A survey of LiDAR-camera calibration: from explicit geometric constraints to differentiable scene representations

LiDAR–camera extrinsic calibration is essential for reliable multi-sensor perception, as even small pose errors can induce noticeable misalignment between projected point clouds and image structures. While the problem reduces to estimating a six-degree-of-freedom rigid transformation, its fundamental challenge lies in establishing reliable constraints across heterogeneous LiDAR and camera measurements. This survey organizes the literature along the central theme of "from explicit geometric constraints to differentiable scene representations". Existing methods fall into four categories: target-based calibration using explicit geometric constraints, targetless calibration via natural-scene matching, learning-based cross-modal alignment with online correction, and joint calibration leveraging differentiable scene representations. For each category, we examine typical evidence sources, representative optimization formulations, advantages, and limitations. Special focus is placed on recent advances in NeRF, 3D Gaussian Splatting, and 2D Gaussian Splatting, which reformulate calibration from local correspondence estimation into a scene-level differentiable optimization problem. The survey concludes by identifying an emerging trend toward hybrid systems that synergistically integrate explicit geometric cues, learned priors, uncertainty quantification, and efficient differentiable rendering, thereby enabling robust online multi-sensor calibration.