基于分形的地形图像表面重建研究
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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。
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.
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。
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.
引文
[1] B.K.P.Horn and M.J.Brooks, The Variational Approach to Shape from Shading, Computer Vision, Graphics, and Image Processing, 33, 1986, pp 174—208.
[2] M. J. Brooks, Two Results Concerning Ambiguity in Shape from Shading, in Proceedings of the National Conference on Artificial Intelligence, American Association for Artificial Intelligence: Washington, D.C., U.S.A., 1983, pp26-39.
[3] J.Oliensis, Uniqueness in Shape from Shading, International Journal of Computer Vision, 6(2),1991,pp75—104.
[4] P. Dupuis and J. Oliensis, Shape from Shading: Provably Convergent Algorithms and Uniqueness Results, in Proceedings of 1994 European Conference on Computer Vision (ECCV'94), 1994, pp 259—268.
[5] R. Kozera, Uniqueness in Shape from Shading Revisited, Journal of Mathematical Imaging and Vision, 7, 1997, pp 123—138.
[6] G. Ulich, Provably Convergent Methods for the Linear and Nonlinear Shape from Shading Problem, Journal of Mathematical Imaging and vision, 9,1998, pp 69—82.
[7] J.Oliensis, Shape from Shading as a Partially Well-Constrained problem, CVGIP: Image Understanding, 54(2), 1991.9,pp 163—183.
[8] R. Zhang, P.-S.Tsai, J.E.Cryer and M.Shah, Shape from Shading : A Survey, IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 21(8), 1999.8, pp 690—705.
[9] R.T.Frankot and R.Chellappa, A Method for Enforcing Integrability in Shape from Shading Algorithms, IEEE Trans, on Pattern Analysis and Machine Intelligence (PAMI), 10(4), 1988.7,pp 439—451.
[10] T.-C. Pong, R.M.Haralick and L.GSharpiro, Shape from Shading Using the Facet Model,Pattern Recognition, 22(6), 1989, pp 683—695.
[11] K.M.Lee and C.-C. J. Kuo, Shape from Shading with a Linear Triangular Element Surface Model, IEEE Trans, on Pattern Analysis and Machine Intelligence (PAMI), 15(8), 1993.8, pp815—812.
[12] H. Saito and N.Tsunashima, Estimation of 3-D Parametric Models from Shading Image Using Genetic Algorithms, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 668—670.
[13] J.-W. Hsieh, H.-Y.M. Liao, M.-T. Ko and K.-C. Fan, Wavelet-Based Shape from Shading,Graphical Models and Image Processing, 57(4), 1995.7, pp 343—362.
[14] G.-Q. Wei and G. Hirzinger, Parametric Shape-from-Shading by Radial Basis Functions,IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 19(4), 1997.4, pp353—365.
[15] B.-H. Kim and R.-H. Park, Shape from Shading and Photometric Stereo Using Surface Approximation by Legendre Polynomials, Computer Vision and Image Understanding, 66(3), 1997. 6, pp 255—270.
[16] R. Szeliski, Fast Shape from Shading, CVGIP: Image Understanding, 53(2), 1991. 3, pp 129—153.
[17] O. E. Vega and Y. H. Yang, Shading Logic: A Heuristic Approach to Recover Shape from Shading, IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 15(6), 1993. 6, pp 592—597.
[18] S. I. Cho, H. Saito and S. Ozawa, Geometric Solution of Shape from Shading Problem, Korean-Japan Joint Workshop on Computer Vision (FCV'98), Feb. 2, 1998, pp 19-24.
[19] P. -S. Tsai & M. Shah, A Fast Linear Shape from Shading, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp 734—736.
[20] B. K. P. Horn, Height and Gradient from Shading, International Journal of Computer Vision, 5(1), 1990, pp 37—75.
[21] K. Ikeuchi and B. K. P. Horn, Numerical Shape from Shading and Occluding Boundaries, Artificial Intelligence, 17(1981) 141-184.
[22] K. Ikeuchi, Comment On "Numerical Shape from Shading and Occluding Boundaries", Artificial Intelligence, 59, 1993, pp 89—94.
