Estimation of incidence and reflection angles from passive polarimetric imagery: extension to out-of-plane scattering

Passive polarimetric imagery conveys information that complements the information contained in intensity and spectral imagery. Passive polarimetric measurements have been exploited in many remote sensing applications such as shape extraction, surface inspection and object detection/recognition. In previous work Thilak et al. proposed an algorithm to estimate the index of refraction and view angle (object surface orientation) from multiple polarization images where the source position changes between measurements. That work relies on a specular polarimetric bidirectional reflectance distribution function (pBRDF) developed by Priest and Meier. The pBRDF incorporates a Mueller matrix that characterizes the polarized reflection properties of a target for any incident Stokes vector. The results in Thilak et al. assumed that scattering occurs in the plane of incidence, which means that the pBRDF matrix contains many zero elements. In this paper, we extend this work to an out-of-plane scattering geometry, which implies that the pBRDF matrix contains more non-zero elements. In the initial work presented here, a nonlinear optimization approach is utilized to estimate the incident and reflection angles from a single polarization measurement assuming knowledge of the surface index of refraction and azimuthal angle between source and receiver. The effectiveness of the proposed method is verified through computer simulation.