Biomimetic, adaptive, optimum polarization-opponent imaging of scenes with preferential polarization distributions

Certain animal species have visual systems that are sensitive to light’s polarization [1-3]. The human eye, on the other hand, is not capable of “seeing” polarization information, without any instrument. However, man-made imaging systems can collect polarization information from a scene, in addition to luminance and spectral information. One of the important issues in polarization imaging is how to process the polarization information after (or while) it is collected by the imaging system. As one possible processing technique, in our earlier work we introduced the methods of “polarization-difference imaging” (PDI), inspired by polarization vision in certain species, and we demonstrated that optical imaging systems utilizing PDI techniques may facilitate the detection of targets in scattering media, even when the targets produce only very weak polarization, and that such enhancement can increase the distance over which targets can be detected [4-6]. In that work, we showed that in the PDI technique, the intensities of the two orthogonal polarization components of imaging-forming light for each pixel at (x, y), i.e., I║ (x, y) and I⊥ (x, y), were captured and then the “polarization-sum” (PS) and “polarization difference” (PD) intensities were formed as IPS (x, y) =I║ (x, y) +I⊥ (x, y) and IPS (x, y) = I║ (x, y)– I⊥ (x, y) Furthermore, it was shown by Tyo [7] that the optimum linear combination of I║ (x, y) and I⊥ (x, y) channels for a scene, in which the polarization angle is assumed to be a random variable with a uniform probability density function, are indeed PS and PD signals, utilizing the analogy and parallelism with the biology of color vision in the human visual system and related principle component analysis done by Buchsbaum and Gottschalk [8]. Therefore, in that scenario the PS and PD channels were optimum in the information theoretic sense, i.e., their contents were statistically uncorrelated, requiring minimum bandwidth [7]. However, the situation may differ when the scene statistically has a preferential polarization distribution with a non-uniform probability density function for the state of polarization. What would then be the optimum linear combination for polarization channels in this case? We have been investigating techniques to adaptively form such optimum linear combination for polarization channels. Specifically, the two linear channels in general can be expressed as I P S a d a p t i v e (x, y) =a I║ (x, y) + β I⊥ (x, y) and I P D a d a p t i v e (x, y) = γ I║ (x, y) + ζ I⊥ (x, y) with unequal weighting coefficients a, b, g, and z, which should be determined based on the statistics of the polarization distribution in any given scene. Utilizing the technique of principal components analysis for non-uniform distributions of polarization state in an image, we determine the appropriate values for these coefficients for forming the optimum linear combination of polarization channels. These coefficients, therefore, depend on the polarization statistics of the scene, and can be adaptively adjusted as the imaging system observes different environments. Such optimum combinations for polarization channels with unequal weighting coefficients suitable for environment with preferential polarization distribution (such as under water) may point to an interesting processing in the polarization vision in certain aquatic species, and can lead to images with higher contrast and better target detection for man-made imaging systems.