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Recent advances in 3D Gaussian Splatting (3DGS) have enabled highly efficient and photorealistic novel view synthesis. However, segmenting objects accurately in 3DGS remains challenging due to the discrete nature of Gaussian representations, which often leads to aliasing and artifacts at object boundaries. In this paper, we introduce NG-GS, a novel framework for high-quality object segmentation in 3DGS that explicitly addresses boundary discretization. Our approach begins by automatically identifying ambiguous Gaussians at object boundaries using mask variance analysis. We then apply radial basis function (RBF) interpolation to construct a spatially continuous feature field, enhanced by multi-resolution hash encoding for efficient multi-scale representation. A joint optimization strategy aligns 3DGS with a lightweight NeRF module through alignment and spatial continuity losses, ensuring smooth and consistent segmentation boundaries. Extensive experiments on NVOS, LERF-OVS, and ScanNet benchmarks demonstrate that our method achieves state-of-the-art performance, with significant gains in boundary mIoU. Code is available at this https URL.