Interactive albedo editing in path-traced volumetric materials

Materials such as clothing or carpets, or complex assemblies of small leaves, flower petals, or mosses, do not fit well into either BRDF or BSSRDF models. Their appearance is a complex combination of reflection, transmission, scattering, shadowing, and inter-reflection. This complexity can be handled by simulating the full volumetric light transport within these materials by Monte Carlo algorithms, but there is no easy way to construct the necessary distributions of local material properties thatwould lead to the desired global appearance. In this article, we consider one way to alleviate the problem: an editing algorithm that enables a material designer to set the local (singlescattering) albedo coefficients interactively, and see an immediate update of the emergent appearance in the image. This is a difficult problem, since the function from materials to pixel values is neither linear nor low-order polynomial. We combine the following two ideas to achieve high-dimensional heterogeneous edits: precomputing the homogeneous mapping of albedo to intensity, and a large Jacobian matrix, which encodes the derivatives of each image pixel with respect to each albedo coefficient. Combining these two datasets leads to an interactive editing algorithm with a very good visual match to a fully path-traced ground truth.