完备正交V-系统与点云数据拟合

Complete Orthogonal Function System V and Points cloud Fitting

提出了对点云数据进行曲面拟合的一种新方法,它基于一类L2[0,1]上完备正交的函数系(称之为V-系统)。V-系统由分段多项式组成,它包括各个层次的间断函数,具有多分辨分析特性和局部性。给出了k次V-系统(k=0,1,2,3)的具体表达式;利用有限项Fourier-V级数展开式,高效地生成点云数据显示的被测量对象的几何造型。检测例子表明,这种方法对很广泛遇到的一类问题而言,处理过程简单、速度快、精度高。

A novel approach to points cloud fitting was given. The work is based on a class of complete orthogonal k-degree polynomials in L^2[0, 1] （called V-system）. V-system which is composed of piecewise polynomials including every degree polynomials has advantageous properties of multi-resolution analysis and local. The expression of k-degree （k = 0,1,2,3） V-system was given, which effectively generated geometrical sculpt from surveying object displayed of points cloud by using limited number items of Fourier-V progression. The experimentations indicate that this approach has simple processing, fast calculating and high precision for some ordinary project.