针对采用偏心格式求解明暗恢复形状问题中的图像辐照方程时只能针对特定光源计算的特点,提出了一种新的稳定差分解法。首先使用泰勒展式线性化反射图函数,然后结合定解条件,讨论了一种新的交错差分格式用于求解图像辐照方程的具体算法,并给出了新差分格式稳定性和收敛性的具体证明。结合最佳松弛因子的选取方法,表面高度的最终值采用超松弛法迭代计算求得。经过多组图像计算可知,该新方法适用于任意的光照环境,且重构精度高于已有算法。

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 cross difference scheme,combining with initial and boundary conditions.We prove its stability and convergence in detail.Surface height is obtained iteratively by successive over-relaxation method,and the method of selecting optimization factor is also given in the paper.Experimental results on synthetic images demonstrate the new algorithm suits for any light direction and the reconstruction results are better than the traditional ones.