【作者】 乌秀春；

【导师】 郭东明；

【作者基本信息】 大连理工大学 ， 机械制造及其自动化， 2002， 博士

【摘要】 直接由物体的二维灰度图像恢复其三维几何形状(由明暗恢复形状)的曲面测量方法和技术，能以自然方式提取物体表面的形状信息，且易于实现系统间的信息集成，尤其是该方法属于非接触测量方法，特别适合于测量由弹性模量低的易变形材料制成的零件，近年来一直是基于视觉的图像测量领域研究的难点和热点问题。本文以高分辨率的数字相机为实验手段，以光度学原理及非线性偏微分方程理论和数值解法为基础，探讨根据曲面的二维图像灰度信息获取曲面三维几何形状信息的理论和方法，并利用优化方法确定光照模型的光照参数，减小了模型参数不准确带来的测量误差，为发展由明暗恢复形状的复杂曲面(又称自由曲面)非接触测量方法和技术做一些初步的研究工作。 结合光度学原理，从实验研究入手，通过用数字相机实际拍摄的典型曲面(球面)的二维灰度图像，应用非线性最小二乘优化方法研究确定了现有的Lambert、Phong、Torrance-Sparrow和Cook-Torrance四种常用局部光照模型的光照参数，利用统计分析原理分析了这四种光照模型在当前实验条件下对实际图像灰度数据的拟合精度，并对拟合精度较高的Torrance-Sparrow光照模型加以完善和改进，发展出一种适合于曲面测量的改进光照模型。 在针对理想朗伯漫反射模型所提出的由单幅灰度图像重构曲面的理论和计算方法基础上，导出了基于改进光照模型的单幅灰度图像光照度方程，揭示出基于单幅灰度图像的曲面重构问题实质是一个非线性偏微分方程的求解问题。考虑到该方程具有病态特性，求得的解不唯一，具有一般数学物理反问题的特征，利用变分原理，将其转化为一个泛函的极小化问题，通过正则化处理，使原问题具有唯一解；然后应用有限差分思想和求解非线性最小二乘问题的方法，将泛函中的变量离散化和线性化，进而转化为一个标准最小二乘问题来求解。 为了提高曲面测量精度，本文还开展了基于单目多幅图像的曲面重构工作。以非线性最小二乘理论为基础，以典型曲面上各点的理论灰度值与实测灰度值的误差平方和最小为目标建立非线性方程组，通过求解非线性方程组来确定光照模型的各个光照参数。根据多幅图像上固定位置一点灰度值的变化列多个非线性方程，通过求解该非线性方程组，确定出各选取点的法向量；然后通过复化积分确定选取点的高度值，并利用变分和有限差分思想对所得表面进行进一步的迭代和修正，以减小重构误差。 最后对一个典型曲面——球体表面进行模拟计算和实际三维重构实验，实验和计算结果表明，本文的算法具有一定的准确性和适用性。并在Windows操作平台上，采用VC++编程技术，开发研制了基于二维图像灰度信息的三维曲面重构软件。更多还原

【Abstract】 Measuring method and technique that 3D surface shape is recovered from 2D gray image (shape from shading) can obtain surface shape by natural way and easily realize the information integration of intersystem. Particularly, this technique belongs to non-contact measurement, and it has become a puzzle and hotspot question in image measuring domain based on vision in recent years. In this paper, with high resolution digital camera as experimental means, and based on principle of photometry and theory and numerical solution for nonlinear partial differential equation, research is developed around the theory and technique to reconstruct 3D surface shape from 2D gray image. The parameters of illumination model are determined by optimization method, so as to reduce the error caused inaccurate illumination parameters. It is our purpose to do some initial work in order to develop non-contact measuring method and technique for complex surface (free-form surface) based on shape from shading.For consideration of principle of photometry and experimental research, with 2D gray image of typical surface (spherical surface) taken with digital camera, and by use of nonlinear least square optimizing method, the illumination parameters of four local illumination models, that are Lambert, Phong, Torrance-Sparrow and Cook-Torrance model, are determined. And with statistics analytical principle, regression analyses are made to compare the fitting precision of these illumination models under the current experiment condition. Comparing Torrance-Sparrow model with others, an improved illumination model for measurement of surface is developed.With the basis of the theory and numerical solution of ideal Lambert diffuse model on shape from shading, the image irradiance equation based on improved illumination model is derived, thereby the fact is disclosed that the question of reconstruction from a single gray image is how to solve a nonlinear partial differential equation. In view of ill-posed characteristic of the equation, with variational principle, solving of a nonlinear hyperbolic equation is attributed to minimization of a functional. So the equation has unique solution through regularization theory. Then variables of the functional are discretized and linearized with finite difference and nonlinear least squares techniques, accordingly minimization of the functional is converted into standard least square question.With a view to the difficulty and precision of surface reconstruction from a single image, the reconstruction from monocular multiple images is developed in the paper. With the basis of nonlinear least squares theory, the system of nonlinear equations is established by minimizing the error quadratic sum of theoretical and actual gray level of the points on the typical surface, and the parameters of the illumination models can be determined by means of the least-squares procedure. A new system of nonlinear equations can be formed from the variation gray of same point in multiple images and the optimum solution of the system canbe obtained, so that the normal vector at that point of the surface can be defined. Then we can get the surface height at the point by applying composite numerical integration. According to variational calculus and finite difference method, the fitted surface is further iterated and modified, so the reconstruction error can be reduced.The accuracy of the algorithm is verified with synthetic and real image of spherical surface. The result of experiment and calculation shows that the algorithm is effective and feasible and has stated application value. 3D surface reconstruction software based on 2D gray images has been developed with Visual C++ Programming language on the platform of Windows operation system.更多还原