Geometric Properties Estimation From Line Point Clouds Using Gaussian-Weighted Discrete Derivatives

With the rapid development of 3D scanning technology,3D point clouds data has been widely used in industrial buildings and daily life,for example,industrial detection,architectural measurement,virtual reality,etc.The processing of 3D point clouds data is the basis of the above applications and plays an extremely important role in related fields.In the processing of 3D point clouds data,the estimation of geometric characteristics,as the processing method of 3D point clouds data,lays a solid foundation for regional segmentation,model reconstruction and other work,and also has a direct impact on the application effect of 3D point clouds data.Generally speaking,3D point clouds data can be divided into line point clouds data and point clouds data.The main research object of this paper is the 3D line point clouds data.How to analyze and process the line point clouds data and estimate its geometric characteristics is a problem we are concerned about.In this paper,an estimation method of the first order derivative of line point clouds based on gaussian weight is proposed.The method uses the idea of weighted linear regression and linear regression with linear constraints,and combines differential geometry theory to estimate the first order discrete derivatives of line point clouds more accurately.Similarly,the higher order discrete derivatives of line point clouds are defined and their convergence is analyzed.Based on Gaussian-weighted discrete derivatives,we can also obtain the geometric properties,such as curvature(second derivative),principal(minor)normal vector,torsion and so on.In the real environment,due to environmental factors or objective factors such as machines and equipment,the 3D point clouds data are often noisy.The method proposed in this paper can not only improve the accuracy of estimation without noise,but also reduce the impact of noise in the case of noise.In the process of estimating the derivative of line point clouds,the selection of multiple parameters is involved,such as the bandwidth(wavelength)parameter of weight function,sampling density,neighborhood radius,noise intensity,etc.Under the condition that the sampling density is determined,this paper gives a method to estimate the noise intensity.This method can not only estimate noise intensity,but also get the recommended value of neighborhood radius,which makes it unnecessary for us to spend a lot of time in parameter selection.This method not only avoids the inaccuracy of the results caused by blindly selecting parameters,but also reduces the time consumed by parameter selection.The accuracy of the estimation results is also improved.In order to analyze the method proposed in this paper for estimating the geometric characteristics of 3D line point clouds,the experimental operations are carried out for plane line point clouds data of different shapes and spatial line point clouds data,and the comparison is made with other relevant methods.The results show that the method proposed in this paper has high universality for line and point clouds data of different shapes.It improves the accuracy of estimation results under the condition of no noise and reduces the impact of noise under the condition of noise.In order to analyze the problem of parameter selection,this paper proposes a method to estimate noise intensity,and conducts many experiments on plane line point clouds and space line point clouds.The experimental results show that the method proposed in this paper has high accuracy in estimating noise intensity,and it provides convenience for solving the parameter selection problem involved in the derivative estimation of line point clouds data.