基于表面局部最高点估计的明暗恢复形状算法

基于数据逼近强约束的针图恢复算法是近年来提出的一种较为成功的从明暗恢复形状（shape from shading）的算法，但由于该算法在非垂直光线下得到的初始化针图的误差较大，并且不能保证法向量有解或有唯一解，为了解决SFS算法存在的问题，提出了一种改进的SFS算法。该改进算法从分析非垂直光线下图像梯度图与针图之间的关系入手，首先检测图像局部最亮点位置；然后根据照度方程估计表面局部最高点的位置，同时对梯度方向进行调整，并建立方程组；最后针对方程组解的不同情况，提出了相应的处理方法。改进后的算法，对于垂直光线和非垂直光线下的情况同样有效，从而扩大了基于数据逼近强约束的SFS算法的适用范围。从合成图像和实际图像的实验结果可以看出，采用改进的算法可以得到比基于数据逼近强约束的算法更接近真实表面的初始化针图和初始化高度。

Shape from Shading by Estimating the Local Highest Points of Surface

Imposing data-closeness as a hard constraint to needle-map of surface is proved to be a successful approach of shape from shading(SFS)technique in recent years, but the initialization needle map of the algorithm is much different from the true one of surface when the light source direction is not vertical and the uniqueness of needle map cannot be ensured.Aiming at avoiding the drawbacks of the algorithm based on the hard constraint, a modified method is presented in this paper.After the relationship of image gradient map and surface needle map is analyzed, the positions of the local brightest points of image are firstly detected and the positions of the local highest points of surface are estimated according to the irradiance equation.Secondly, at each point, the gradient direction of image is updated and the equation group is set up.For different cases of the equations, corresponding solutions are presented in this algorithm.The modified algorithm is effective when the illuminant direction is either vertical or non-vertical and the applicability of the algorithm is improved. Experimental results on synthetic and real images show that much accurate initial needle map and height are obtained.