Various types of systems or technologies can be used to collect data in a 3D space. For example, LiDAR (light detection and ranging) and RADAR (radio detection and ranging) systems are commonly used to generate point cloud data for 3D space around vehicles, for such functions as localization, mapping, and tracking. This disclosure provides improvements for processing the point cloud data that has been collected. The processing improvements include using a three dimensional polar depth map to assist in performing nearest neighbor analysis on point cloud data for object detection, trajectory detection, freespace detection, obstacle detection, landmark detection, and providing other geometric space parameters.