[23] 刘辉、谈正，从遮挡边缘和局部阴影恢复表面形状，中国图像图形学报，3 (7)，1998．7， pp 588—590。
[24] K. Atsuta, M. Sanoworasil and S. Kondo, A New Method of Estimating Shape from Shading by using a Constraint at Zero-crossings of Image Brightness, in Proceedings of 9th International Conference on Pattern Recognition, vol. 2, 1988, pp 666-668.
[25] D. Lee, Algorithms for Shape from Shading and Occluding Boundaries, in Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition, 1988, pp 478-485.
[26] M. Shao, T. Simchony, and R. Chcllappa, Direct analytical methods for solving Poisson equations in computer vision problems, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (5), May 1990, pp 435-446.
[27] R. T. Frankot and R. Chellappa, A method for enforcing integrability in shape from shading algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), July 1988, pp 439-451.
[28] Y. Choc and R. L. Kashyap, A 3-D Texture Model Of Natural Scene Image, in Proceedings of Twenty-Second Asilomar Conference on Signals, Systems and Computers, 1988, Vol 1, pp 463-467.
[29] M. A. Penna, A shape from shading analysis for a single perspective image of a polyhedron, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(6), June 1989, pp 545-554.
[30] N. Shrikhande and G. Stockman, Surface orientation from a projected grid, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (6), June 1989, pp 650-655.
[31] K. Hartt and M. Carlotto, A method for shape-from-shading using multiple images acquired under different viewing and lighting conditions, in Proceedings of IEEE Computer Society Conference on ,Computer Vision and Pattern Recognition, 1989, pp 53 -60.
[32] Y.-S. Choi, S.-C. Chung and J.-S. Choi, Reinforced Shape From Shading Using Multigrid Techniques, in Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics, 1988(2), pp 766 -770.
[33] G. Ron and S. Peleg, Nonlinear multiresolution: a shape-from-shading example, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(12), Dec. 1990, pp 1206-1210.
[34] D. Forsyth and A. Zisserman, Mutual illumination, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1989, pp 466 -473.
[35] M. J. Korsten and Z. Houkes, Parametric descriptions and estimation, a synergetic approach to resolving shape from shading and motion, in Proceedings of Third International Conference on Image Processing and its Applications, 1989, pp 5 -9.
[36] Q. Zheng and R. Chellappa, Estimation of surface topography from stereo SAR images, in Proceedings of International Conference on Acoustics, Speech, and Signal Processing,1989(3),pp 1614-1617.
[37] J. Thomas, W. Kober and F. Leberl, Multiple-image Sar Shape From Shading, in Proceedings of 12th International Geoscience and Remote Sensing Symposium, Canadian Symposium on Remote Sensing, 1989(2), pp 592 -596.
[38] Y. Iwahori, H. Sugie and N. Ishii, Reconstructing shape from shading images under point light source illumination, in Proceedings of 10th International Conference on Pattern Recognition, 1990(1), pp 83 -87.
[39] J. J. Clark and A. L. Yuille, Shape from shading via the fusion of specular and Lambertian image components, in Proceedings of 10th International Conference on Pattern Recognition,1990(1),pp88-92.
[40] B. Guindon, Development Of A Shape-from-shading Technique For The Extraction Of Topographic Modem From Individual Spaceborne Sar Images, 12th International Canadian Symposium on Remote Sensing, Geoscience and Remote Sensing Symposium, 1989(2), pp597 -602.
[41] B. Guindon, Development of A Shape-from-Shading Technique for the Extraction of Topographic Models from Individual Spaceborne SAR Images, IEEE Trans. Geoscience and Remote Sensing, vol. 28 no. 4, pp. 654-661.
[42] P. K. Bora, Y. V. Venkatesh, and K. R. Ramakrishnan, Shape from shading using discrete polynomials, ACE '90. Proceedings of XVI Annual Convention and Exhibition of the IEEE In India, 1990, pp 260-264.
[43] Q.Zheng and R.Chellappa, Estimation of Illuminant Direction, Albedo, and Shape from Shading, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7), July 1991,pp 680-702.
