GR-GS: Geometric Regularization 3D Gaussian Splatting Segmentation

Recent advances in 3D Gaussian Splatting (3DGS) have achieved remarkable success in real-time scene rendering. However, interactive 3DGS scene segmentation remains challenging. Current MLLM-based agents often treat spatial grounding as a black box, propagating multi-instance ambiguities into the 3D domain where an absence of structural constraints allows boundary Gaussians to erroneously elongate along viewing rays. In this paper, we introduce GR-GS, a unified framework that tightly couples explicit topological reasoning with physical covariance regularization to achieve high-fidelity 3D segmentation. Rather than relying on unstable multi-view voting to resolve semantic ambiguities, our framework introduces an LLM-Driven Relational Extraction (LDRE) module that enforces rigorous, pre-lifting topological constraints, isolating the exact target directly in 2D before spatial corruption can occur. To ensure these precise semantic boundaries are preserved during 3D optimization, we propose a Ray-Aligned Covariance Penalty (RACP). Instead of generic regularization, RACP leverages cross-view Jacobian projection to artificially inflate the screen footprint of ill-posed, elongated Gaussians. This forced boundary spillover triggers steep positional gradients that reactivate the splitting mechanism, organically compressing artifacts without additional parameters. Extensive experiments demonstrate that GR-GS achieves state-of-the-art results on NVOS and LERF-OVS. By treating semantic grounding and geometric fidelity as a coupled optimization problem, our method delivers superior relational reasoning and flawlessly delineated object boundaries.