Scattering model for polarized reflection with a Monte Carlo-based approach

The polarization reflection model is a fundamental framework describing the changes in both intensity and polarization of light following reflection. Materials with distinct properties exhibit unique polarization reflection characteristics. However, traditional models assume that the scattered light from diffuse reflection is completely depolarized after undergoing internal scattering, regardless of the scattering properties of the object. In reality, multiple scattering events do not completely depolarize the scattered light. To address this discrepancy, we first established a reference coordinate system for the scattering process. Subsequently, we employed polar decomposition methods to analyze the subsurface scattering Mueller matrix. Building upon this analysis, we introduced polarization Monte Carlo simulations to empirically construct a novel polarimetric bidirectional subsurface scattering reflectance distribution function (pBSSRDF) model. We also explored the relationship between the depolarization and scattering coefficient and developed a comprehensive optimization process for the object's pBSSRDF parameters, thereby avoiding the limitations associated with coaxial and coplanar assumptions. Our experiments, conducted on both synthetic and real data for opaque and translucent objects, demonstrate high accuracy in representing the polarization states of scattered light.