【作者】 廖熠；

【导师】 赵荣椿；

【作者基本信息】 西北工业大学 ， 计算机应用技术， 2006， 博士

【摘要】 本课题来源于国家自然科学基金项目“三维表面形状被动重构方法研究”(项目号：60141002)利“十五”国防预研课题“军用图像并行处理算法技术”(项目号：413160103)，并且得到了与英国Surrey大学共同申请的英国皇家学会基金项目“三维表面重构(3D SurfaceReconstruction)”(批准号：Q775)的经费支持。在国防和民用等应用领域中，地形模型一直扮演着一个非常重要的角色。尽管大量遥感图像(航片、卫片等)间接提供了丰富的地形信息，但现有三维表面重建技术未能从中有效提取地形表面。另一方面，分形技术已被广泛应用于地形模拟，但却没有与三维重构技术有效结合。为此本文以一种重要的三维重构技术——从明暗恢复形状(Shape-From-Shading，SFS)技术为主，研究和探讨了基于分形的地形图像表面三维重建问题，不仅在方法上克服了传统分形描述工具难以直接与观测图像数据相结合的困难，而且在一定误差范围内可以从观测地形图像中有效提取相应地表形状。本文做出了以下贡献：通过回顾和分析不同约束条件和先验知识在SFS问题中的应用，本文得出以下结论：(1)无论给出确定性约束条件还是随机先验分布，相应的SFS问题均可表示为一个优化问题；(2)SFS问题的约束条件需同时满足先验知识要求和算法稳定性；(3)SFS算法中参数确定和表面形状获取交互迭代或同时迭代；(4)由于反射函数的高度非线性，在SFS算法中采用泰勒线性化方法容易使求解过程陷入局部极小状态。本文在分析分形布朗曲面各分形指标计算的共性基础上，提出了一种利用分形特征变量相关性获取近似分形表面模型的一般性方法。并分别以基于方差图、功率谱、逐层增量以及小波等分析方法为基础，实现了四种基于不同特征变量的具体分形表面模型。构造结果表明，这四种具体近似模型均能有效地反映分形表面的统计特征，较好地逼近了非线性分形表面模型。与传统分形工具相比，本文方法构造的分形表面模型更为直观，易于控制和推广，便于与观测数据相结合并可简化计算。求解高度非线性的SFS问题时，需要构造一系列线性最小二乘子问题。通常采用泰勒线性化并假定其规测噪声为Gauss分布，容易导致求解过程陷入局部极小。为此本文提出了一种改进方法，即应用Pentland线性化结构将SFS问题的非线性部分转化为系统参数，使其观测噪声具有非Gauss分布，并可通过本文分形模型对其进行估计。实验表明，该办法可较好，地避免问题的解陷入局部极小状态。本文利用正则化理论将基于分形的SFS问题表述为一个分形正则化问题，并提出了一种分形正则化SFS算法。其特点是可由迭代次数控制表面分形维数，且具有可控性和灵活性。实验表明，该算法可有效地从地形图像中恢复地表形状。与传统SFS方法相比，该方法的地表恢复结果保持了地形原有的分形特征，而又不易受到噪声影响。对于表面呈现非均匀分形特征的情况，本文利用局部分形分析，分形正则化算法和块Jacobi迭代框架，提出了一种具有内外层迭代结构的局部分形正则化SFS算法。其内层各块迭代次数控制了相应的局部分形维数，外层循环次数则控制了表面的整体一致性。实验表明，该算法可有效地从复杂图像中提取地形表面，可在一定程度上消除某些具体应用中出现的表面拓扑错误。针对复杂的多重分形地形图像的SFS问题，本文提出了一种基于多级优化方法(Multi-Level Optimization，MLO)的多尺度分形正则化SFS算法。该方法利用较大尺度取得的表面结果，对较小尺度中的局部分形迭代常量作修正，达到多尺度分形约束的效果。其各尺度段子块的迭代次数控制了多重分形特征。实验表明，该算法可有效提取复杂地表形状。与经典SFS算法相比，本文算法易于作并行计算和处理大型图像问题，并可灵活控制分形特征，具有可扩展性。更多还原

