3D Gaussian Splatting has achieved remarkable success in novel view synthesis. However, extracting high-fidelity surfaces directly from 3DGS remains challenging due to its discrete and unstructured nature. Existing 3DGS-based reconstruction methods typically rely on multi-view geometric consistency or local constraints. Without an explicit structured geometric prior during optimization, these methods often struggle to resolve structural ambiguities, leading to artifacts and floaters, particularly in textureless or occluded regions. To address this limitation, we propose TopoSurfel, a novel framework that closes the loop between Gaussian surfels and continuous meshes. Unlike recent methods that incorporate mesh extraction into the differentiable pipeline by introducing auxiliary neural networks or extra per-Gaussian parameters, we dynamically extract a continuous proxy mesh via a non-trainable differentiable iso-surfacing process. Leveraging this differentiable connection, we introduce a mesh-guided surfel evolution strategy, including normal alignment and geometry-aware density control, to effectively suppress floaters and fill surface holes. Furthermore, to address the initialization challenges in large-scale environments, we propose a spatially aware hybrid re-initialization strategy that ensures robust reconstruction across complex scenes. Extensive experiments demonstrate that TopoSurfel achieves competitive geometric reconstruction accuracy while maintaining high-quality mesh-based novel view synthesis. The code for our method is available at https://github.com/Fan-Treasure/TopoSurfel.
3D Gaussian Splatting (3DGS) gives high-quality novel-view synthesis, but its adaptive radiance primitives are not directly usable as structured assets: opacity is not an additive area measure, refinement can change the induced geometry, and watertight mesh extraction can hallucinate collision surfaces in unobserved regions. We introduce Manifold-GS, a certified hybrid asset layer for Gaussian scenes. The method separates appearance opacity from geometric quadrature mass, represents surface-like Gaussians as a discrete unoriented varifold, and exports only confidence-certified open surface patches while retaining uncertified content as residual splats. It provides refinement-conservative mass transport, local realizability diagnostics, source-preserving patch bindings, and conservative collision candidates. On three DTU scenes, a frozen asset benchmark shows zero patch-defined edit leakage, texture round-trip PSNR of 30.1/35.3/33.7 dB, and lower collision floater area than official 2DGS meshes on all scenes, with large gaps on two scenes. The result is a precision-coverage tradeoff rather than a universal reconstruction claim. External-region annotations, phantom-collision probes, and 5k-face simplification further support the certified asset interpretation, while RGB-only experiments show that local realizability is not sufficient for sparse-view surface identifiability.
Incremental scene reconstruction is essential for real-world applications. Although 3D Gaussian Splatting shows strong potential, most existing approaches require offline conversion of the optimized Gaussians into an intermediate implicit field for explicit mesh extraction, which hinders seamless integration with downstream tasks. To address this limitation, we propose a novel online framework that incrementally reconstructs and updates high-fidelity explicit meshes by directly triangulating a dense geometric Gaussian representation, which supports both high-quality rendering and incremental surface reconstruction. Moreover, we present a direct meshing algorithm that efficiently extracts and updates the mesh from the Gaussian set. To ensure mesh accuracy, we enforce a plane-based pulling constraint that dynamically aligns 3D Gaussian primitives to the approximated local surface. Furthermore, our framework significantly reduces memory and computational overhead during long-sequence processing by dynamically freezing fully optimized historical regions. Experiments on public datasets demonstrate that our method outperforms conventional Gaussian-based methods on both rendering quality and reconstruction accuracy.