c) Orthographic projections of the reconstructed surface in region C.
Fig. 12
Fig. 12 Flat black plastic surface mounted on a rotational stage inside the experimental setup. The rotational stage is rotated at 45° with respect to the camera’s x-axis.
Fig. 13
Fig. 13 (a) DoCP vs zenith angle, θi. Dashed red shows the theoretical data using an index of refraction of 1.40 and an S3 incident component of −0.86. Solid blue line shows the measured data using our method. (b) Measured errors between the calculated zenith angle and the true stage’s rotation.

Equations (22)

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I( α,ϕ )= 1 2 ( S 0 + S 1 cos2α + S 2 sin2αcosϕ S 3 sin2αsinϕ )
S 0 = 1 2 ( I( 0°,ϕ )+I( 45°,ϕ )+ I( 90°,ϕ )+I( 135°,ϕ ) ), ϕ[ 0°,180° ]
S 1 =I( 0°,0° )I( 90°,0° )
S 2 =I( 45°,0° )I( 135°,0° )
S 3 =I( 135°,90° )I( 45°,90° )
DoLP= S 1 2 + S 2 2 S 0 , DoLP[ 0,1 ]
DoCP= S 3 S 0 , DoCP[ 1,1 ]
AoP= 1 2 arctan( S 2 S 1 ), AoP[ 0°,180° ]
sin θ i sin θ r = n 2 n 1
S out =M S in
M R ( θ i , θ r )= 1 2 ( tan θ sin θ + ) 2 ×( cos 2 θ + cos 2 θ + cos 2 θ cos 2 θ + 0 0 cos 2 θ cos 2 θ + cos 2 θ + cos 2 θ + 0 0 0 0 2cos θ + cos θ 0 0 0 0 2cos θ + cos θ ) Where θ = θ i θ r , θ + = θ i + θ r
M rot ( θ )=( 1 0 0 0 0 cos2θ sin2θ 0 0 sin2θ cos2θ 0 0 0 0 1 )
S out =[ M rot ( 2θ ) M R ( θ i , θ r ) M rot ( 2θ ) ] S in
AoP=θ
DoLP= 2sin θ i tan θ i n 2 sin 2 θ i n 2 2 sin 2 θ i + tan 2 θ i
S in = { 1 0 0 p } T DoCP= 2pcos θ cos θ + cos 2 θ + cos 2 θ + Where θ = θ i θ r , θ + = θ i + θ r θ r =arcsin( sin θ i n ) for an air-object medium
φ=θ±90°
φ=AoP±90°
z=f( x,y )
n ={ δf( x,y ) δx δf( x,y ) δy 1 }={ tan θ i cosφ tan θ i sinφ 1 }
ε= c d a b ( z ^ x ( x,y ) z x ( x,y ) ) 2 + ( z ^ y ( x,y ) z y ( x,y ) ) 2 dxdy Where z ^ x and z ^ y represent the measured gradient
ε= Z ^ x Z x F 2 + Z ^ y Z y F 2

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