Author ORCID Identifier

https://orcid.org/0009-0006-2961-6839

Date of Award

Spring 5-20-2026

Document Type

Thesis (Master's)

Department or Program

Computer Science

First Advisor

Wojciech Jarosz

Abstract

Gaussian Process Implicit Surfaces (GPISes) provide a powerful and unified stochastic geometry representation for rendering surfaces, volumes, and the rich continuum between them. Recent work has shown that GPISes can model a broad space of visual appearances under a unified light transport framework. However, practical rendering with GPISes remains challenging: existing estimators can become inefficient for particular correlation structures, and highly anisotropic or heightfield-like GPISes require specialized treatment to obtain robust variance reduction.

This thesis extends recent work on GPIS rendering by introducing a new next-event estimation (NEE) technique for anisotropic GPISes.We show that standard NEE provides diminishing benefits as GPIS correlations become highly anisotropic. In the limiting case of heightfield-like GPISes, where correlations are perfect along one axis, the set of admissible light paths collapses to a lower-dimensional manifold, causing previous NEE strategies to fail. We analyze this degenerate transport configuration and derive a sampling strategy that explicitly samples the manifold of admissible outgoing directions within the spherical cap subtended by a spherical light source.

Our method enables NEE for heightfield-like GPISes for the first time, while also providing substantial variance reduction for more general anisotropic GPIS configurations. We support arbitrary emitter shapes by sampling directions toward a bounding-sphere proxy of the light geometry. Finally, we further combine the proposed estimator with existing sampling strategies using multiple importance sampling, yielding a robust rendering framework across a wide range of correlation regimes.

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