Abstract

In the framework of Stokes parameters imaging, polarization-encoded images have four channels which makes physical interpretation of such multidimensional structures hard to grasp at once. Furthermore, the information content is intricately combined in the parameters channels which involve the need for a proper tool that allows the analysis and understanding this kind of images. In this paper we address the problem of analyzing polarization-encoded images and explore the potential of this information for classification issues and propose ad hoc color displays as an aid to the interpretation of physical properties content. The color representation schemes introduced hereafter employ a technique that uses novel Poincaré Sphere to color spaces mapping coupled with a segmentation map as an a priori information in order to allow, at best, a distribution of the information in the appropriate color space. The segmentation process relies on the fuzzy C-means clustering algorithms family where the used distances were redefined in relation with our images specificities. Local histogram equalization is applied to each class in order to bring out the intra-class’s information smooth variations. The proposed methods are applied and validated with Stokes images of biological tissues.

© 2006 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  4. J. Zallat, C. Collet, and Y. Takakura, "Clustering of polarization-encoded images," Appl. Opt. 43,1-10 (2004).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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  10. R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, Inc, New Jersey, 2002).
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    [CrossRef] [PubMed]
  12. 12. C. Zang and P. Wang, "A new method of color image segmentation based on intensity and hue clustering," presented at the ICPR'00, Barcelona, Spain, 2000.

2004 (3)

2003 (1)

J. M. Bueno and M. C. W. Campbell, "Polarization properties of the in vitro old human crystalline lens," Ophthalmic and Physiological Optics 23,109-118 (2003).
[CrossRef] [PubMed]

2002 (1)

S. L. Jiao and L. H. V. Wang, "Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography," J. Biomed. Opt. 7,350-358 (2002).
[CrossRef] [PubMed]

2000 (1)

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surgery and Medicine 26, 119-129 (2000).
[CrossRef] [PubMed]

1998 (1)

1997 (1)

1995 (1)

1994 (1)

L. B. Wolff, "Polarization camera for computer vision with a beam splitter," J. Opt. Soc. Am. 11,2935-2945 (1994).
[CrossRef]

Alfano, R. R.

Bueno, J. M.

J. M. Bueno and M. C. W. Campbell, "Polarization properties of the in vitro old human crystalline lens," Ophthalmic and Physiological Optics 23,109-118 (2003).
[CrossRef] [PubMed]

Campbell, M. C. W.

J. M. Bueno and M. C. W. Campbell, "Polarization properties of the in vitro old human crystalline lens," Ophthalmic and Physiological Optics 23,109-118 (2003).
[CrossRef] [PubMed]

Collet, C.

Demos, S. G.

Drévillon, B.

Engheta, N.

Jacques, S. L.

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surgery and Medicine 26, 119-129 (2000).
[CrossRef] [PubMed]

Jiao, S. L.

S. L. Jiao and L. H. V. Wang, "Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography," J. Biomed. Opt. 7,350-358 (2002).
[CrossRef] [PubMed]

Jr, E. N.

Jr, E. N. P.

Laude-Boulesteix, B.

Lee, K.

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surgery and Medicine 26, 119-129 (2000).
[CrossRef] [PubMed]

Martino, A. D.

Pugh, E. N.

Roman, J. R.

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surgery and Medicine 26, 119-129 (2000).
[CrossRef] [PubMed]

Rowe, M. P.

Schwartz, L.

Takakura, Y.

Tyo, J. S.

Wang, L. H. V.

S. L. Jiao and L. H. V. Wang, "Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography," J. Biomed. Opt. 7,350-358 (2002).
[CrossRef] [PubMed]

Wolff, L. B.

L. B. Wolff, "Polarization camera for computer vision with a beam splitter," J. Opt. Soc. Am. 11,2935-2945 (1994).
[CrossRef]

Zallat, J.

Appl. Opt. (3)

J. Biomed. Opt. (1)

S. L. Jiao and L. H. V. Wang, "Jones-matrix imaging of biological tissues with quadruple-channel optical coherence tomography," J. Biomed. Opt. 7,350-358 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

L. B. Wolff, "Polarization camera for computer vision with a beam splitter," J. Opt. Soc. Am. 11,2935-2945 (1994).
[CrossRef]

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

Lasers in Surgery and Medicine (1)

S. L. Jacques, J. R. Roman, and K. Lee, "Imaging superficial tissues with polarized light," Lasers in Surgery and Medicine 26, 119-129 (2000).
[CrossRef] [PubMed]

Ophthalmic and Physiological Optics (1)

J. M. Bueno and M. C. W. Campbell, "Polarization properties of the in vitro old human crystalline lens," Ophthalmic and Physiological Optics 23,109-118 (2003).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Other (2)

R. C. Gonzalez and R. E. Woods, Digital Image Processing (Prentice-Hall, Inc, New Jersey, 2002).

12. C. Zang and P. Wang, "A new method of color image segmentation based on intensity and hue clustering," presented at the ICPR'00, Barcelona, Spain, 2000.

