  3D reconstruction from multi-view images is one of the fundamental challenges
in computer vision and graphics. Recently, 3D Gaussian Splatting (3DGS) has
emerged as a promising technique capable of real-time rendering with
high-quality 3D reconstruction. This method utilizes 3D Gaussian representation
and tile-based splatting techniques, bypassing the expensive neural field
querying. Despite its potential, 3DGS encounters challenges, including
needle-like artifacts, suboptimal geometries, and inaccurate normals, due to
the Gaussians converging into anisotropic Gaussians with one dominant variance.
We propose using effective rank analysis to examine the shape statistics of 3D
Gaussian primitives, and identify the Gaussians indeed converge into
needle-like shapes with the effective rank 1. To address this, we introduce
effective rank as a regularization, which constrains the structure of the
Gaussians. Our new regularization method enhances normal and geometry
reconstruction while reducing needle-like artifacts. The approach can be
integrated as an add-on module to other 3DGS variants, improving their quality
without compromising visual fidelity.
