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.
出处
《大连理工大学学报》
CAS
CSCD
北大核心
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).
