Robust estimation of shape and polarisation using blind source separation

In this paper we show how to use blind source separation to estimate shape from polarised images from a fixed viewing and illumination direction. Our method does not require prior knowledge of the polariser angles nor the refractive index. We use weighted singular vector decomposition (SVD) to estimate the unknown parameters, where the weights are dictated by the physics of polarisation. In a two-step process, we firstly use least square fitting to obtain the polariser angles, and then estimate the refractive index using a mutual information criterion function. We show that the proposed method is capable of calculating robust shape information compared with alternative approaches relying on the same input information. The proposed method can be applied when using uncalibrated polarisation filters. It can also be used effectively when the subject moves during image capture.

► We show how to estimate polarisation state without knowing polariser orientations.
► The estimation algorithm is based on a two-step process using Newton’s method.
► The criterion function is to compare the phase estimate with that obtained using SFS.
► Fresnel theory is here used for surface normal and refractive index estimation.