Spatial Subdivision for Path Guiding

Path guiding is a technique to facilitate Monte-Carlo-based rendering algorithms by incorporating the scene's spatial-directional incident radiance information into local sampling decisions. State-of-the-art path-guiding methods typically use a k-d tree to subdivide the scene space, and then cache the directional incoming light distribution at the tree's leaf nodes. While significant work has been done to improve the representation of directional components, the spatial structure remains underexplored, often relying on simple subdivision heuristics based on the number, mean, and variance of samples arriving at each node.

This thesis mainly focuses on k-d-tree-based spatial subdivision schemes for path guiding. We decompose the problem into "when and where to split" and address them separately. For "when to split", we present two adaptive splitting algorithms either based on divergence estimates or multiple importance sampling, which make split decisions responsive to the light change at a node. For "where to split", we propose several geometry- and lighting-aware algorithms derived from decision trees metrics. We demonstrate their ability to improve the subdivision quality by fitting the shapes of geometries or lighting in the scene.

Finally, we introduce our comprehensive models by combining the "when and where to split" algorithms. Rendering experiments across diverse scenes show that our best models consistently outperform previous methods while maintaining an equal or lower tree node budget. Additionally, we explore alternative spatial structures beyond k-d trees.