FeatureGS: Eigenvalue-Feature Optimization in 3D Gaussian Splatting for Geometrically Accurate and Artifact-Reduced Reconstruction

TL;DR

FeatureGS augments 3D Gaussian Splatting with eigenvalue-derived geometric losses to align Gaussian centers and surfaces with object geometry while suppressing floater artifacts. By incorporating four formulations—Gaussian planarity and neighborhood-based planarity, omnivariance, and eigenentropy—the approach improves geometric accuracy and memory efficiency, achieving up to ~30% accuracy gains and ~95% reduction in Gaussians with only modest PSNR trade-offs. Evaluated on 15 DTU scenes, FeatureGS demonstrates strong geometry, fewer artifacts, and substantial storage savings, enabling direct use of Gaussian centers for geometric representation. The method offers a practical, robust path to geometrically faithful, compact 3D reconstructions suitable for large-scale applications.

Abstract

3D Gaussian Splatting (3DGS) has emerged as a powerful approach for 3D scene reconstruction using 3D Gaussians. However, neither the centers nor surfaces of the Gaussians are accurately aligned to the object surface, complicating their direct use in point cloud and mesh reconstruction. Additionally, 3DGS typically produces floater artifacts, increasing the number of Gaussians and storage requirements. To address these issues, we present FeatureGS, which incorporates an additional geometric loss term based on an eigenvalue-derived 3D shape feature into the optimization process of 3DGS. The goal is to improve geometric accuracy and enhance properties of planar surfaces with reduced structural entropy in local 3D neighborhoods.We present four alternative formulations for the geometric loss term based on 'planarity' of Gaussians, as well as 'planarity', 'omnivariance', and 'eigenentropy' of Gaussian neighborhoods. We provide quantitative and qualitative evaluations on 15 scenes of the DTU benchmark dataset focusing on following key aspects: Geometric accuracy and artifact-reduction, measured by the Chamfer distance, and memory efficiency, evaluated by the total number of Gaussians. Additionally, rendering quality is monitored by Peak Signal-to-Noise Ratio. FeatureGS achieves a 30 % improvement in geometric accuracy, reduces the number of Gaussians by 90 %, and suppresses floater artifacts, while maintaining comparable photometric rendering quality. The geometric loss with 'planarity' from Gaussians provides the highest geometric accuracy, while 'omnivariance' in Gaussian neighborhoods reduces floater artifacts and number of Gaussians the most. This makes FeatureGS a strong method for geometrically accurate, artifact-reduced and memory-efficient 3D scene reconstruction, enabling the direct use of Gaussian centers for geometric representation.

Figures (9)

• Figure 1: Methodology of FeatureGS: Geometric loss based on 3D shape features added to 3DGS 3DGS. The features are derived from eigenvalues of the covariance matrix from individual Gaussians or the covariance matric from Gaussians in a local neighborhood surrounding each Gaussian center. The geometric loss is combined with the photometric loss in 3DGS.
• Figure 2: Additional geometric loss of FeatureGS, illustrated by a 3D feature from Gaussians and a 3D feature from Gaussian centers in a local neighborhood. For example, through the loss with planarity of Gaussians, the Gaussians become more planar, and through the loss with planarity, omnivariance, or eigenentropy in the Gaussian neighborhood, the alignment of the Gaussian centers in the neighborhood becomes more planar. All configurations have the effect that the Gaussians move closer to the object surface and are less randomly oriented. This enables the Gaussian centers to serve as a geometric representation of the surface.
• Figure 3: \ref{['fig:gaussian_ellipsoid']} Representation of a single Gaussian ellipsoid with the three eigenvectors ($\mathbf{\epsilon_1}, \mathbf{\epsilon_2}, \mathbf{\epsilon_3}$) and the corresponding eigenvalues ($s_1, s_2, s_3$) in the three-dimensional coordinate system. \ref{['fig:neighborhood_ellipsoid']} Representation of an ellipsoid from the neighborhood points represented by the Gaussian centers with the three eigenvectors ($\mathbf{\epsilon_1}, \mathbf{\epsilon_2}, \mathbf{\epsilon_3}$) and the corresponding eigenvalues ($\lambda_1, \lambda_2, \lambda_3$) in the three-dimensional coordinate system.
• Figure 4: Geometric accuracy during training process on the DTU scan40. Chamfer cloud-to-cloud distances $\downarrow$ in mm for points $\leq$10 mm and all points (floater artifacts). The curves show for the different loss types.
• Figure 5: Numbers of Gaussians during training process on the DTU scan40. The curves show for the different loss types.