FeatureGS: Eigenvalue-feature optimization in 3D Gaussian Splatting for geometrically accurate and artifact-reduced reconstruction

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, typically given in man-made environments. 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. On the small-scale DTU benchmark with man-made scenes, FeatureGS achieves a 20% improvement in geometric accuracy, suppresses floater artifacts by 90%, and reduces the number of Gaussians by 95%. FeatureGS proves to be a strong method for geometrically accurate, artifact-reduced and memory-efficient 3D scene reconstruction, enabling the direct use of Gaussian centers for geometric representation.