A method to remove random errors from 3D point clouds is proposed. It is based on the estimation of a local geometric descriptor of each point. For mobile mapping LiDAR and airborne LiDAR, a combined standard mesurement uncertainty of the LiDAR system may supplement a geometric approach. Our method can be applied to any point cloud, acquired by a fixed, a mobile or an airborne LiDAR system. We present the principle of the method and some results from various LiDAR system mounted on UAVs. A comparison of a low-cost LiDAR system and a high-grade LiDAR system is performed on the same area, showing the benefits of applying our denoising algorithm to UAV LiDAR data. We also present the impact of denoising as a pre-processing tool for ground classification applications. Finaly, we also show some application of our denoising algorithm to dense point clouds produced by a photogrammetry software.