Constrained Gaussian Splatting via Implicit TSDF Hash Grid for Dense RGB-D SLAM

3D Gaussian Splatting (3DGS) has emerged as a promising technique in SLAM due to its rapid and high-quality rendering capabilities. However, its reliance on discrete Gaussian primitives limits its effectiveness in capturing essential geometric features crucial for accurate pose estimation. To overcome this limitation, we propose a novel dense RGB-D SLAM system that integrates an implicit Truncated Signed Distance Function (TSDF) hash grid to constrain the distribution of Gaussian primitives. This innovative approach enables precise estimation of the scene’s geometric structure by smoothing the discrete Gaussian primitives and anchoring them to the scene’s surface. Acting as a low-pass filter, the implicit TSDF hash grid mitigates the inductive biases inherent in traditional 3DGS methods while preserving rendering quality. Our geometrically constrained map also significantly enhances generalization capabilities for depth estimation in novel views. Extensive experiments on the Replica, ScanNet, and TUM datasets demonstrate that our system achieves state-of-the-art tracking and mapping accuracy at speeds up to 30 times faster than existing 3DGS-based systems.