Manifold-Aware Spectral Compaction: A Graph Signal Processing Perspective on Online Gaussian Reduction for 3DGS SLAM

3D Gaussian Splatting (3DGS) has established itself as apremier technique for high-fidelity radiance field rendering. However, itsapplication in SLAM tasks is frequently hindered by the explosive growthof redundant Gaussian primitives, which imposes prohibitive memoryand rendering overhead. Existing compaction strategies predominantlyrely on heuristic pruning based on importance scores; such methods oftenfail to provide global fidelity guarantees and can disrupt the optimizationcontinuity required for online tracking. To address these challenges, weintroduce Manifold-Aware Spectral Compaction (MASC), a frameworkthat reformulates map reduction as a continuous signal reconstructiontask mapped onto a Riemannian manifold. We first construct a topology-aware graph representation using Symmetrized Kullback-Leibler diver-gence to precisely capture the statistical connectivity between primi-tives. To ensure real-time efficiency, we implement an incremental Nys-tröm spectral embedding strategy to project the Gaussian map onto alow-dimensional spectral subspace. We further derive a mathematicallyrigorous, closed-form solution for primitive aggregation leveraging Bures-Wasserstein barycenters, which theoretically ensures the conservation oflocal radiance field moments. Extensive evaluations on the Replica andTUM RGB-D datasets demonstrate that MASC achieves a 2.8× reduc-tion in GPU memory and a 2.4× speedup in rendering throughput.Remarkably, our method maintains or even enhances tracking accuracywhile eliminating approximately 60% of redundant primitives, achiev-ing an ATE of 0.98 cm on the TUM dataset. These results substantiatethat MASC provides an efficient and principled plug-and-play pathwayfor scalable, long-term neural rendering SLAM.