A Fully-statistical Wave Scattering Model for Heterogeneous Surfaces

Heterogeneous surfaces exhibit spatially varying geometry and material, and therefore admit diverse appearances. Existing computer graphics works can only model heterogeneity using explicit structures or statistical parameters that describe a coarser level of detail. We extend the boundary by introducing a new model that describes the heterogeneous surfaces fully statistically at the microscopic level, with rich geometry and material details that are comparable to the wavelengths of light. We treat the heterogeneous surfaces as a mixture of stochastic vector processes. We adapt the well-known generalized Harvey-Shack theory to quantify the mean scattered intensity, i.e., the BRDF of these surfaces. We further explore the covariance statistic of the scattered field and derive its rank-1 decomposition. This leads to a practical algorithm that samples the speckles (fluctuating intensities) from the statistics, enriching the appearance without explicit definition of heterogeneous surfaces. The formulations are analytic, and we validate the quantities by comprehensive numerical simulations. Our heterogeneous surface model demonstrates various applications including corrosion (natural), particle deposition (man-made), and height-correlated mixture (artistic). Code for this paper is available at https://github.com/Rendering-at-ZJU/HeteroSurface.