【摘要】 基于物体表面图像灰度信息的三维几何形状反求(由明暗恢复形状),已成为工业界和学术界研究的热点问题之一。首先给出描述该问题的数学物理模型,并利用变分原理将其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方法,将该泛函极小化问题归结为求解线性方程组。最后利用该算法产生的迭代公式对合成图像进行计算,并应用曲面造型软件CAXA(制造工程师)进行曲面重构,从而验证了该方法的有效性和可行性。更多还原

【Abstract】 The reverse of 3D figures based on 2D gray image of the surface (shape from shading) has become the focus topic in industry and academia. Firstly the mathematical physics model that describes the question is presented and is converted into minimization of functional with variational principle, and with finite difference and nonlinear least square method, the question of minimization is come down to solving system of linear equations. Finally, using the iterative formula that the algorithm produces, a synthetic image is calculated. And the surface is reconstructed in the software CAXA. The result shows the reconstructing method is efficiency and feasible.更多还原