基于梯度场的紧致差分最小二乘面形重建算法

Least square surface reconstruction method with compact finite difference scheme from measured gradient field

为快速准确根据测得的梯度场重建表面面形,针对基于最小二乘全局积分的重建技术,采用紧致差分算子建立全局最优化的代价函数以提高重建精度,将代价函数表示为Sylvester方程,利用Hessenberg-Schur算法求解,将常用最小二乘全局积分技术的空间和时间复杂度分别从O (N2)和O (N3)降低到O(N)和O(N3/2)。实验结果表明:采用四阶精度的紧致差分算子时,文中算法重建精度比高阶截断误差最小二乘积分法(HFLI)和全局最小二乘法(GLS)提高了一个数量级,采用六阶精度的紧致差分算子时重建精度比基于样条的最小二乘积分法(SLI)提高了一个数量级;鲁棒性优于GLS,弱于HFLI和SLI;重建速度显著优于HFLI和SLI,略优于GLS。

In order to reconstruct the 3D surface from gradient fields quickly and accurately, a new fast and accurate least squares integration algorithm was proposed. Compact finite difference scheme was introduced into optimization equation for better accuracy. Then the objective function was represented as a Sylvester function. With Hessenberg-Schur algorithm, the space and time complexity were reduced from O(N2) and O(N3) to O(N) and O(N3/2), respectively. The experiment result showed that when the 4 thorder compact scheme is used, the accuracy of the new method is improved by one order higher than Higher-order Finite-difference-based Least-squares Integration(HFLI) and Global Least-Squares(GLS).While with 6 th-order compact scheme, the accuracy is improved by one order higher than Spline-based Least-squares Integration(SLI). The robustness of the proposed method is weaker than that of HFLI and SLI, but better than GLS. The reconstruction speed was obviously faster than that of HFLI and SLI.