Inverse volume rendering with material dictionaries

Translucent materials are ubiquitous, and simulating their appearance requires accurate physical parameters. However, physically-accurate parameters for scattering materials are difficult to acquire. We introduce an optimization framework for measuring bulk scattering properties of homogeneous materials (phase function, scattering coefficient, and absorption coefficient) that is more accurate, and more applicable to a broad range of materials. The optimization combines stochastic gradient descent with Monte Carlo rendering and a material dictionary to invert the radiative transfer equation. It offers several advantages: (1) it does not require isolating single-scattering events; (2) it allows measuring solids and liquids that are hard to dilute; (3) it returns parameters in physically-meaningful units; and (4) it does not restrict the shape of the phase function using Henyey-Greenstein or any other low-parameter model. We evaluate our approach by creating an acquisition setup that collects images of a material slab under narrow-beam RGB illumination. We validate results by measuring prescribed nano-dispersions and showing that recovered parameters match those predicted by Lorenz-Mie theory. We also provide a table of RGB scattering parameters for some common liquids and solids, which are validated by simulating color images in novel geometric configurations that match the corresponding photographs with less than 5% error.