Quality point cloud normal estimation by guided least squares representation

• A guided subspace clustering framework and its theoretical analysis are presented.
• SGLRS is proposed as a special case of the framework.
• A rapid algorithm with a natural parallelism is devised for SGLRS.
• A quality normal estimation method is proposed based on SGLRS.
• A subspace structure propagation algorithm is designed to speed up the estimation.

In this paper, we present a quality point cloud normal estimation method via subspace segmentation based on guided least squares representation. A structure guided low-rank subspace segmentation model has been employed in normal estimation (LRRSGNE). In order to select a consistent sub-neighborhood for a point, the subspace segmentation model is adopted to analyze the underlying structure of its neighborhood. LRRSGNE generates more faithful normals than previous methods but at the price of a long runtime which may take hours. Following its framework, two improvements are proposed. We first devise a novel least squares representation based subspace segmentation model with structure guiding (LSRSG) and design a numerical algorithm which has a natural parallelism for solving it. It segments subspaces as quality as the low-rank model used in LRRSGNE but with less runtime. We prove that, no matter whether the subspaces are independent or disjoint, it generates a block-diagonal solution which leads to a quality subspace segmentation. To reduce the computational cost of the normal estimation framework further, we develop a subspace structure propagation algorithm. Only parts of the candidate feature points’ neighborhoods are segmented by LSRSG and those of the rest candidate points are inferred via the propagation algorithm which is faster than LSRSG. The experiments exhibit that our method and LRRSGNE generate comparable normals and are more faithful than other state-of-the-art methods. Furthermore, hours of runtime of LRRSGNE is reduced to just minutes.

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