一种从明暗恢复形状的快速黏性解算法  

A Fast Viscosity Solution Algorithm for Shape from Shading

作　　者：王国珲[1] 韩九强[1] 贾洪海[1] 张新曼[1] 

机构地区：[1]西安交通大学电子与信息工程学院,西安710049

出　　处：《西安交通大学学报》2009年第6期43-47,共5页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(60602025);教育部高等学校博士点专项科研基金资助项目(20050698025)

摘　　要：针对传统的从明暗恢复形状(SFS)算法存在误差大、耗时长的问题,提出了一种SFS的快速黏性解算法(PSFS-FVS).首先假定物体表面反射模型为朗伯模型,建立透视投影下的图像辐照度方程,然后将该方程转化为包含物体表面深度信息的静态Hamilton-Jacobi偏微分方程,使用非线性规划原理逼近该微分方程的黏性解,进而得到物体表面的三维形状.合成花瓶图像的实验结果表明:与Prados-Faugeras算法相比,PSFS-FVS算法在相同迭代次数时,恢复三维形状高度的平均相对误差降低了8.7%;在相同的误差条件下,所需的CPU运行时间减少了23.5%.实际人脸图像的三维形状恢复结果表明,PSFS-FVS算法在恢复局部细节信息时更加准确有效.Focusing on the high error and time consuming of the algorithms for shape from shading （SFS）, a fast viscosity solution algorithm of perspective SFS （PSFS-FVS） is proposed. The image irradiance equation is established on the basis of Lambertian reflectance model and perspective camera projection. Then the equation is transformed into a static Hamilton-Jacobi partial differential equation （PDE） that contains the shape information of a surface. The viscosity solution of the resulting PDE is approximated by using a nonlinear programming method, and then the surface shape is generated. Experimental results and comparisons with the Prados-Faugeras algorithm on synthetic vase image show that the mean relative error of the height of the PSFS-FVS algorithm is reduced by 8. 7% with the same iterations, and the CPU time of the PSFS-FVS algorithm is decreased by 23. 5% at the same error, respectively. Reconstruction results from real face image show that the PSFS-FVS algorithm is more accurate and effective than the Prados-Faugeras algorithm in dealing with the local of the surface.

关 键 词：从明暗恢复形状 黏性解 透视投影 非线性规划 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]