Path Guiding with Vertex Triplet Distributions

Abstract

Good importance sampling strategies are decisive for the quality and robustness of photorealistic image synthesis with Monte Carlo integration. Path guiding approaches use transport paths sampled by an existing base sampler to build and refine a guiding distribution. This distribution then guides subsequent paths in regions that are otherwise hard to sample. We observe that all terms in the measurement contribution function sampled during path construction depend on at most three consecutive path vertices. We thus propose to build a 9D guiding distribution over vertex triplets that adapts to the full measurement contribution with a 9D Gaussian mixture model (GMM). For incremental path sampling, we query the model for the last two vertices of a path prefix, resulting in a 3D conditional distribution with which we sample the next vertex along the path. To make this approach scalable, we partition the scene with an octree and learn a local GMM for each leaf separately. In a learning phase, we sample paths using the current guiding distribution and collect triplets of path vertices. We resample these triplets online and keep only a fixed-size subset in reservoirs. After each progression, we obtain new GMMs from triplet samples by an initial hard clustering followed by expectation maximization. Since we model 3D vertex positions, our guiding distribution naturally extends to participating media. In addition, the symmetry in the GMM allows us to query it for paths constructed by a light tracer. Therefore our method can guide both a path tracer and light tracer from a jointly learned guiding distribution.