Research On B-spline Fitting Algorithm Based On Dense Point Cloud Data

At present,curve and surface fitting is widely used in three-dimensional measurement,industrial design,archaeology,medicine and other fields,and curve and surface fitting has also become a hot and difficult point.As early as the 1970 s,curve fitting has begun to take shape,but due to the complexity of the data,the diversity of the surface,the smooth splicing requirements and the different smoothness requirements,the research on curve and surface fitting So far there is no uniform and universal method.The research object of this paper is the dense point cloud data that is actually scanned,and the point cloud is collected by scanning equipment.Dense point cloud data has a high degree of freedom and a large amount of data,which increases the difficulty of interpolation and fitting,and may also cause overfitting.Therefore,a B-spline fitting algorithm is proposed to solve the over-fitting problem.The data is divided into blocks and then spliced,so that the amount of data for a single process is reduced.The main work is as follows:1.Analyze the actual data points,and perform preprocessing such as denoising,filtering,and compression on the data.2.Analyze the basic fitting function Bézier,B-spline and NURBS spline,compare their advantages and disadvantages according to the differences in their principles and applications,and select the B-spline function as the fitting function model.3.Perform a smoothness analysis on the data,combine the requirements of existing algorithms,the nature of the function model,and the accuracy requirements to determine the smoothness conditions that need to be met.Different smoothing requirements have different restrictions on the conditions of curve fitting.4.This article uses cubic B-spline interpolation algorithm as the curve fitting model.B-spline fitting has the advantages of continuity and locality,but it does not necessarily pass through the value points and cannot make full use of high-precision data;while interpolation fitting can pass through the value points,but its ability to locally modify is poor.Combining the two can make the fitting curve pass through the value points one by one and have the advantages of continuity and locality.5.In the B-spline interpolation algorithm,a feature point selection algorithm is proposed,which is more targeted for dense point cloud data on the basis of the general cubic B-spline interpolation algorithm.Due to the huge amount of collected dense point cloud data,the time complexity and algorithm complexity are greatly increased.The feature point selection algorithm retains the feature points and removes the non-feature points.Under the premise of meeting the accuracy requirements of the final fitting curve,the number of fitting segments minimize.6.Although segmented fitting surface patches can reduce the amount of data processed in a single time,the ultimate goal of our fitting is to restore the three-dimensional model of the object,so we also need to splice the fitted surface patches.The splicing of Bézier surfaces has been very mature,so a B-spline surface splicing method introduced in this article is to transform the boundary into a Bézier curve and then directly splice it.The other is to introduce a "transition surface" to achieve smooth splicing between two curved surfaces.Using point cloud data for instance verification,it can be seen that the feature point selection algorithm,cubic B-spline interpolation algorithm and surface stitching algorithm are correct in principle and technically feasible.