由灰度图像重构曲面三维形状算法研究与实现  

Study of algorithm of reconstructing 3D figures from 2D gray image and its realization

作　　者：乌秀春[1] 郭东明[1] 王晓明[1] 丁梦蛟[1] 周伟峰[1] 

机构地区：[1]大连理工大学机械工程学院,辽宁大连116024

出　　处：《大连理工大学学报》2002年第6期701-705,共5页Journal of Dalian University of Technology

基　　金：国家自然科学基金资助项目(59975016).

摘　　要：由物体表面的二维灰度图像重构其三维几何形状法(由明暗恢复形状法),其关键是寻求对应的数学物理模型稳定可靠的数值解法.首先利用变分原理,将一个非线性的双曲方程问题转化为一个泛函的极小化问题;然后应用有限差分思想和非线性最小二乘问题的高斯-牛顿法将泛函中的变量离散化和线性化;最后应用高斯-塞德尔迭代法形成了曲面各点的梯度值及高度值.对合成和实际图像的计算及数控仿形加工实验验证表明,该算法有效可行.Reconstructing 3D figures of the surface from 2D gray image (shape from shading), the key is the method of setting up stable and reliable numerical solution for the mathematic\|physical model. Firstly, with variational principle, a nonlinear hyperbolic equation is converted into a question of minimization of functional; and variables of functional are discretized and linearized applying finite difference theory and Gauss\|Newton iterative; finally the surface gradient and height are reconstructed with Gauss\|Seidel iterative. The result of reconstruction from a synthetic and real image and numerical control machining shows that the algorithm is efficient and feasible.

关 键 词：灰度图像 三维形状算法 最小二乘法 明暗恢复形状法 曲面重构 迭代算法 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]