In this paper we present an edge-based hardware and software framework for the 3D detection and mapping of parked vehicles on a mobile mapping platform for the use case of on-street parking statistics. First, we investigate different point cloud-based 3D object detection methods on our extremely dense and noisy depth maps obtained from low-cost RGB-D sensors to find a suitable object detector and determine the optimal preparation of our data. We then retrain the chosen object detector to detect all types of vehicles, rather than standard cars only. Finally, we design and develop a software framework integrating the newly trained object detector. By repeating the parking statistics of our previous work (Nebiker et al., 2021), our software is tested regarding the detection accuracy. With our edge-based framework, we achieve a precision and recall of 100% and 98% respectively on any parking configuration and vehicle type, outperforming all other known work on on-street parking statistics. Furthermore, our software is evaluated in terms of processing speed and volume of generated data. While the processing speed reaches only 1.9 frames per second due to limited computing resources, the amount of data generated is just 0.25 KB per frame.