Crease-Aware Normal Vectors from Unstructured Point Clouds

Abstract We propose a method to estimate normal vectors from noisy 3D point cloud data, with a focus on preserving first-order discontinuities of the underlying surface. The crease-aware normal vector (CNV) is computed per point without requiring any triangulated surface nor connectivity information. The main idea of the proposed work is to find a suitable subset of the neighborhood which gives denoised surface normals close to the true ones, especially near the crease, e.g., ridges and valleys. We first introduce a flatness measure for any given set of points in $$\mathbb {R}^{3}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mrow> <mml:mi>R</mml:mi> </mml:mrow> <mml:mn>3</mml:mn> </mml:msup> </mml:math> by considering the local principal directions. We propose a method to partition the neighborhood and select the flattest one through our flatness measure. We provide analysis to show that the proposed subset can give the true normal vectors for points near creases. We present various numerical experiments showing that the proposed method gives clearer first-order discontinuities, and we further showcase its applications to surface reconstruction from noisy and incomplete point clouds, and solving PDEs on unstructured point clouds using crease-aware normal vectors.