[44] R. -X. Li and S. Pai, Improvement Of Bathymetric Data Bases By Shape From Shading Technique Using Side-scan Sonar Images, in Proceedings of Ocean Technologies and Opportunities in the Pacific for the 90's (OCEANS '91), 1991(1), pp 320 -324.
[45] B. Kim and P. Burger, Depth and Shape from Shading Using the Photometric Stereo Method,in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991, pp 416—427.
[46] S. Banerjee, P. S. Sastry, and Y. V. Venkatesh, Surface reconstruction from disparate shading: an integration of shape-from-shading and stereopsis, in Proceedings of 11th International Conference on Pattern Recognition (Conference A: Computer Vision and Applications),1992(1),pp 141 -144.
[47] K. M. Lee and C.-C. J. Kuo, Shape from shading with a linear triangular element surface model, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(8), Aug. 1993,pp815-822.
[48] P.Dupuis and J.Oliensis, Direct Method for Reconstructing Shape from Shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp 453-458.
[49] M.Bichsel and A.P.Pentland, A Simple Algorithm for Shape from Shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp459—465.
[50] B. V. Funt and M. S. Drew, Color space analysis of mutual illumination, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(12), Dec. 1993, pp 1319 -1326.
[51] W.-S. Ching, P.-S. Toll, and W.-L. Goh, Concurrent acquisition and processing of multi-spectral shadow information for 3D computer vision, in Proceedings of the International Conference on Industrial Electronics, Control, and Instrumentation, 1993(3), pp1736-1741.
[52] J. E. Crycr, P.-S. Tsai, and M. Shah, Integration of shape from X modules: combining stereo and shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1993, pp 720 -721.
[53] D. R. Hougen and N. Ahuia, Adaptive polynomial modelling of the reflectance map for shape estimation from stereo and shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 991 -994.
[54] M. S. Langer and S. W. Zucker, Diffuse shading, visibility fields, and the geometry of ambient light, in Proceedings of Fourth International Conference on Computer Vision, April 1993,pp 138-147.
[55] H. Schultz, Retrieving shape information from multiple images of a specular surface, IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(2), Feb. 1994, pp 195 -201.
[56] A. P. R. Cooper, A Simple Shape-From-Shading Algorithm Applied to Images of Ice-Covered Terrain, IEEE Transactions on Geoscienee and Remote Sensing, 32(6), Nov. 1994, pp 1196-1198.
[57] A. G. Jones and C. J. Taylor, Automated interpretation of SEM images, in Proceedings of IEEE Region 10's Ninth Annual International Conference on Theme of Frontiers of Computer Technology, 1994(2), pp 872 -876.
[58] W. P. Cheung, C. K. Lee, and K. C. Li, Surface reconstruction by integrating stereo vision with shading, in Proceedings of the 20th International Conference on Industrial Electronics, Control and Instrumentation, 1994(2), pp 968 -971.
[59] T. Wada, H. Ukida, and T. Matsuyama, Shape from shading with interreflections under proximal light source-3D shape reconstruction of unfolded book surface from a scanner image, in Proceedings of the Fifth International Conference on Computer Vision, 1995, pp 66-71.
[60] M. Jones and J. P. Oakley, A new shape representation for fast 3D reconstruction from multiple 2D perspective images, in Proceedings of IEE Colloquium on New Developments in 3D Image Capture and Application, 1995, pp 4/1 -4/3.
[61] Y. Numagami, Y. Kajiwara, O. Nakamura, and T. Minami, Reconstruction of the 3-D shape of an object from a 2-D intensity image, in Proceedings of Canadian Conference on Electrical and Computer Engineering, 1995(2), pp 1188 -1191.
[62] G.-Q. Wei and G. Hirzinger, Parametric shape-from-shading by radial basis functions, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(4), April 1997, pp 353 -365.
[63] A.J.Stewart and M. S. Langer, Towards accurate recovery of shape from shading under diffuse lighting, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996, pp 411 -418.
[64] K. Deguchi and T. Okatani, On identification of singular points using photometric invariants for global shape from shading problem, in Proceedings of the Fourteenth International Conference on Pattern Recognition, 1998(2), pp 1787 -1790.
