3DGEER: Exact and Efficient Volumetric Rendering with 3D Gaussians
Journal:
arXiv
Published Date:
May 29, 2025
Abstract
3D Gaussian Splatting (3DGS) marks a significant milestone in balancing the
quality and efficiency of differentiable rendering. However, its high
efficiency stems from an approximation of projecting 3D Gaussians onto the
image plane as 2D Gaussians, which inherently limits rendering
quality--particularly under large Field-of-View (FoV) camera inputs. While
several recent works have extended 3DGS to mitigate these approximation errors,
none have successfully achieved both exactness and high efficiency
simultaneously. In this work, we introduce 3DGEER, an Exact and Efficient
Volumetric Gaussian Rendering method. Starting from first principles, we derive
a closed-form expression for the density integral along a ray traversing a 3D
Gaussian distribution. This formulation enables precise forward rendering with
arbitrary camera models and supports gradient-based optimization of 3D Gaussian
parameters. To ensure both exactness and real-time performance, we propose an
efficient method for computing a tight Particle Bounding Frustum (PBF) for each
3D Gaussian, enabling accurate and efficient ray-Gaussian association. We also
introduce a novel Bipolar Equiangular Projection (BEAP) representation to
accelerate ray association under generic camera models. BEAP further provides a
more uniform ray sampling strategy to apply supervision, which empirically
improves reconstruction quality. Experiments on multiple pinhole and fisheye
datasets show that our method consistently outperforms prior methods,
establishing a new state-of-the-art in real-time neural rendering.
