基于平均差分计算的任意光照环境下三维表面重建算法

针对采用偏心格式求解图像辐照方程时只能针对特定光源计算的特点，提出了一种针对不同光照方向环境下求解明暗恢复形状(SFS)问题的有限差分算法。这个方法利用泰勒展开线性化反射图函数，设计了一种新的平均加权差分格式求解图像辐照方程。由于新差分格式无条件稳定且具有二阶截断误差，它可以有效地克服偏心差分格式条件稳定和一阶截断误差精度不高的不足。理论分析和实验结果表明，文中提出的无条件稳定的差分算法对各种光照环境均能给出一个理想的恢复结果，且计算精度优于以往的算法。

A Shape Reconstruction Method for Any Light Direction Based on Weighted Difference Scheme

A new finite difference method is proposed to solve the image irradiance equation of shape from shading. Firstly, the non-linear term in the reflectance map is approximated by a Taylor-expansion. Then the resulting linear partial difference equation is solved numerically by a semi-implicit average difference scheme under initial and boundary conditions. Surface height is obtained iteratively by successive over-relaxation method, and the method for selecting optimal relaxation factor is also given in the paper. Experiments with synthetic images demonstrate that the new algorithm is suitable for any light direction and the reconstruction results compare favorably to the traditional ones.