Adaptive Ray Marching for Rendering Gaussian Process Implicit Surfaces

Ground Truth Ours MSE: 0.007 Seyb et al. MSE: 0.321 Fig. 1. GPIS is a probabilistic representation of 3D shapes, bridging the gap between microfacets, participating media and measurement uncertainties. Despite its usefulness, it has been historically challenging to render. Our method accelerates computing the ensemble averaged light transport by orders of magnitude compared to Seyb et al. [2024], by adaptively tracing the Gaussian process and drawing values using an online sampler. The figure renders a bunny-shaped Gaussian field with our method and Seyb et al. [2024] at equal time (7.5 minutes).

Gaussian Process Implicit Surfaces (GPIS) represent geometry as a distribution over implicit functions. Modeling an object's appearance as the expected rendering of a GPIS yields a unified framework that captures diverse light-transport effects including microfacet-like reflections and volumetric scattering. Despite this generality, computing GPIS-ray intersections requires sampling conditional multivariate Gaussian distributions along each ray and remains prohibitively expensive. We introduce an online sampling algorithm that draws these distributions incrementally, and an adaptive marching scheme that takes large steps where the surface is provably absent, minimizing the probability of missed intersections. Together, these ideas reduce rendering MSE by up to 46× at equal time compared to existing methods.