应用于偏振重构方法中的高精度梯度场积分法

A High-precision Gradient Field Integration Method Applied to Shape from Polarization Method

提出一种改进的梯度场积分方法,用于减小偏振重构方法重建透明表面的误差,在模式法的基础上,选取复指数函数作为展开式的基函数,采用更加精确的差分采样模型构建差分与被测斜率之间的关系。为使新模型计算的差分数据满足离散傅里叶变换对于尺寸和周期性的要求,采用反对称扩展与周期性扩展相结合的方法扩展被测斜率数据。通过一系列对比仿真实验去分析提出方法的精度,结果显示其重建后的误差明显低于Frankot-Chellapa算法。为了验证提出的算法在偏振重构方法中的性能,对一个半径为101.89 mm的透镜表面进行了重建实验,提出的方法能够获取较高质量的表面点云数据,相比于Frankot-Chellapa算法的结果(均方根误差为0.129764 mm),该方法重建表面的误差(均方根误差为0.017239 mm)有明显的降低。

An improved gradient field integration method is presented to reduce the error of the Shape from polarization method in reconstructing transparent surfaces.Based on the modal method,the complex exponential function is chosen as the basis of the expansion.A more accurate differential sampling model is used to construct the difference-slope relationship.In order to satisfy the size and periodicity requirements of discrete Fourier transform for the difference data calculated by the new model,the measured slope data are extended by combining the anti-symmetric extension with the periodic extension.The accuracy of the proposed method has been analyzed by a series of comparative simulation experiments.The results show that the reconstruction error of our method is significantly lower than that of the Frankot-Chellapa algorithm.In order to verify the performance of the proposed algorithm in Shape from polarization method,the reconstruction experiment of lens surface with a radius of 101.89 mm has been carried out in this paper.Compared with the result of the Frankot-Chellapa algorithm(root mean square error is 0.129764 mm),the reconstruction error of this method(root mean square error is 0.017239 mm)is significantly reduced.