Markov-Renewal Single-Photon LiDAR Simulator

Single-photon LiDAR (SP-LiDAR) simulators face a dilemma:fast but inaccurate Poisson models or accurate but prohibitively slow se-quential models. This paper breaks that compromise. We present a sim-ulator that achieves both fidelity and speed by focusing on the critical,yet overlooked, component of simulation: the photon count statistics. Ourkey contribution is a Markov-renewal process (MRP) formulation that,for the first time, analytically predicts the distribution of registered pho-ton counts under dead time. To make this MRP model computationallytractable, we introduce a spectral truncation rule that efficiently com-putes the complex covariance statistics. By proving the shift-invarianceof the process, we extend this per-pixel model to full histogram cubegeneration via a precomputed lookup table. Our method generates 3Dcubes indistinguishable from the sequential gold standard, yet is ordersof magnitude faster. This finally enables large-scale, physically faithfuldata generation for learning-based SP-LiDAR reconstruction. Projectpage: https://mars-splidar.github.io/.