GRE-GS: Geometry Repair and Gaussian Extrapolation for Sparse-View 3D Gaussian Splatting

3D Gaussian Splatting (3DGS) achieves real-time, high-quality novel-view synthesis through explicit Gaussian primitives. However, under sparse-view settings, limited observations provide insufficient geometric support, yielding unreliable geometry and incomplete scene coverage. To address this issue, we present GRE-GS (Geometry Repair and Gaussian Extrapolation for Sparse-View Gaussian Splatting), a reconstruction framework that explicitly separates the two failure modes of sparse-view 3DGS—unreliable geometry and incomplete coverage—and addresses them with geometry repair and Gaussian extrapolation, respectively. For regions covered by training views, GRE-GS repairs the initial point cloud generated by a pretrained geometric model. It completes missing surfaces via locally aligned depth propagation and corrects depth errors via structural conflict correction. For uncovered regions, GRE-GS extrapolates new Gaussians from the trained Gaussian representation—extending their positions using projected DA3 depths and synthesizing colors with an MLP conditioned on neighboring Gaussian appearance. We also introduce a training-view safety mechanism that constrains and filters newly added Gaussians to keep them from disrupting the existing representation. Extensive experiments on Mip-NeRF360, Tanks and Temples, and DTU demonstrate that our method substantially improves novel-view rendering quality across different sparse-view settings.