## 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

Full Article |

PDF Article
### Equations (17)

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

(1)
$$\mathbf{S}=\left(\begin{array}{c}{S}_{0}\\ {S}_{1}\\ {S}_{2}\\ {S}_{3}\end{array}\right)=\left[\begin{array}{c}\u3008{E}_{x}{E}_{x}^{*}\u3009+\u3008{E}_{y}{E}_{y}^{*}\u3009\\ \u3008{E}_{x}{E}_{x}^{*}\u3009-\u3008{E}_{y}{E}_{y}^{*}\u3009\\ 2\mathrm{Re}\left(\u3008{E}_{x}^{*}{E}_{y}\u3009\right)\\ 2\mathrm{Im}\left(\u3008{E}_{x}^{*}{E}_{y}\u3009\right)\end{array}\right]$$
(2)
$${S}_{0}^{2}\ge {S}_{1}^{2}+{S}_{2}^{2}+{S}_{3}^{2}$$
(3)
$$\mathit{DOP}=\frac{\sqrt{{S}_{1}^{2}+{S}_{2}^{2}+{S}_{3}^{2}}}{{S}_{0}}$$
(4)
$$\varphi ={0.5\mathrm{tan}}^{-1}\left(\frac{{S}_{2}}{{S}_{1}}\right)$$
(5)
$$\chi ={0.5\mathrm{sin}}^{-1}\left(\frac{{S}_{3}}{\sqrt{{S}_{1}^{2}+{S}_{2}^{2}+{S}_{3}^{2}}}\right)$$
(6)
$$H={\mathrm{tan}}^{-1}\left(\frac{{\overline{S}}_{2}}{{\overline{S}}_{1}}\right)$$
(7)
$$S={\left({\overline{S}}_{1}^{2}+{\overline{S}}_{2}^{2}\right)}^{\frac{1}{2}}$$
(8)
$$V=0.5\left(1-{\overline{S}}_{3}\right)$$
(9)
$$L=100\left({\overline{S}}_{3}-min\left({\overline{S}}_{3}\right)\right)\u2044\left(max\left({\overline{S}}_{3}\right)-min\left({\overline{S}}_{3}\right)\right)$$
(10)
$$a={a}_{m}+\left({a}_{M}-{a}_{m}\right)\left({\overline{S}}_{2}-min\left({\overline{S}}_{2}\right)\right)\u2044\left(max\left({\overline{S}}_{2}\right)-min\left({\overline{S}}_{2}\right)\right)$$
(11)
$$b={b}_{m}+\left({b}_{M}-{b}_{m}\right)\left({\overline{S}}_{1}-min\left({\overline{S}}_{1}\right)\right)\u2044\left(max\left({\overline{S}}_{1}\right)-min\left({\overline{S}}_{1}\right)\right)$$
(12)
$${\psi}_{H}={\left({\mu}_{i}^{H}(x,y)\right)}_{i=1,k}$$
(13)
$${\psi}_{V}={\left({\mu}_{i}^{V}(x,y)\right)}_{i=1,k}$$
(14)
$$\psi (x,y)=(\underset{i=1,k}{max}{\mu}_{i}^{H}(x,y),\underset{i=1,k}{max}{\mu}_{i}^{V}(x,y))$$
(15)
$${\delta}_{i}={\mathrm{tan}}^{-1}\frac{{a}_{i}}{{b}_{i}}+\pi .{\mu}_{0}\left(-{b}_{i}\right).\mathit{sign}\left({a}_{i}\right)$$
(16)
$${\lambda}_{i}={\mathrm{cos}}^{-1}\left(\frac{{l}_{i}}{\sqrt{{l}_{i}^{2}+{a}_{i}^{2}+{b}_{i}^{2}}}\right)$$
(17)
$$d({X}_{1},{X}_{2})=2R{\mathrm{sin}}^{-1}\sqrt{{\mathrm{sin}}^{2}\left(\frac{{\delta}_{1}-{\delta}_{2}}{2}\right)+\mathrm{cos}{\delta}_{1}\mathrm{cos}{\delta}_{2}{\mathrm{sin}}^{2}\left(\frac{{\lambda}_{1}-{\lambda}_{2}}{2}\right)}$$