GVKF: Gaussian Voxel Kernel Functions for Highly Efficient Surface Reconstruction in Open Scenes

TL;DR

GVKF tackles open-scene 3D surface reconstruction by marrying fast Gaussian splatting with an implicit, kernel-regressed opacity field to form a continuous scene representation. It uses a sparse voxel grid to manage Gaussian primitives and models along-ray opacity as ρ(t) and transmission T(t) = exp(-∫_0^t ρ(w) dw), aligning with volume rendering while enabling kernel regression over discrete Gaussians. A logistic surrogate maps the opacity field to a surface distance D(t) to enable direct mesh extraction, linking density to an explicit surface. Experiments on Waymo Open Scene, Tanks & Temples, and Mip-NeRF 360 demonstrate high reconstruction fidelity, real-time rendering, and substantial storage/memory savings compared with both explicit and implicit baselines, illustrating the practical impact for autonomous driving and virtual reality.

Abstract

In this paper we present a novel method for efficient and effective 3D surface reconstruction in open scenes. Existing Neural Radiance Fields (NeRF) based works typically require extensive training and rendering time due to the adopted implicit representations. In contrast, 3D Gaussian splatting (3DGS) uses an explicit and discrete representation, hence the reconstructed surface is built by the huge number of Gaussian primitives, which leads to excessive memory consumption and rough surface details in sparse Gaussian areas. To address these issues, we propose Gaussian Voxel Kernel Functions (GVKF), which establish a continuous scene representation based on discrete 3DGS through kernel regression. The GVKF integrates fast 3DGS rasterization and highly effective scene implicit representations, achieving high-fidelity open scene surface reconstruction. Experiments on challenging scene datasets demonstrate the efficiency and effectiveness of our proposed GVKF, featuring with high reconstruction quality, real-time rendering speed, significant savings in storage and training memory consumption.

Figures (11)

• Figure 1: Framework of Gaussian Voxel Kernel Functions (GVKF) for scene representation. In this framework, discrete Gaussian primitives $\mathcal{G}$ represent continuous opacity density $\rho(t)$ on the ray via kernel regression. After slightly modifying the rasterization pipeline, the kernel function can be integrated into alpha blending rasterization without introducing dense points sampling. Additionally, we directly define the mapping relationship between the neural opacity field and the implicit surface.
• Figure 2: Comparison of Volume Rendering, 3D Gaussian Splatting with Alpha Blending, and GVKF Rendering.
• Figure 3: Illustration of functions $\Phi(u),\Phi^\prime(u),\rho(u)$.
• Figure 4: Illustration of opacity to SDF mapping.(Eq. \ref{['eq-map']})
• Figure 5: Qualitative comparison of novel view synthesis and surface reconstruction on the Waymo Open Dataset Sun, with each subplot annotated with PSNR values to quantify image quality. Our method shows higher geometric precision and detail, validating its efficiency and superiority in processing open scenes, especially in geometric accuracy and detail reproduction.