Recently, 3D Gaussian Splatting (3DGS) has emerged as an efficient representation for novel view synthesis, offering fast differentiable rendering and high visual fidelity, and has increasingly been extended to surface reconstruction. However, the relationship between depth information and reconstruction error remains insufficiently explored, limiting the principled design of geometric optimization strategies. To fill the above gap, we propose DepthGS, a depth-guided Gaussian splatting framework. We derive theoretical relations between depth discrepancies and reconstruction error under single-view and multi-view settings, and rigorously establish corresponding upper bounds on reconstruction error. The above analysis informs the design of adaptive regularization strategies in both single-view and multi-view optimization. More specifically, for single-view optimization, we propose a depth-difference-guided adaptive normal regularization strategy that modulates the normal constraint strength using a geometric reliability weight computed from local depth differences. For multi-view optimization, we introduce a cross-view depth consistency regularization strategy that promotes consistency between neighboring-view depth maps and the corresponding depth predictions obtained by transforming the current view's depth predictions into those neighboring views. Extensive experiments on DTU, Mip-NeRF360, and Tanks and Temples demonstrate that DepthGS achieves competitive performance in both surface reconstruction and novel view synthesis.

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