[65] C.-K. Huang, C. Pai, and W.-T. Chang, Shape from shading using Ritz method with tent basis,in Proceedings of the 13th International Conference on Pattern Recognition, 1996(1), pp 398-402.
[66] J. Y. Zheng, H. Kakinoki, K. Tanaka, and N. Abe, Computing 3D models of rotating objects from moving shading, in Proceedings of the 13th International Conference on Pattern Recognition, 1996(1), pp 800 -804.
[67] A. Goller, Concurrent radar image shape-from-shading on high-performance computers, in Proceedings of the 13th International Conference on Pattern Recognition, 1996(3), pp 589-593.
[68] R. Lengagne, J.-P. Tarel, and O. Monga, From 2D images to 3D face geometry, in Proceedings of the Second International Conference on Automatic Face and Gesture Recognition, 1996, pp 301 -306.
[69] C. R. Guarino, SAR interferometry: a novel method for enhancing elevation maps by combining interferometry with shape-from-shading, in Proceedings of International Conference on Image Processing, 1996(1), pp 45 -48.
[70] P. L. Worthington and E. R. Hancock, Shape from Shading using Robust Statistics, in Proceedings of 13th International Conference on Digital Signal Processing, 1997(2), pp 1145-1148.
[71] T.-E. Kim, S.-H. Lee, S.-H. Ryn, and J.-S. Choi, Shape recovery of hybrid reflectance surface using neural network, in Proceedings of International Conference on Image Processing,1997(3),pp416-419.
[72] N. Barnes and Z.-Q. Liu, A knowledge based approach to shape from shading, in Proceedings of IEEE International Conference on Intelligent Processing Systems, 1997(2), pp 1390 -1394.
[73] J. Ben-Arie and D. Nandy, A neural network approach for reconstructing surface shape from shading, in Proceedings of 1998 International Conference on Image Processing, 1998(2), pp972 -976.
[74] A. Z. Kouzani, F. He, and K. Sammut, Example-based shape from shading: 3D heads form 2D face images, in Proceedings of 1998 IEEE International Conference on Systems, Man,and Cybernetics, 1998(4), pp 4092 -4097.
[75] S. M. Yamany and A. A. Farag, A system for human jaw modeling using intra-oral images, in Proceedings of the 20th Annual IEEE International Conference on Engineering in Medicine and Biology Society, 1998(2), pp 563 -566.
[76] B. L. Craine, E. R. Craine, C. J. O'Toole, and Q. Ji, Digital imaging colposcopy: corrected area measurements using shape-from-shading, IEEE Transactions on Medical Imaging, 17(6),Dec. 1998, pp 1003-1010.
[77] D. Samaras and D. Metaxas, Coupled Lighting Direction and Shape Estimation from Single Images, in Proceedings of the Seventh IEEE International Conference on Computer Vision,1999(2),pp868-874.
[78] R. C. Wilson and E. R. Hancock, A radar reflectance model for terrain analysis using shape from shading, IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(8), Aug.1999,pp690-706.
[79] S.-Y. Cho and T. W. S. Chow, Shape Recovery from Shading.by a New Neural-Based Reflectance Model, IEEE Transactions on Neural Networks, 10(6), Nov. 1999, pp 1536-1541.
[80] W. Y. Zhao and R. Chellappa, SFS Based View Synthesis for Robust Face Recognition, in Proceedings of the Fourth IEEE International Conference on Automatic Face and Gesture Recognition, 2000, pp 285 -292.
[81] A. G. Bors, E. R. Hancock, and R. C. Wilson, 3-D Terrain from Synthetic Aperture Radar Images, in Proceedings of 2000 IEEE Workshop on Computer Vision Beyond the Visible Spectrum: Methods and Applications, 2000, pp 63 -72.
[82] A. G. Bors, E. R. Hancock, and R. C. Wilson, A Bayesian Framework for Radar Shape-from-shading, in Proceedings of 2000 IEEE Conference on Computer Vision and Pattern Recognition, 2000(1), pp 262 -268.
[83] J. R. A. Torreao, Shape from shading and intensity gradient, in Proceedings of XIII Brazilian Symposium on Computer Graphics and Image Processing, 2000, pp 7-14.