【Abstract】 This project is sponsered by National Natural Science Foundation of China, National Defense Pre-Research Foundation of China, and The Royal Society Foundation of UK.In many applications in the fields of national defense and daily life, terrain model plays an important role. Although plenty of indirect terrain information is available from remote-sensing images, direct 3D terrain surfaces have not been efficiently extracted applying the latest 3D reconstruction techniques. On the other hand, the fractal techniques have been widely applied to terrain simulation but not been explicitly combined with 3D reconstruction techniques. So this thesis researches and discusses the problems of fractal-based 3D terrain surface reconstruction on both models and algorithms. The thesis focuses on Shape-From-Shading(SFS) as one of the most important 3D reconstruction techniques. This not only overcomes the difficulties of applying traditional fractal techniques to the observed images, but also efficiently obtains the terrain surface shape from the observed images within tolerable errors. And the following are the main contributions in this thesis.By reviewing and analyzing the SFS applications with different constraints and prior knowledge we conclude that (1) regardless of the deterministic constraint or given stochastic prior distribution, the corresponding SFS problem can be formed as an optimization problem, (2) the constraints in SFS problems have to meet the requirement of the prior knowledge and algorithm stability, (3) the parameter determining and surface shape extracting iterate one after another or at the same time in the SFS algorithms, and (4) due to the high nonlinearity of the reflectance function, applying the Tailor linearization method to SFS algorithm tends to local minimum state.Based on the analysis of the common features of computing different fractal parameters, we propose a general method to construct an approximated fractal model by using the correlation of fractal feature variables. And then four fractal models with different features are provided based on Variogram Analysis, Power Spectra Analysis, Layered-increment Analysis and Wavelet Analysis respectively. The constructed results show that these four approximating fractal models can give the statistic fractal features and efficiently approximate the nonlinear fractal model. Compared to common fractal tools, the fractal model constructed by our method is more intuitive, easier to control, very convenient to combine with observed data and more amenable to computing.A series of linear MSE sub-problems have to be formed to solve the highly non-linear SFS problem. Generally, Tailor linearization method is adopted and Gaussian noise is assumed, which can easily lead to local minimums. So we provide a modified method in which the nonlinear parts in the SFS problem are transformed as systematic parameters by applying Pentland linearization method, the noise of which has non-Gaussian distribution and can be estimated by our fractal model. The experimental results show that the proposed method can avoid the local minimum state better than the traditional methods. The fractal-based SFS problem is formed as a fractal regularization problem in this thesis and an iterative algorithm is provided by using the regularization theory. An advantage of this method is that the fractal dimension of the recovered surface can be controlled by the number of iterations, which is controllable and flexible. The experimental results show that our method can efficiently recover the surface shape from the terrain image. Compared to traditional SFS methods, the recovered terrain surface by our method keeps the fractal features of the terrain while is not easily affected by the noises.As the non-homogeneously fractal surface being considered, a local fractal regularization SFS algorithm with an inner-outer loop structure is proposed based on the block-Jacobi iteration scheme, the local fractal analysis and our fractal regularization method. The local fractal dimension is controlled by the number of iterations of the corresponding block in the inner loop, while the global surface consistency is determined by the number of iterations of outer loop. The experimental results show that our method can efficiently recover the surface shape from the complicated terrain image and get rid of the topological errors appearing in some applications.As for the SFS problem of the complicated multi-fractal terrain image, a multi-scale fractal regularization method, based on the theories of Multi-Level Optimization (MLO) methods is proposed. The proposed method achieves multi-scale fractal constraints through adjusting the constant vector in the local fractal regularization SFS problem in the smaller scale by the recovered surface obtained in the larger scale. The multi-fractal features of the recovered surface are dominated by the number of iterations relating to the different block in the different scale. The experimental results show that our multi-scale fractal regularization method can efficiently recover the surfhce shape from the complicated terrain image.Compared to the typical SFS methods, our methods are easier to compute, lends itself to parallel computational techniques, and are more suitable for large image problems. Furthermore, our methods can flexibly control the fractal features of the recovered surface and be extended to combine with other models.更多还原