FGS-SLAM: Fourier-based Gaussian Splatting for Real-time SLAM with Sparse and Dense Map Fusion Y ansong Xu 1, 2, Junlin Li 1, Wei Zhang 1, Siyu Chen 1, 2, Shengyong Zhang 1, Y uquan Leng 3, Weijia Zhou 1 Abstract -- 3D gaussian splatting has advanced simultaneous localization and mapping (SLAM) technology by enabling real-time positioning and the construction of high-fidelity maps. However, the uncertainty in gaussian position and initialization parameters introduces challenges, often requiring extensive iterative convergence and resulting in redundant or insufficient gaussian representations. T o address this, we introduce a novel adaptive densification method based on Fourier frequency domain analysis to establish gaussian priors for rapid convergence. Additionally, we propose constructing independent and unified sparse and dense maps, where a sparse map supports efficient tracking via Generalized Iterative Closest Point (GICP) and a dense map creates high-fidelity visual representations. This is the first SLAM system leveraging frequency domain analysis to achieve high-quality gaussian mapping in real-time. Experimental results demonstrate an average frame rate of 36 FPS on Replica and TUM RGB-D datasets, achieving competitive accuracy in both localization and mapping. I NRODUCTION With the rapid development of fields such as robotics [1], augmented reality (AR), and drones, there is an increasing demand for efficient and accurate 3D environmental perception. As a result, the importance of Simultaneous Localization and Mapping (SLAM) technology in these applications has grown significantly. The main challenge of SLAM is achieving both autonomous localization and 3D map construction in unknown environments. However, traditional SLAM methods still face significant challenges in balancing real-time performance and scene accuracy.

We present an improvement to the DP-SLAM algorithm for simultane- ous localization and mapping (SLAM) that maintains multiple hypothe- ses about densely populated maps (one full map per particle in a par- ticle filter) in time that is linear in all significant algorithm parameters and takes constant (amortized) time per iteration. This means that the asymptotic complexity of the algorithm is no greater than that of a pure localization algorithm using a single map and the same number of parti- cles. We also present a hierarchical extension of DP-SLAM that uses a two level particle filter which models drift in the particle filtering process itself. The hierarchical approach enables recovery from the inevitable drift that results from using a finite number of particles in a particle filter and permits the use of DP-SLAM in more challenging domains, while maintaining linear time asymptotic complexity.

A spatial AI that can perform complex tasks through visual signals and cooperate with humans is highly anticipated. To achieve this, we need a visual SLAM that easily adapts to new scenes without pre-training and generates dense maps for downstream tasks in real-time. None of the previous learning-based and non-learning-based visual SLAMs satisfy all needs due to the intrinsic limitations of their components. In this work, we develop a visual SLAM named Orbeez-SLAM, which successfully collaborates with implicit neural representation and visual odometry to achieve our goals. Moreover, Orbeez-SLAM can work with the monocular camera since it only needs RGB inputs, making it widely applicable to the real world. Results show that our SLAM is up to 800x faster than the strong baseline with superior rendering outcomes. Code link: https://github.com/MarvinChung/Orbeez-SLAM.