We present LiV-GS, a LiDAR-visual SLAM system in outdoor environments that leverages 3D Gaussian as a differentiable spatial representation. Notably, LiV-GS is the first method that directly aligns discrete and sparse LiDAR data with continuous differentiable Gaussian maps in large-scale outdoor scenes, overcoming the limitation of fixed resolution in traditional LiDAR mapping. The system aligns point clouds with Gaussian maps using shared covariance attributes for front-end tracking and integrates the normal orientation into the loss function to refines the Gaussian map. To reliably and stably update Gaussians outside the LiDAR field of view, we introduce a novel conditional Gaussian constraint that aligns these Gaussians closely with the nearest reliable ones. The targeted adjustment enables LiV-GS to achieve fast and accurate mapping with novel view synthesis at a rate of 7.98 FPS. Extensive comparative experiments demonstrate LiV-GS's superior performance in SLAM, image rendering and mapping. The successful cross-modal radar-LiDAR localization highlights the potential of LiV-GS for applications in cross-modal semantic positioning and object segmentation with Gaussian maps.

翻译：本文提出LiV-GS，一种适用于室外环境的激光雷达-视觉SLAM系统，其利用三维高斯作为可微分空间表征。值得注意的是，LiV-GS是首个在大规模室外场景中直接将离散稀疏的激光雷达数据与连续可微分高斯地图进行对齐的方法，克服了传统激光雷达建图中固定分辨率的局限。该系统通过共享协方差属性将点云与高斯地图对齐以实现前端跟踪，并将法向方向整合至损失函数中以优化高斯地图。为可靠稳定地更新激光雷达视场外的高斯单元，我们提出一种新颖的条件高斯约束，使这些高斯单元与最近邻可靠高斯单元紧密对齐。通过针对性调整，LiV-GS能够以7.98 FPS的速率实现快速精准建图及新颖视角合成。大量对比实验证明LiV-GS在SLAM、图像渲染与建图方面具有优越性能。成功的跨模态雷达-激光雷达定位突显了LiV-GS在基于高斯地图的跨模态语义定位与物体分割领域的应用潜力。