  Recent advancements in novel view synthesis have enabled real-time rendering
speeds and high reconstruction accuracy. 3D Gaussian Splatting (3D-GS), a
foundational point-based parametric 3D scene representation, models scenes as
large sets of 3D Gaussians. Complex scenes can comprise of millions of
Gaussians, amounting to large storage and memory requirements that limit the
viability of 3D-GS on devices with limited resources. Current techniques for
compressing these pretrained models by pruning Gaussians rely on combining
heuristics to determine which ones to remove. In this paper, we propose a
principled spatial sensitivity pruning score that outperforms these approaches.
It is computed as a second-order approximation of the reconstruction error on
the training views with respect to the spatial parameters of each Gaussian.
Additionally, we propose a multi-round prune-refine pipeline that can be
applied to any pretrained 3D-GS model without changing the training pipeline.
After pruning 88.44% of the Gaussians, we observe that our PUP 3D-GS pipeline
increases the average rendering speed of 3D-GS by 2.65$\times$ while retaining
more salient foreground information and achieving higher image quality metrics
than previous pruning techniques on scenes from the Mip-NeRF 360, Tanks &
Temples, and Deep Blending datasets.