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Figures (10)

Fig. 1.
Fig. 1.

Geometrical representation of the Lab color space (a) and the HSV color space (b).

Fig. 2.
Fig. 2.

The HSV color space in cylindrical coordinates

Fig. 3.
Fig. 3.

I1. S 0 (a), S 1 (b), S 2(c), and S 3 (d) images of a histological section of a bone died with red picosirius and imaged at 650 nm wavelength. The image at the upper left is to be compared with a conventional intensity image. The scale in the intensity channel (S 0) is in arbitrary units. In the three remaining channels, the scales are relative to the first one.

Fig. 4.
Fig. 4.

I2. S 0 (a), S 1 (b), S 2 (c), and S 3 (d) images of a histological section of a healthy vessel. The image at the upper left is to be compared with the conventional intensity image. The scale in the intensity channel (S 0) is in arbitrary units. In the three remaining channels, the scales are relative to the first one.

Fig. 5.
Fig. 5.

I3. S 0 (a), S 1 (b), S 2 (c), and S 3 (d) images of a histological section of a pathological vessel. The image at the upper left is to be compared with the conventional intensity image. The scale in the intensity channel (S 0) is in arbitrary units. In the three remaining channels, the scales are relative to the first one.

Fig. 6.
Fig. 6.

The Poincaré Sphere. Completely polarized states lie on the surface of the sphere. Partially polarized radiations lie inside the sphere.

Fig. 7.
Fig. 7.

Resulting color channels representation of the normalized Stokes image I1. (a) H channel, (b) S channel, and (c) V channel. (d) L channel, (e) a channel, and (f) b channel.

Fig. 8.
Fig. 8.

4 classes label maps obtained using our clustering algorithms with the I1 image. (a) corresponds to the result obtained with the HSV-means, and (b) corresponds to the result obtained with the LAB-means. Each gray level corresponds to one class.

Fig. 9.
Fig. 9.

Brightness-channels images after histogram equalization for each class. (a) Equalized V-channel and (b) equalized L-channel. These images have to be compared to those of Figures 7(c) and 7(d).

Fig. 10.
Fig. 10.

Color previews of the three images I1, I2 and I3. (a), (b), and (c) correspond respectively to the HSV color maps. (d), (e), and (f) correspond to the LAB color maps.

Equations (17)

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S = ( S 0 S 1 S 2 S 3 ) = [ E x E x * + E y E y * E x E x * E y E y * 2 Re ( E x * E y ) 2 Im ( E x * E y ) ]
S 0 2 S 1 2 + S 2 2 + S 3 2
DOP = S 1 2 + S 2 2 + S 3 2 S 0
ϕ = 0.5 tan 1 ( S 2 S 1 )
χ = 0.5 sin 1 ( S 3 S 1 2 + S 2 2 + S 3 2 )
H = tan 1 ( S ¯ 2 S ¯ 1 )
S = ( S ¯ 1 2 + S ¯ 2 2 ) 1 2
V = 0.5 ( 1 S ¯ 3 )
L = 100 ( S ¯ 3 min ( S ¯ 3 ) ) ( max ( S ¯ 3 ) min ( S ¯ 3 ) )
a = a m + ( a M a m ) ( S ¯ 2 min ( S ¯ 2 ) ) ( max ( S ¯ 2 ) min ( S ¯ 2 ) )
b = b m + ( b M b m ) ( S ¯ 1 min ( S ¯ 1 ) ) ( max ( S ¯ 1 ) min ( S ¯ 1 ) )
ψ H = ( μ i H ( x , y ) ) i = 1 , k
ψ V = ( μ i V ( x , y ) ) i = 1 , k
ψ ( x , y ) = ( max i = 1 , k μ i H ( x , y ) , max i = 1 , k μ i V ( x , y ) )
δ i = tan 1 a i b i + π . μ 0 ( b i ) . sign ( a i )
λ i = cos 1 ( l i l i 2 + a i 2 + b i 2 )
d ( X 1 , X 2 ) = 2 R sin 1 sin 2 ( δ 1 δ 2 2 ) + cos δ 1 cos δ 2 sin 2 ( λ 1 λ 2 2 )

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