Compression, interpolation, and importance sampling for polarized BRDF models

In this work, the KAIST Mueller measurement database is compressed by assuming a triply degeneracy (TD) in the Cloude coherency eigenspectrum. This assumption compresses the database by a factor of two by reparameterizes the database into eight parameters, maintains physicality when interpolated for non-measured geometries, and is shown to retain the dominant polarimetric properties for both diffuse and specular light-matter interactions. For each 4 × 4 Mueller matrix, the 8 TD parameters are: the radiometric average throughput, a depolarization parameter, and 6 parameters to describe the dominant coherent process. Polarimetric importance sampling is made possible by interpreting the eigenspectrum as probabilities. To evaluate the proposed methods, a sphere is rendered using the pink silicone material from the KAIST pBRDF database and compared to a TD compressed and polarimetric importance sampled pBRDF rendering. The average deviation in the polarizance angle and degree of linear polarization (AoLP and DoLP) deviation was 16.9° and 1.1% for both the TD compressed and polarimetric importance sampled pBRDF model as compared to the KAIST pBRDF model, respectively. The pBRDF models are also compared by rendering two scenes containing multiple surface interactions and several material types. Polarimetric importance sampling convergence and its dependence on the materials' depolarization and ray depth are reported for these scenes.