Normal estimation of point cloud based on sub-neighborhood clustering

Abstract

In this paper, we propose a method to estimate normal vectors based on neighborhood clustering segmentation, which improves the accuracy of normal-vector estimation for sharp features. The proposed method adjusts the neighborhood through Gauss mapping and clustering segmentation to solve the problem of inaccurate estimation of the normal vector in the sharp-feature region. First, the normal vectors of the point cloud are initially estimated by principal component analysis (PCA). Next, the neighborhood of points from different patches, which are close to the sharp feature, are mapped to a unit Gauss sphere, and the point cloud on the unit sphere is clustered. All points of the cluster belonging to the target point are divided into sub-neighborhoods. Finally, with this sub-neighborhood as input, the normal vector of the point is accurately calculated by PCA. Experiments show that, even for noise and non-uniform sampling, the method proposed herein outperforms previous methods in terms of quality of results and running time.

An error compensation method for 3D measurement of step edge in fringe projection profilometry

“…Then point cloud is reconstructed by FPP. Then a normal estimation based on PCA is adopted [16], since PCA finds an orthogonal basis that best represents a given data set and estimates normal accurately.…”

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“…The normal vector ($$$ \mathbb{N} $$$) of a surficial material point $$$ {\boldsymbol{x}}_{\mathrm{i}} $$$ can be estimated using Equation (22). 41 $$$$ {\mathbb{N}}_{{\boldsymbol{x}}_i}=\frac{1}{N}\sum \limits_{k=1}^N\kappa \left({\boldsymbol{x}}_k-{\boldsymbol{x}}_i\right),\kern2em \mathbf{\forall}{\boldsymbol{x}}_i\in \Omega, \kern0.5em {\boldsymbol{x}}_k\in {H}_{{\boldsymbol{x}}_i}, $$$$ where $$$ N $$$ is the number of material points in the point cloud ($$$ {H}_{{\mathbf{x}}_{\mathrm{i}}} $$$) and $$$ \kappa $$$ is Gauss weight. Surficial material points are divided into two types: featured and ordinary.…”

“…If $$$ c $$$ is larger than a value calculated based on the density of the point cloud and the noise scale, $$$ {\boldsymbol{x}}_{\mathrm{i}} $$$ is considered as a featured point, otherwise it is an ordinary one 41 …”

“…If c is larger than a value calculated based on the density of the point cloud and the noise scale, x i is considered as a featured point, otherwise it is an ordinary one. 41 In step (1-c), the algorithm calculates a hypothetical radius ( r x i ) of all surficial material points x i and all adjacent material points in H x i and L x i which can be given by Equation (26). The reason why a hypothetical radius is determined…”