[84] C. H. Q. Forster, C. L. Tozzi, Towards 3D Reconstruction of Endoscope hnages Using Shape from Shading, in Proceedings of ⅩⅢ Brazilian Symposium on Computer Graphics and Image Processing, 2000, pp 90-96.
[85] A. Ortiz and G. Oliver, Shape from shading for multiple albedo images, in Proceedings of 15th International Conference on Pattern Recognition, 2000(1), pp 786-789.
[86] K. M. Lee and C. -C. J. Kuo, Shape from Shading with a Generalized Reflectance Map Model, Computer Vision and Image Understanding, 67(2), 1997. 8, pp 143—160.
[87] S. Pankanti and A. K. Jain, On Integration of Vision Modules, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994(1), pp 316—322.
[88] M. G. -H. Mostafa, S. M. Yamany and A. A. Farag, Integrating Shape from Shading and Range Data Using Neural Networks, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999(1), pp 15—20.
[89] M. S. Lee and G. Medioni, Grouping., -, →, θ, into Regions, Curves, and Junctions, Computer Vision and Image Understanding, 76(1), Oct. 1999, pp 54—69.
[90] D. Nandy and J. B. -Arie, Shape from Recognition and Learning: Recovery of 3-D Face Shapes, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999(1), pp 2—7.
[91] K. M. Lee and C. -C. J. Kuo, Shape from Shading with Perspective Projetion, CVGIP: Image Understanding, 59(2), Mar. 1994, pp 202—212.
[92] 蔚艳、杨振华、王成道，多方法相融合的复杂物体深度信息的恢复，中国图像图形学报，4 (A4)，April 1999，pp 285—288。
[93] L. B. Wolff, S. K. Nayar and M. Oren, Improved Diffuse Reflection Models for Computer Vision, international Journal of Computer Vision, 30(1): 55～71, 1998.
[94] A. M. Bruckstein, On Shape from Shading, Computer Vision, Graphics and image Processing (CVGIP), 44, 1988, pp 139-154.
[95] R. Kimmel and A. M. Bruckstein, Tracking Level Sets by Level Stes: A Method for Solving the Shape from Shading Problem, Computer Vision and Image Understanding (CVIU), 62(2), July 1995, pp 47-58.
[96] R. Kimmel and A. M. Bruckstein, Global Shape from Shading, Computer Vision and Image Understanding (CVIU), 62(3), Nov. 1995, pp 360-369.
[97] I. Shimshoni, R. Kimmel and A. M. Bruckstein, Dialogue: Global Shape from Shading, Computer Vision and Image Understanding (CVIU), 64(1), July 1996, pp 188-189.
[98] E. Rouy and A. Tourin, A Viscosity Solutions Approach to Shape-from-Shading, SIAM Journal of Numerical Analysis, 29(3), June 1992, pp 867-884.
[99] S. Osher, A Level Set Formulation for the Solution of the Diricblet Problem for Hamilton-Jacobi Equations, SIAM J. Math. Anal. 24(5), Sept. 1993, pp 1145-1152.
[100] A. P. Pentland, Local Shading Analysis, IEEE Transactions on Pattern Analysis and Machine Inteligence (PAMI), 6(2), Mar. 1984, pp 170-187.
[101] C.-H Lee and A.Rosenfeld, Impoved Methods of Estimating Shape from Shading Using the Light Source Coordinate System, Artificial Inteligence, 26, 1985, pp 125-143.
[102] A. Pentland, Shape Information from Shading: A Theory about Human Perception, in Proceedings of Internationall Conference on Computer Vision,1988, pp 404-413.
[103] J. E. Cryer, P.-S. Tsai, and M. Shah, Integration of Shape from Shading and Stereo, Pattern Recognition, 28(7), 1995, pp 1033-1043.
[104] Tutorial for Green's Functions: Introduction to Green's Functions, http://www.boulder.nist.gov/div853/greenfn/tutorial.html.
[105] W.-J. Zhang and Y.-H. Zhou, An improved method for shape from shading, in Proceedings of the 9th International Conference on Pattern Recognition, 1988(2), pp 1106-1108.
