Point Cloud Normal Estimation by Fast Guided Least Squares Representation

Normal estimation is an essential task for scanned point clouds in various CAD/CAM applications. The method (GLSRNE) based on guided least squares representation (GLSR) balances speed with quality well among state-of-the-art methods. First, it segments each neighborhood into multiple sub-neighborhoods. For some neighborhoods, the segmentation is obtained by GLSR which is an efficient subspace segmentation model and widely applied in other applications. The segmentation of the rest neighborhoods is inferred via the subspace structure propagation (SSP) algorithm. Then, each sub-neighborhood is fitted by a plane. The plane achieving the minimum distance with the current point is selected for the final normal estimation. We make improvements for effectiveness and efficiency in the following three aspects. First, to improve the speed of GLSR, we propose a novel iterative algorithm to reduce the computation complexity from $O(n^{3})$ to $O(n^{2})$ with its convergence guaranteed theoretically, where $n$ represents the number of the data points. Moreover, this proposed algorithm will also be useful for other applications. Second, we add a normal constraint for SSP to improve accuracy. Third, when selecting one plane to estimate the final normal, we consider the match between the plane and all neighbors, whereas GLSRNE only considers the match between the plane and the current point. The experiments exhibit that our method is faster than GLSRNE and more effective than GLSRNE and other state-of-the-art methods.