ICML 2025

Stochastic Poisson Surface Reconstruction with One Solve
using Geometric Gaussian Processes
Sidhanth Holalkere 1 David S. Bindel 1 Silvia Sellán 2 3 Alexander Terenin 1
Abstract
Poisson Surface Reconstruction is a widely-used
algorithm for reconstructing a surface from an ori-
ented point cloud. To facilitate applications where
only partial surface information is available, or
scanning is performed sequentially, a recent line
of work proposes to incorporate uncertainty into
the reconstructed surface via Gaussian process
models. The resulting algorithms first perform
Gaussian process interpolation, then solve a set
of volumetric partial differential equations glob-
ally in space, resulting in a computationally ex-
pensive two-stage procedure. In this work, we
apply recently-developed techniques from geo-
metric Gaussian processes to combine interpo-
lation and surface reconstruction into a single
stage, requiring only one linear solve per sam-
ple. The resulting reconstructed surface samples
can be queried locally in space, without the use of
problem-dependent volumetric meshes or grids.
These capabilities enable one to (a) perform prob-
abilistic collision detection locally around the re-
gion of interest, (b) perform ray casting without
evaluating points not on the ray’s trajectory, and
(c) perform next-view planning on a per-ray ba-
sis. They also do not requiring one to approxi-
mate kernel matrix inverses with diagonal matri-
ces as part of intermediate computations, unlike
prior methods. Results show that our approach
provides a cleaner, more-principled, and more-
flexible stochastic surface reconstruction pipeline.
1. Introduction
Surface reconstruction algorithms are used to process
point cloud data—the most-common format in which real-
Code: HTTPS://GITHUB.COM/SHOLALKERE/GEOSPSR.
1Cornell University 2Columbia University 3MIT. Correspon-
dence to: Sidhanth Holalkere <sh844@cornell.edu>.
Proceedings of the 42 nd International Conference on Machine
Learning, Va...