During the Gaussian Splatting optimization process, the scene's geometry can
gradually deteriorate if its structure is not deliberately preserved,
especially in non-textured regions such as walls, ceilings, and furniture
surfaces. This degradation significantly affects the rendering quality of novel
views that deviate significantly from the viewpoints in the training data. To
mitigate this issue, we propose a novel approach called GeoGaussian. Based on
the smoothly connected areas observed from point clouds, this method introduces
a novel pipeline to initialize thin Gaussians aligned with the surfaces, where
the characteristic can be transferred to new generations through a carefully
designed densification strategy. Finally, the pipeline ensures that the scene's
geometry and texture are maintained through constrained optimization processes
with explicit geometry constraints. Benefiting from the proposed architecture,
the generative ability of 3D Gaussians is enhanced, especially in structured
regions. Our proposed pipeline achieves state-of-the-art performance in novel
view synthesis and geometric reconstruction, as evaluated qualitatively and
quantitatively on public datasets.

通过 GeoGaussian 方法，采用高斯喷洒优化过程，保留场景几何结构的特性和纹理，提高了 3D 高斯在结构化区域中的生成能力，在公共数据集中定性和定量评估中实现了最先进的新视图合成和几何重建性能。

GeoGaussian：面向场景渲染的几何感知高斯喷射

GeoGaussian: Geometry-aware Gaussian Splatting for Scene Rendering

Interesting data often concentrate on low dimensional smooth manifolds inside
a high dimensional ambient space. Random projections are a simple, powerful
tool for dimensionality reduction of such data. Previous works have studied
bounds on how many projections are needed to accurately preserve the geometry
of these manifolds, given their intrinsic dimensionality, volume and curvature.
However, such works employ definitions of volume and curvature that are
inherently difficult to compute. Therefore such theory cannot be easily tested
against numerical simulations to understand the tightness of the proven bounds.
We instead study typical distortions arising in random projections of an
ensemble of smooth Gaussian random manifolds. We find explicitly computable,
approximate theoretical bounds on the number of projections required to
accurately preserve the geometry of these manifolds. Our bounds, while
approximate, can only be violated with a probability that is exponentially
small in the ambient dimension, and therefore they hold with high probability
in cases of practical interest. Moreover, unlike previous work, we test our
theoretical bounds against numerical experiments on the actual geometric
distortions that typically occur for random projections of random smooth
manifolds. We find our bounds are tighter than previous results by several
orders of magnitude.

通过研究典型的高斯随机流形的随机投影所产生的畸变，我们发现了一种明确可计算的近似理论界限来确保这些流形的几何形状的精度，我们的理论界限比之前的研究结果紧凑了几个数量级。