A Physically Admissible Stokes Vector Reconstruction in Linear Polarimetric Imaging

Polarization encoded images improve on conventional intensity imaging techniques by providing access to additional parameters describing the vector nature of light. In a polarimetric image, each pixel is related to a 4 x 1 vector named Stokes vector (3 x 1 in a linear configuration, which is the framework retained afterwards). Such images comprise a valuable set of physical information on the objects they contain, amplifying subsequently the accuracy of the analysis that can be done. A Stokes imaging polarimeter yields data named radiance images from which Stokes vectors are reconstructed, supposed to comply with a physical admissibility constraint. Classical estimation techniques such as pseudo-inverse approach exhibit defects, hampering any relevant physical interpretation of the scene: (i) first, due to their sensitivity to noise and errors that may contaminate the observed radiance images and that may then propagate to the evaluation of the Stokes vector components, thus justifying an ad hoc a posteriori treatment of Stokes vectors; (ii) second, in not taking this physical admissibility criterion explicitly into account. Motivated by this observation, the proposed contribution aims to provide a method of reconstruction addressing both issues, thus ensuring smoothness and spatial consistency of the reconstructed components, as well as compliance with the prescribed physical admissibility constraint. A by-product of the algorithm is that the resulting angle of polarization reflects more faithfully the physical properties of the materials present in the image. The mathematical formulation yields a non-smooth convex optimization problem that is then converted into a min-max problem and solved by the generic Chambolle-Pock primal-dual algorithm. Several mathematical results (such as existence/uniqueness of the minimizer of the primal problem, existence of a saddle point to the associated Lagrangian, etc.) are supplied and highlight the well-posed character of the modelling. Experiments demonstrate that our method provides significant improvements (i) over the least square-based method both in terms of quantitative criteria (physical admissibility constraint automatically met) and qualitative assessment (spatial regularization/coherency), (ii) over the physical consistency of related relevant polarimetric parameters such as the angle and degree of polarization, (iii) robustness of the method when applied on real outdoor scenes acquired in degraded conditions (poor weather conditions, etc.).