  In this paper, we present an implicit surface reconstruction method with 3D
Gaussian Splatting (3DGS), namely 3DGSR, that allows for accurate 3D
reconstruction with intricate details while inheriting the high efficiency and
rendering quality of 3DGS. The key insight is incorporating an implicit signed
distance field (SDF) within 3D Gaussians to enable them to be aligned and
jointly optimized. First, we introduce a differentiable SDF-to-opacity
transformation function that converts SDF values into corresponding Gaussians'
opacities. This function connects the SDF and 3D Gaussians, allowing for
unified optimization and enforcing surface constraints on the 3D Gaussians.
During learning, optimizing the 3D Gaussians provides supervisory signals for
SDF learning, enabling the reconstruction of intricate details. However, this
only provides sparse supervisory signals to the SDF at locations occupied by
Gaussians, which is insufficient for learning a continuous SDF. Then, to
address this limitation, we incorporate volumetric rendering and align the
rendered geometric attributes (depth, normal) with those derived from 3D
Gaussians. This consistency regularization introduces supervisory signals to
locations not covered by discrete 3D Gaussians, effectively eliminating
redundant surfaces outside the Gaussian sampling range. Our extensive
experimental results demonstrate that our 3DGSR method enables high-quality 3D
surface reconstruction while preserving the efficiency and rendering quality of
3DGS. Besides, our method competes favorably with leading surface
reconstruction techniques while offering a more efficient learning process and
much better rendering qualities. The code will be available at
https://github.com/CVMI-Lab/3DGSR.
