| With the continuous change and rapid development of data acquisition technology,all visible things of the real world can be transformed into data.The 3D point cloud are widely used in many fields such as architecture,military affairs,historical relics protection,virtual reality and so on because of its advantage of recording the surface properties of objects.Generally,3D point cloud data can be divided into curve point cloud data and surface point cloud data.The research of this paper is aimed at the latter.As far as surface point cloud data are concerned,the local structure information is reflected in the geometric properties such as principal curvature,normal and principal direction,which provides a basis for regional segmentation and model reconstruction.Therefore,the accuracy of geometric properties estimation directly affect the application effect of surface point cloud data.According to the theory of differential geometry,the geometric properties of continuous surface are determined by the first fundamental quantity and the second fundamental quantity,and partial derivative is the basis of all these.In this paper,in order to improve the accuracy,universality and robustness of geometric properties estimation,the classical theories of these continuous surfaces are improved and applied to discrete scenes,and the geometric properties estimation of regular gridded point cloud data is deeply studied.The main contributions are as follows:1.In order to calculate the partial derivative of each discrete point in 3D point cloud,this paper proposes a discrete partial derivative estimation method.Firstly,the parameter interval of quadratic differentiable surface with the shape of z=f(x,y) is segmented,and the gridded sampling points formed constitute discrete surfaces.Because the partial derivative of continuous surface is the rate of change of function caused by the change of another parameter when one parameter is constant,the discrete point cloud is similar.In this paper,according to the geometric meaning of tangent,the tangent along two parameter directions and are fitted by the least square method,and the discretization form of each order partial derivative are given.Then,the convergence of discrete partial derivatives of each order are proved,that is,when the sampling density is infinite,the estimated value of partial derivative of discrete point clouds approach the real values infinitely.In order to study the accuracy of partial derivative estimation and the influencing factors of estimation effect,we conducted experiments under different sampling density,neighborhood radius and noise intensity.The experimental results show that the discrete partial derivative estimation method proposed in this paper has high accuracy,strong robustness to noise,and is suitable for different geometric shapes.2.In this paper,the discrete partial derivative estimation method is combined with differential geometry theory,and the calculation formulas of geometric properties such as principal curvature of continuous parametric surfaces are discretized.In order to reduce the influence of noise,this paper selects two groups of different position parameters and their corresponding parameter line directions,and parameterizes them along the two groups of parameter line directions according to chord length,and establishes one-to-one correspondence between discrete points and parameters,then estimating the geometric properties of point cloud data.Finally,the two estimation results are combined.In the experimental stage of chapter 3,this paper selects different shapes of spatial discrete point clouds to study,including discrete point clouds sampled from continuous parametric surfaces and real scene point cloud data,and makes error comparison with other related methods.The results show that this method does not depend on any surface or curve model,and has good universality for any shape of point cloud data.For data with noise,this method can effectively weaken the influence of noise.In the indoor areas and spaces,our method can also clearly extract the boundary between those regions with different regional characteristics. |
