Demonstrating unambiguous shape from polarization for Mueller imaging

Polarization imaging is highly sensitive to surface shape but is inherently ambiguous, as measurements depend only on the projected surface normal orientation. This shape-from-polarization algorithm introduces a method to recover unique surface normals from monocular Mueller images. We formulate the inverse problem as the estimation of the scattering geometry, enabling the extraction of unambiguous depth information from otherwise ambiguous normal data. Simulations show that while the initial ambiguous surface normal estimates are robust to noise, the subsequent depth recovery and disambiguation are more noise-sensitive. For simple object shapes, the method resolves ambiguities with mean angular errors below 10° at an SNR of 100. However, complex shapes require an SNR of 1,000 to achieve comparable accuracy. Notably, as the polarimetric capture system is simplified, the disambiguation performance approaches that of random selection for linear Stokes images.