We address the problem of autonomous exploration of unknown environments using a Micro Aerial Vehicle (MAV) equipped with an active depth sensor. As such, the task consists in mapping the gradually discovered environment while planning the envisioned trajectories in real-time, using on-board computation only. To do so, we present SplatPlanner, an end-to-end autonomous planner that is based on a novel Permutohedral Frontier Filtering (PFF) which relies on a combination of highly efficient operations stemming from bilateral filtering using permutohedral lattices to guide the entire exploration. In particular, our PFF is computationally linear in input size, nearly parameter-free, and aggregates spatial information about frontier-neighborhoods into density scores in one single step. Comparative experiments made on simulated environments of increasing complexity show our method consistently outperforms recent state-of-the- art methods in terms of computational efficiency, exploration speed and qualitative coverage of scenes. Finally, we also display the practical capabilities of our end-to-end system in a challenging real-flight scenario.