Bounding Stratified Bernoulli Impulses for Ray Marching Gaussian Process Implicit Surfaces

The theory of light transport on Gaussian process implicit surface (GPIS) provides a unified framework for rendering surfaces, participating media, and the intermediate spectrum. However, previous approaches rely on brute-force ray marching for surface intersections, requiring full noise evaluations at each marching point, whether using multivariate Gaussian sampling or sparse convolution noise approximation. This imposes a severe limitation on the rendering efficiency. In this paper, we derive bounds to significantly reduce the total number of full noise evaluations, leading to efficient ray marching for ray-surface intersections. We introduce stratified Bernoulli impulses, enabling a fast point-level bound for individual realizations to replace unnecessary full noise evaluations. To further reduce the number of point-level bound evaluations, we propose a region-level bound, leveraging a spatial acceleration structure to prune probabilistically empty regions, thereby avoiding unnecessary marching points in advance. By combining these two bounds, our bounded ray marching accelerates ray-surface intersections in GPIS, and consequently significantly improves overall GPIS rendering efficiency. Code for this paper are at https://github.com/Cchen-77/bounded-gpis.