基于混合反射模型的SFS有限元方法的研究

Study on Finite Element Algorithm of Shape from Shading Based on Hybrid Reflection Model

提出了基于混合反射模型的由明暗恢复物体三维形状的有限元算法。用正方形面元逼近光滑曲面,把曲面表示为所有节点基函数的线性组合;基于既含有漫反射成分又有镜面反射成分的混合模型,结合节点基函数,将反射图线性化。考虑数字图像的特点,直接使用离散形式的SFS问题的亮度约束形式,用最小化方法得到高度满足的线性方程;使用Kaczmarz算法计算出表面三维形状。使用合成图像和实际图像验证该文算法的有效性,探讨了该算法的性能。

A finite element algorithm of shape from shading based on hybrid reflection is proposed in this paper.A smooth surface,which is approximated by surface elements,is expressed by a linear combination of a set of basis functions.Hybrid reflection models which containing diffuse reflectance and specular reflectance are used.Based on a set of basis functions which using discrete finite element technique,the hybrid reflection models are linearized.Digital image＇s characteristic is considered,so the discrete form of total brightness error of input image and reflection map is used.Then a set of linear equations about the unknown surface is derived using minimization approaches.The relative height of unknown surface is calculated using these equations by Kaczmarz algorithm.Then experiment on synthetic images and real images is given to illuminate the efficiency of the present method.At last performance of the method is also discussed.