Geometric Properties Estimation And Feature Identification From 3D Point Cloud

With the rapid developments of 3D rangefinder technology,3D point cloud data have been applied to many application domains, such as reverse engineering, industrial inspection, autonomous navigation, protection of historical relics, and virtual reality. As the foundation for achieving these applications, the processing techniques of 3D point cloud data play a crucial role. In the processing techniques, the geometric properties estimation and feature identification from 3D point cloud data are two key techniques, because they are the basis of the follow-up processing, such as multi-view registration, region segmentation, and geometric modeling, and have a very important effect on actual applications. Therefore, it is very significant for improving the application level of 3D point cloud data to research accurate geometric properties estimation and reliable feature identification.Generally, two types of discrete geometric graphics can be obtained from 3D point cloud data:curve point cloud data and surface point cloud data. The curve point cloud data are composed of a series of sequential discrete points on the curves of physical objects, and in geometry the curve point cloud data are also called the discrete curve. The surface point cloud data are composed of a set of discrete points on the surfaces of physical objects, and in geometry the surface point cloud data are also called the discrete surface. Therefore, geometric properties estimation from 3D point cloud data are correspondingly categorized into two types:geometric properties estimation from discrete curves and geometric properties estimation from discrete surfaces. In order to improve the accuracy, robustness, and suitability of the geometric properties estimation from 3D point cloud data, this paper will do an in-depth research on the geometric properties estimation from discrete curves and discrete surfaces, and then achieve the feature identification from regular 3D point cloud data based on these estimation methods. The main contributions of this paper are as follows:1. Geometric properties estimation from discrete curves based on discrete derivativesGeometric properties estimation from discrete curves focuses on estimating the ge-ometric properties of curves, such as unit tangent vectors, principal normal vectors, bi-normal vectors, curvatures, and torsions, from discrete curves. In this paper, a novel method is proposed for estimating the geometric properties from discrete curves based on discrete derivatives. The proposed method combines derivative estimation with classical differential geometry theory, and discretizes the geometric properties of the parametrized differential curve based on the definitions of the discrete derivatives. Then, the geometric properties are estimated from discrete curves by using the discrete approximation. The proposed method avoids the problem of the arc length approximation, which can improve the estimation accuracy. Furthermore, the proposed method is independent of any con-tinuous curve model and estimates the geometric properties directly from discrete data points, which makes it suitable for different geometric shapes of discrete curves. Another advantage of the proposed method is the robustness to noise, because of the calculation characteristics of the discrete derivatives.2. Geometric properties estimation from discrete surfaces based on discrete curve modelGeometric properties estimation from discrete surfaces focuses on estimating the geometric properties of surfaces, such as surface normals, principal curvatures, principal directions, Gaussian curvature, and mean curvature, from discrete surfaces. In this paper, a novel method is proposed for estimating the geometric properties from discrete surfaces based on discrete curve model. The proposed method uses multiple discrete curves to model the local discrete surface at a given point by constructing the discrete curve model of the discrete surface at that point. The discrete curve model has much more degrees of freedom, and therefore can better represent the local surface geometry, which will improve the estimation accuracy. Based on the discrete curve model, the geometric properties are estimated from discrete surfaces according to the Meusnier theorem and the Euler formula by using the geometric properties of the discrete curves which is defined in this paper. Because this proposed estimation method for discrete surfaces is based on the above-mentioned estimation method for discrete curves, it inherits the similar advantages:high estimation accuracy, good suitability for different geometric shapes of discrete surfaces, and strong robustness to noise.3. Feature identification from 3D point cloud data based on principal curvature behaviorsFeature identification from 3D point cloud data focuses on identifying various kinds of geometric discontinuity points, such as C0 discontinuity points, C1 discontinuity points, and C2 discontinuity points, from 3D point cloud data. These geometric discontinuity points constitute the important geometric and topological information of object surfaces, and present the shape features of physical objects. In this paper, a novel feature identi- fication method is proposed for identifying the C0. C1, and C2 discontinuity points from regular 3D point cloud data based on principal curvature behavior. The proposed method estimates the principal curvatures and principal directions from 3D point cloud data at first. Then, the behaviors of the principal curvatures along the principal directions are deeply researched at the geometric discontinuities, and the C0 and C1 discontinuity points are identified by finding the extrema and zero-crossings of the principal curvatures. Fur-thermore, the proposed method calculates the similarity indicator at a given point by using the principal curvature variations in the two neighborhoods of that point along the principal directions. Then, based on the similarity indicators, the C2 discontinuity points are identified. The threshold value of the similarity indicator is taken from [0,1], which characterises the relative relationship, makes the identification of the C2 discontinuity points easier and more reasonable, and improves the performance of feature identifica-tion.In order to analyze the performance of the proposed methods for estimating the geometric properties from 3D point cloud data, the geometric properties estimation ex-periments are made on discrete curves and discrete surfaces, and the proposed estimation methods are compared with other typical approaches. The experimental results demon-strate that the proposed estimation methods have good performance, and are robust to noise and suitable for different geometric shapes of discrete curves and discrete surfaces. Based on the geometric properties estimation from 3D point cloud data, the feature iden-tification experiments are also made on 3D point cloud data, The experimental results demonstrate that the proposed identification method is efficient and reliable.