Extracting structured, parametric 3D representations from raw images remains a fundamental challenge in computer vision and graphics. While recent advancements in the 3D Gaussian Splatting (3DGS) pipeline integrate planar primitives to yield compact and editable geometry, these approaches typically treat planes as isolated, discrete sets. This lack of topological connectivity hinders robust geometric reasoning, leading to fragmented reconstructions and misaligned boundaries that fall short of the precision for rigorous spatial analysis and professional design workflows. To address this, we introduce TopoGS, the first 3DGS framework to explicitly integrate both planar and topological constraints for coherent 3D reconstruction. Specifically, we extract global 2D topological relationships from multi-view image segmentations and anchor Gaussian primitives to these structural elements. This formulation enables the joint optimization of plane parameters, rendering fidelity, and topological adjacency. By enforcing strict multi-view consistency alongside these topological constraints, our method significantly mitigates geometric misalignments and produces connected, structured 3D models. Extensive evaluations on the ScanNet++ dataset demonstrate that TopoGS achieves state-of-the-art performance, providing a highly robust solution for generating accurate, topologically sound, and visually faithful scene representations.
High-fidelity surface reconstruction from multi-view images is a core problem in 3D computer vision. While neural implicit surfaces like SDFs offer smooth geometry, they are often bottlenecked by the computational intensity of volume rendering. Conversely, 3D Gaussian Splatting (3DGS) provides rapid training but lacks geometry continuity, often leading to fragmented surfaces. This paper presents a novel framework that integrates Signed Distance Fields directly into the splatting pipeline. By leveraging the continuous nature of SDFs to regularize Gaussian primitives, our method effectively fills geometric holes and suppresses noise inherent in sparse point clouds. Unlike hybrid approaches that rely on heavy volumetric sampling, our approach utilizes the efficiency of splatting to achieve faster convergence. Extensive evaluations demonstrate that our method produces high-quality surfaces with significantly fewer primitives, offering a more compact and efficient representation for both indoor and outdoor environments.
Dimensionality reduction algorithms map high-dimensional data into visualizable 2D or 3D spaces, but traditionally rely on a discrete point-cloud paradigm. This discrete abstraction is susceptible to visual occlusion and artificial discontinuities, often failing to represent the continuous density of the underlying manifold. To address these limitations, we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process. Instead of standard photometric losses, Topo-GS is driven by local geometric constraints. By solving orthogonal Procrustes targets, the optimization enforces an As-Rigid-As-Possible prior while explicitly aligning the spatial covariance of each Gaussian to the local tangent space. Recognizing that unrolling data of varying intrinsic dimensionalities requires distinct spatial treatments, we utilize a topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces. Quantitative and visual evaluations demonstrate that Topo-GS successfully transforms discrete scatter plots into continuous volumetric representations, where inherent projection distortions explicitly manifest as observable geometric variations, while preserving local topological fidelity comparable to discrete baselines.
Large-scale 3D surface reconstruction from aerial imagery is fundamental to geospatial mapping and urban modeling. Recent advances in 3D Gaussian Splatting (3DGS) have demonstrated considerable potential for this task. However, existing methods still face three major challenges in large and complex scenes: scene partitioning may split continuous scene elements across independently optimized sub-regions; geometric constraints mainly focus on the attributes of individual Gaussians while overlooking their local organization; and uniform regularization struggles to accommodate heterogeneous geometric structures. To address these issues, we propose STARS-GS, a structure-aware 3DGS framework for large-scale surface reconstruction. First, we introduce a structure-aware scene partitioning strategy that better preserves continuous scene structures during partitioning and reduces cross-region geometric inconsistencies and stitching artifacts through boundary refinement. Second, we develop neighborhood-aware Gaussian organization that extends geometric constraints from individual primitives to their neighborhood organization, encouraging Gaussians to better conform to local surface geometry. Third, we introduce adaptive surface regularization that adjusts the regularization strength according to local geometric characteristics, promoting geometric consistency in structured regions while preserving plausible variations in unstructured regions. Extensive experiments on large-scale aerial photogrammetry benchmarks demonstrate that STARS-GS consistently outperforms the evaluated Gaussian-based methods in surface reconstruction. It increases the average F1-score from 0.640 for the second-best method to 0.698, corresponding to a relative improvement of approximately 9.1%, demonstrating effective improvements in geometric accuracy and surface completeness.