[106] T. Simchony, R. Chellappa, and Z. Lichtenstein, Pyramid implementation of optimal-step conjugate-search algorithms for some low-level vision problems, IEEE Transactions on Systems, Man and Cybernetics, 19(6), Nov.-Dec. 1989, pp 1408 -1425.
[107] S. Peleg and G. Ron, Nonlinear Multiresolution: A Shape-from-Shading Example, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(12), Dec. 1990, pp 1206-1210.
[108] D. Keren and M. Werman, Variations on regularization, in Proceedings of the 10th International Conference on Pattern Recognition, 1990(1), pp 93 -98.
[109] J. Thomas and W. Kober, Using a Range Constraints In Terrain Reconstruction Using Multiple Image Sar Shape-from-shading, in Proceedings of the 10th Annual International Geosciencc and Remote Sensing Symposium on Remote Sensing Science for the Nineties,1990,pp 1439-1439.
[110] Y. G. Leclerc and A. F. Bobick, The direct computation of height from shading, in Proceedings of 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991, pp 552 -558.
[111] T. A. Mancini and L. B. Wolff, 3 D shape and light source location from depth and reflectance, in Proceedings of 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp 707 -709.
[112] J.-Y. Herve and Y. Aloinionos, Exploratory active vision: theory, in Proceedings of 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp10-15.
[113] K. Ikeuchi, Numerical Shape from Shading and Occluding Contours in a Single View,Artificial Intelligence Lab., MIT, Cambridge, AI Memo 566, 1980.
[114] R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, Shape-from-shading: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(8), Aug. 1999, pp 690 -706.
[115] R. Zhang and M. Shah, Height Recovery from Intensity Gradient, in Proceedings of 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994,pp508-513.
[116] D. Suter, Motion estimation and vector splines, in Proceedings of 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 939 -942.
[117] D. R. Hougen and N. Ahuja, Adaptive Polynomial Modelling of the Reflectance Map for Shape Estimation from Stereo and Shading, in Proceedings of 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 991 -994.
[118] S. Bakshi and Y.-H. Yang, Shape from shading for non-Lambertian surfaces, in Proceedings of 1994 IEEE International Conference Image Processing, 1994(2), pp 130 -134.
[119] Y. Sato and K. Ikeuchi, Reflectance analysis under solar illumination, in Proceedings of the Workshop on Physics-Based Modeling in Computer Vision, 1995, pp 180 -187.
[120] Y.-L. Tian and H. T. Tsui, Shape from shading for non-Lambertian surfaces from one color image, in Proceedings of the 13th International Conference on Pattern Recognition,1996(1),pp258-262.
[121] S.-H. Lai and B.-C. Vemuri, Physically based adaptive preconditioning for early vision,IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6), June 1997, pp 594-607.
[122] A. Yuille, M. Ferraro, and T. Zhang, Surface shape from warping, in Proceedings of 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1997,pp846-851.
[123] E. Kobayashi, T. Fukuda, K. Shimojima, and T. Takusagawa, Shape reconstruction system integrating stereo vision and shape-from-shading-shape reconstruction using pair improvement method, in Proceedings of 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1998(3), pp 1847 -1852.
[124] R. Zhang and M. Shah, Shape from Intensity Gradient, IEEE Transactions on Systems,Man and Cybernetics, Part A, 29(3), May 1999, pp 318 -325.
[125] P. L. Worthington and E. R. Hancock, Data-driven Shape-from-Shading using Curvature Consistency, in Proceedings of 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999(1), pp 288 -293.
[126] H. Lange, Advances in the cooperation of shape from shading and stereo vision, in Proceedings of the Second International Conference on 3-D Digital Imaging and Modeling,1999, pp46-58.
[127] N. J. Ferrier and R. W. Brockett, Reconstructing the Shape of a Deformable Membrane form Image Data, The International Journal of Robotics Research, 19(9), Sept. 2000, pp795-816.
[128] S.-Y. Cho and T. W. W. Chow, Shape and Surface Measurement Technology by an Improved Shape-From-Shading Neural Algorithm, IEEE Transactions on Industrial Electronics, 47(1), Feb. 2000, pp 225 -230.
