Quantifying surface normal estimation

Abstract

An inverse algorithm for surface normal estimation from thermal polarimetric imagery was developed and used to quantify the requirements on a priori information. Building on existing knowledge that calculates the degree of linear polarization (DOLP) and the angle of polarization (AOP) for a given surface normal in a forward model (from an object's characteristics to calculation of the DOLP and AOP), this research quantifies the impact of a priori information with the development of an inverse algorithm to estimate surface normals from thermal polarimetric emissions in long-wave infrared (LWIR). The inverse algorithm assumes a polarized infrared focal plane array capturing LWIR intensity images which are then converted to Stokes vectors. Next, the DOLP and AOP are calculated from the Stokes vectors. Last, the viewing angles, θ v , to the surface normals are estimated assuming perfect material information about the imaged scene. A sensitivity analysis is presented to quantitatively describe the a priori information's impact on the amount of error in the estimation of surface normals, and a bound is determined given perfect information about an object. Simulations explored the impact of surface roughness (σ) and the real component (n) of a dielectric's complex index of refraction across a range of viewing angles (θ v ) for a given wavelength of observation.

Three-dimensional polarimetric computational integral imaging

“…As stated in [26], the accurate measurement of the Stokes parameters by this technique requires the precise alignment of the axis of both the LP and the QWP. In our experiments this adjustment is achieved by means of the setup shown in Fig.…”

“…Methods have also been developed to extract 3D shape information from polarimetric imagery through the relationship between the surface normal and the angle or degree of reflected or emitted polarization [23,24]. While these techniques offer the potential to extract 3D information from single polarimetric images, there are limitations to the estimation process due to the complexity of the relationship between the polarimetric measurements and the surface normal; this includes the dependence on unknown parameters such as the material optical constants and surface roughness [25,26]. Such methods also do not exhibit the ability to image through occlusions supported by integral imaging.…”