Consistent ICP for the registration of sparse and inhomogeneous point clouds Hiˆ ep Quang Luong *† , Michiel Vlaminck * , Werner Goeman ‡ and Wilfried Philips * * Image Processing and Interpretation research group Department of Telecommunications and Information Processing Ghent University - iMinds, Ghent, Belgium † Email: hiep.luong@UGent.be ‡ Grontmij, Ghent, Belgium Abstract—In this paper, we derive a novel iterative closest point (ICP) technique that performs point cloud alignment in a robust and consistent way. Traditional ICP techniques minimize the point-to-point distances, which are successful when point clouds contain no noise or clutter and moreover are dense and more or less uniformly sampled. In the other case, it is better to employ point-to-plane or other metrics to locally approximate the surface of the objects. However, the point-to-plane metric does not yield a symmetric solution, i.e. the estimated transformation of point cloud p to point cloud q is not necessarily equal to the inverse transformation of point cloud q to point cloud p. In order to improve ICP, we will enforce such symmetry constraints as prior knowledge and make it also robust to noise and clutter. Experimental results show that our method is indeed much more consistent and accurate in presence of noise and clutter compared to existing ICP algorithms. I. I NTRODUCTION The registration or alignment of point clouds is an important process in 3D mobile mapping, which is the process of collect- ing geospatial data from a mobile vehicle. In general, mobile mapping employs a wide range of different sensors, which can roughly be divided in two categories: the measurement sensors (e.g. 360-degrees vision cameras and LiDAR scanners) and positioning sensors (e.g. global positioning system (GPS), wheel encoders and inertial navigation system (INS)). GPS and inertial measurement units (IMU) allow for rapid and quite accurate determination of the position and attitude of the equipment or vehicle, or in other words, estimating the ego-localization. Still there are some shortcomings: e.g. GPS relies on external communication and lacks accuracy, while se- quential IMU data (e.g. from gyroscopes and accelerometers) suffers from drift and must therefore be processed, e.g. by Kalman filters [5]. An alternative approach to ego-localization (when GPS and IMU are missing or unavailable) is to perform relative positioning based on images or overlapping point clouds. The class of algorithms that jointly estimates ego-localization (or odometry when we observe the positions over time) and the 3D reconstruction/mapping is called simultaneous localization and mapping (SLAM). The performance of visual SLAM (based on images or video) heavily depend on the environment such as weather and light conditions (e.g. overexposure due to direct sunlight). On the other hand, LiDAR technology is more robust to these conditions. A very popular and simple technique that performs LiDAR odometry and mapping is iterative closest point (ICP). ICP is the main component in large-scale 3D mapping and often it is combined with other techniques such as global pose graph optimization or loop closure in a larger framework to minimize drift and to enforce consistency on a global scale. In this paper, we will concentrate on improving the accuracy and consistency of the core ICP algorithm, which then can be plugged in large-scale 3D mapping frameworks. LiDAR technology measures the distance between the ob- jects and the device by illuminating the target with a laser light. The main advantage of LiDAR is that it can provide a lot of range measurements within small time window with errors that are relatively constant irrespective of the distances measured. An example of LiDAR scanners is the Velodyne series 1 , which produce enormous point clouds, capturing the scene at approximately 10Hz using a relative low number of scan lines (typically 16, 32 or 64 lines). Each full rotation or sweep produces an inhomogeneous point cloud that is densely sampled along the scan lines, but is sparse in the direction across the scan lines. This type of point clouds puts additional challenges in the alignment process, especially ICP: the measured points in two subsequent moved point clouds are (almost) never physically the same, which is a different starting point compared to the basic definition of ICP, which effectively minimizes the distances of the closest points assuming that they are physically the same. By locally approximating the surface of the scanned objects and minimizing the distance between a point and this surface, the registration is improved greatly. With the emergence of affordable LiDAR technology, mo- bile mapping systems are evolved into the third generation. These new scanners become more lightweight, smaller and cheaper, which make them more attractive to be mounted on (aerial) drones or to be used in hand-held devices. We refer the interested reader to an extended review on existing mobile mapping technology [17] and overviews of commercially available mobile mapping systems, e.g. [14] and [22]. In the next sections, we briefly discuss the state-of-the-art 1 http://velodynelidar.com