Recent 3D Gaussian Splatting (3DGS) representations have demonstrated remarkable performance in novel view synthesis; further, material-lighting disentanglement on 3DGS warrants relighting capabilities and its adaptability to broader applications. While the general approach to the latter operation lies in integrating differentiable physically-based rendering (PBR) techniques to jointly recover BRDF materials and environment lighting, achieving a precise disentanglement remains an inherently difficult task due to the challenge of accurately modeling light transport. Existing approaches typically approximate Gaussian points' normals, which constitute an implicit geometric constraint. However, they usually suffer from inaccuracies in normal estimation that subsequently degrade light transport, resulting in noisy material decomposition and flawed relighting results. To address this, we propose GeoSplatting, a novel approach that augments 3DGS with explicit geometry guidance for precise light transport modeling. By differentiably constructing a surface-grounded 3DGS from an optimizable mesh, our approach leverages well-defined mesh normals and the opaque mesh surface, and additionally facilitates the use of mesh-based ray tracing techniques for efficient, occlusion-aware light transport calculations. This enhancement ensures precise material decomposition while preserving the efficiency and high-quality rendering capabilities of 3DGS. Comprehensive evaluations across diverse datasets demonstrate the effectiveness of GeoSplatting, highlighting its superior efficiency and state-of-the-art inverse rendering performance. The project page can be found at https://pku-vcl-geometry.github.io/GeoSplatting/.

We study the problem of multi-robot active mapping, which aims for complete scene map construction in minimum time steps. The key to this problem lies in the goal position estimation to enable more efficient robot movements. Previous approaches either choose the frontier as the goal position via a myopic solution that hinders the time efficiency, or maximize the long-term value via reinforcement learning to directly regress the goal position, but does not guarantee the complete map construction. In this paper, we propose a novel algorithm, namely NeuralCoMapping, which takes advantage of both approaches. We reduce the problem to bipartite graph matching, which establishes the node correspondences between two graphs, denoting robots and frontiers. We introduce a multiplex graph neural network (mGNN) that learns the neural distance to fill the affinity matrix for more effective graph matching. We optimize the mGNN with a differentiable linear assignment layer by maximizing the long-term values that favor time efficiency and map completeness via reinforcement learning. We compare our algorithm with several state-of-the-art multi-robot active mapping approaches and adapted reinforcement-learning baselines. Experimental results demonstrate the superior performance and exceptional generalization ability of our algorithm on various indoor scenes and unseen number of robots, when only trained with 9 indoor scenes.