Single-View Shape and Depth from Closed-form Polarization Models for Depolarization-Dominated Objects

Closed-form solutions for shape-from-polarization (SfP) generally assume either purely specular or purely diffuse polarized light scattering models. However, polarized light scattering from real-world objects is a mixture of both of these processes. This work makes use of a closed-form expression for polarized light scattering model which combines specular and diffuse contributions. In prior work, we have demonstrated the broad applicability of a triply-degenerate (TD) model which decouples depolarization from the dominant Mueller-Jones matrix (MJM). The depolarization is controlled by a single parameter and the MJM encodes the polarization-dependent properties (e.g. diattenuation, polarizance). In this work, SfP information content is explored using our model for the MJM term which combines diffuse and specular polarization to simulate single-view, noise-free Mueller images. A merit function for simultaneous estimates of per-pixel surface normal and absolute depth is proposed. Cross-sections of this merit function are shown to be convex along depth and contain erroneous ambiguities for the surface normal. While ambiguities in surface normal estimates are well known for existing SfP approaches, these cross-sections show a kind of ambiguity unique to our model. Through investigation of the idealized scenario of an exactly-known pBRDF model and noise-free, infinitely precise polarimetric measurements, we found that simultaneous depth and shape estimation is achievable.