Shape-From-Polarisation: A Nonlinear Least Squares Approach

Ye Yu, Dizhong Zhu, William A. P. Smith; Proceedings of the IEEE International Conference on Computer Vision (ICCV), 2017, pp. 2969-2976

In this paper we present a new type of approach for estimating surface height from polarimetric data. In contrast to all previous shape-from-polarisation methods, we do not first transform the observed data into a polarisation image. Instead, we minimise the sum of squared residuals between predicted and observed intensities over all pixels and polariser angles. This is a nonlinear least squares optimisation problem in which the unknown is the surface height. The forward prediction is a series of transformations for which we provide analytical derivatives allowing the overall problem to be efficiently optimised using Gauss-Newton type methods with an analytical Jacobian matrix. We also propose a variant of the method which uses image ratios to remove dependence on illumination and albedo. We demonstrate our methods on glossy objects, including with albedo variations, and provide a comparison to a state of the art approach.