Point cloud registration is a fundamental problem in 3D computer vision. This paper addresses scan matching for reliable Mobile LiDAR Systems (MLSs) that can traverse different environments and be robust against outliers and noise. High reliability in multiple scenarios is vital to many applications, such as autonomous driving, but poor feature representations often compromise it. This paper introduces an expressive feature called the rectangle-flattening representation to enhance reliability. First, we propose a clustering method based on density, direction and flattening that allows regions to grow in a "planes first, lines second, less flattened structures last" manner. This method can extract rectangles from environments where planes are scarce. Second, we develop a squared point-to-rectangle distance function that is piecewise yet continuously differentiable to leverage the rectangle-flattening representation for scan matching. Unlike the traditional point-to-plane or plane-to-plane residual functions that rely on planar surfaces in other directions to provide translational information, our point-to-rectangle distance function is intrinsically translation-aware. Extensive experiments are conducted on three aspects: scan matching accuracy, robustness, and odometry and mapping on MLSs. We compare our algorithm to several state-of-the-art methods using KITTI and Ford datasets in scan matching accuracy test with environments covering residential areas, highways, rural areas, downtown areas and campuses. Rigorous experiments show that among all of the methods compared, only RectMatch has an overall scan matching success rate surpassing 90% and even 95% across the two datasets. The robustness tests demonstrate that RectMatch can better deal with random outliers and Gaussian noise. For a comprehensive evaluation of RectMatch for MLSs, the third test incorporates five publicly available datasets using different laser scanners on multiple platforms traversing different environments. The results show high algorithm reliability and accuracy.
