Markov Chain Monte Carlo Reflectometry

 This project explores the use of Markov chain Monte Carlo (MCMC) algorithm to directly draw samples from an unknown BRDF. MCMC can produces samples from any function, so long as we can evaluate it. In the case of BRDF acquisition, this means being able to measure the BRDF at any given incident and outgoing directions—this is indeed the main building block of any reflectometry procedure. This will enable our reflectometryprocedure to adapt to the unknown BRDF and measure it at random locations distributed according to the BRDF, without the need to first acquire it. The effectiveness of any MCMC sampling algorithm critically depends on the proposal distribution we use. We developed proposals that facilitate reflectometry, by exploring a few research directions: First, we explored proposals that take advantage of physical and empirical properties of real-world BRDFs—reciprocity, isotropy, bivariate symmetry, and so on. Second, we explored proposals that mimic existing physics-based analytical BRDF models—microfacet, PCA, mixture models. Third, we explored controlled MCMC algorithms, which adapt proposals to previously drawn samples as the MCMC iteration proceeds. Fourth, we explored the state-of-the-art technique of estimating density using normalizing flows and how we can use it as proposal and pdf/BRDF of the material.