Efficient and Accurate Spherical Kernel Integrals Using Isotropic Decomposition

Spherical filtering is fundamental to many problems in image synthesis, such as computing the reflected light over a surface or anti-aliasing mirror reflections over a pixel. This operation is challenging since the profile of spherical filters (e.g., the view-evaluated BRDF or the geometry-warped pixel footprint, mentioned before) typically exhibits both spatial and rotational variation at each pixel, precluding precomputed solutions. We accelerate complex spherical filtering tasks using isotropic spherical decomposition (ISD), decomposing spherical filters into a linear combination of simpler isotropic kernels. Our general ISD is flexible to the choice of the isotropic kernels, and we demonstrate practical realizations of ISD on several problems in rendering: shading and prefiltering with spatially varying BRDFs, anti-aliasing-environment-mapped mirror reflections, and filtering of noisy reflectance data. Compared to previous basis-space rendering solutions, our shading solution generates ground-truth-quality results at interactive rates, avoiding costly reconstruction and large approximation errors.