Cramer-Rao lower bound for the estimation of the degree of polarization in active coherent imagery at low photon level

International audienceThe degree of polarization (DOP) is an important tool in many optical measurement and imaging applications. We address the problem of its estimation in images that are perturbed with both speckle and photon noises, by determining the Cramer-Rao Lower Bound (CRLB) when the illuminated materials are purely depolarizing. We demonstrate that the CRLB is simply the sum of the CRLBs due to speckle noise and to Poisson noise. We use this result to analyze the influence of different optical parameters on DOP estimation

A multiple view polarimetric camera

A multiple view polarimetric camera is developed. The system uses four separate action cameras and software is employed to map the images onto each other in order to generate the Stokes vectors, the degree of linear polarisation and angle images. To ensure robustness, an automated calibration system has been developed that ensures the pixels are correctly mapped. Video frame synchronisation is also developed

Design and experimental validation of a snapshot polarization contrast imager

International audienceWe present a degree of polarization imaging system based on a Wollaston prism and a single CCD camera. This architecture eliminates technical inaccuracies and noise sources that are present in experimental setups containing a polarization switching element. After the acquisition of two images corresponding to two orthogonal states of polarization, one can compute the orthogonal state contrast image (OSCI), which is an estimate of the local degree of polarization of the backscattered light when the observed materials are purely depolarizing. The instrument design coupled to an efficient calibration enables the estimation of the OSCI from a single image acquisition and significant reduction of technical noise present in other polarization imaging systems. The setup was tested in realistic conditions where it represents a real asset

Target detection in active polarization images perturbed with additive noise and illumination nonuniformity.

International audienceActive imaging systems that illuminate a scene with polarized light and acquire two images in two orthogonal polarizations yield information about the intensity contrast and the orthogonal state contrast (OSC) in the scene. Both contrasts are relevant for target detection. However, in real systems, the illumination is often spatially or temporally nonuniform. This creates artificial intensity contrasts that can lead to false alarms. We derive generalized likelihood ratio test (GLRT) detectors, for which intensity information is taken into account or not and determine the relevant expressions of the contrast in these two situations. These results are used to determine in which cases considering intensity information in addition to polarimetric information is relevant or not

Entropy of partially polarized light and application to statistical processing techniques

International audienceWe have analyzed entropy properties of coherent and partially polarized light in an arbitrary number of spatial dimensions. We show that for Gaussian fields, the Shannon entropy is a simple function of the intensity and of the Barakat degree of polarization. In particular, we provide a probabilistic interpretation of this definition of the degree of polarization. Using information theory results, we also deduce some physical properties of partially polarized light such as additivity of the entropy and depolarization effects induced by mixing partially polarized states of light. Finally, we demonstrate that entropy measures can play an important role in segmentation and detection task

Comparative study of the best achievable contrast in scalar, Stokes and Mueller images

International audienceWe compare the relative performance of different active polarimetric imaging architectures for target detection applications. We show that if the noise that affects the measurements is additive and if the only relevant parameter is the contrast between an object of interest and a background with different Mueller matrices, the most efficient imaging architecture consists in acquiring a single intensity image while optimizing the illumination and analysis states of polarization

Detection in polarimetric images in the presence of additive noise and non-uniform illumination

International audienceActive polarimetric imaging systems yield information about the intensity contrast and the Orthogonal State Contrast (OSC) in the scene. However, in real systems, the illumination is often spatially or temporally non uniform which creates artificial intensity contrasts that can lead to false alarms. We derive the Generalized Likelihood Ratio Test (GLRT) detectors when intensity information is taken into account or not. These results are used to determine in which cases considering intensity information in addition to polarimetric information is relevant or no

Joint contrast optimization and object segmentation in active polarimetric images

International audienceWe present a method for automatic target detection based on the iterative interplay between an active polarimetric imager with adaptive capabilities and a snake-based image segmentation algorithm. It successfully addresses the difficult situations where the target and the background differ only by their polarimetric properties. This method illustrates the benefits of integrating digital processing algorithms at the heart of the image acquisition process rather than using them only for postprocessing

Sources of possible artefacts in the contrast evaluation for the backscattering polarimetric images of different targets in turbid medium

International audienceIt is known that polarization-sensitive backscattering images of different objects in turbid media may show better contrasts than usual intensity images. Polarimetric image contrast depends on both target and background polarization properties and typically involves averaging over groups of pixels, corresponding to given areas of the image. By means of numerical modelling we show that the experimental arrangement, namely, the shape of turbid medium container, the optical properties of the container walls, the relative positioning of the absorbing, scattering and reflecting targets with respect to each other and to the container walls, as well as the choice of the image areas for the contrast calculations, can strongly affect the final results for both linearly and circularly polarized light

Statistical algorithms for processing polarimetric images in coherent light

Polarimetric imagery consists in forming an image of the state of polarization of the light basckscattered by a scene. For example, the image of degree of polarization is a powerful method for detecting objects which do not appear in classical intensity images. However, with active imagers which illuminate the scene with coherent light (laser), the images of degree of polarization are strongly perturbed, due to the speckle phenomenon. It is thus necessary to use processing algorithms which are adapted to their statistical properties. We first propose to study a model of the probability density function of the images of degree of polarization, then we analyze the properties of several estimators of the degree of polarization from these images. We then characterize the performance of statistical algorithms for edge and target detection, and of object segmentation methods based on statistical active contours. One of the main conclusions is that for these processing operations, it is preferable not to work on the classical image of degree of polarization, but on a nonlinearly transformed image, which we call “natural representation” of the degree of polarization images.L'imagerie polarimétrique consiste à former une image de l'état de polarisation de la lumière réfléchie par une scène. En particulier, l'image du degré de polarisation constitue une méthode puissante pour détecter des objets qui n'apparaissent pas sur les images d'intensité classiques. Cependant, dans les imageurs actifs illuminant la scène avec une lumière cohérente (laser), les images de degré de polarisation sont fortement perturbées à cause du phénomène de speckle. Il est donc nécessaire d'utiliser des algorithmes de traitement adaptés à leurs propriétés statistiques. Nous proposons tout d'abord d'étudier le modèle de densité de probabilité des images de degré de polarisation, puis nous analysons les propriétés des différents estimateurs du degré de polarisation à partir de ces images. Nous caractérisons ensuite les performances d'algorithmes statistiques de détection de cibles et de bords, ainsi que des méthode de segmentation d'objets par contour actif statistique. L'une des principales conclusions est que pour ces opérations de traitement, il est préférable de travailler non pas avec l'image de degré de polarisation classique, mais avec une transformation non-linéaire de celle-ci, que nous appelons « représentation naturelle » des images de degré de polarisation