[129] A. G. Bors, E. R. Hancock, and R. C. Wilson, Terrain Modeling in Synthetic Aperture Radar Images using Shape-from-Shading, in Proceedings of the 15th International Conference on Pattern Recognition, 2000(1), pp 798 -801.
[130] D. Weinshall, Local Shape Approximation from Shading, Journal of Mathematical Imaging and Vision, 4(2), April 1994, pp 119—138.
[131] D. Baskent and B. Barshan, Surface Profile Determination form Multiple Sonar Data Using Morphological Processing, the International Journal of Robotics Research, 18(8),August 1999,pp788-808.
[132] A. Pentland, Fractal-Based Description of Natural Scenes, IEEE Trans. On Pattern Analysis and Machine Intelligence, 6(6), Nov. 1984, pp 661-674.
[133] P. Kube and A. Pentland, On the Imaging of Fractal Surfaces, IEEE Trans. On Pattern Analysis and Machine Intelligence, 10(5), Sept. 1988, pp 704-707.
[134] R. Szeliski and D. Terzopoulos, From Splines to Fractals, Computer Graphics, 23(3),July 1989,pp51-60.
[135] S. J. Lee, P. Y. Wu, and K. T. Sun, Fractal Image Compression Using Neural Networks,in Proc. of International Joint Conference on Neural Networks (IJCNN'98), pp. 613-618,Anchorage, Alaska.
[136] P. W. Fieguth and A. S. Willsky, Fractal Estimation Using Models on Multiscale Trees, IEEE Trans. On Signal Processing, 44(5), May 1996, pp 1297-1300.
[137] Y. Zhou, P.C. Yip, and H. Leung, On the Efficient Prediction of Fractal Signals, IEEE Trans. On Signal Processing, 45(7), July 1997, pp 1865-1997.
[138] G. W. Wornell, A Karhunen-Loeve-like Expression for 1/f Processes via Wavelets, IEEE Trans. On Information Theory, 36(4), July 1990, pp 859-861.
[139] A. H. Tewlik, Correlation Structure of the Discrete Wavelet Coefficients of Fractional Brownian Motion, IEEE Trans. On Information Theory, 38(2), Mar. 1992, pp 904-909.
[140] A. M. Sabatini, Wavelet-Based Estimation of 1/f-Type Signal Parameters: Confidence Intervals Using the Bootstrap, IEEE Trans. On Signal Processing, 47(12), Dec. 1999, pp3406-3409.
[141] P. Flandrin, Wavelet Analysis and Synthesis of Fractional Brownian Motion, IEEE Trans.On Information Theory, 38(2), Mar. 1992, pp 910-917.
[142] G. W. Wornell and A. V. Oppenheim, Estimation of Fractal Signals from Nosy Measurments Using Wavelets, IEEE Trans. On Signal Processing, 40(3): 611-623, Mar. 1992.
[143] W.-L. Wang, Estimation of Fractional Brownian Motion Embedded in a Noisy Environment Using Nonorthogonal Wavelets, IEEE Trans. On Signal Processing, 47(8):2211-2219, August 1999.
[144] Z. Han and T. S. Denney, A New Method for Fractional Brownian Motion Interpolation,IEEE Trans. On Signal Processing, 47(11): 3159-3164, Nov. 1999.
[145] L. M. Kaplan and C.-C. J. Kuo, Fractal Estimation from Noisy Data via Discrete Fractional Gaussian Noise (DFGN) and the Haar Basis, IEEE Trans. On Signal Processing,41(12): 3554-3562, Dec. 1993.
[146] L. M. Kaplan, Extended Fractal Analysis for Texture Classification and Segmentation,IEEE Trans. On Image Processing, 8(11): 1572-1585, Nov. 1999.
[147] L. M. Kaplan and C.-C. J. Kuo, An Improved Method for 2-D Self-Similar Image Synthesis, On Image Processing, 5(5): 754-760, May 1996.
[148] B. Yazici and R. L. Kashyap, A Class of Second-Order Stationary Self-Similar Processes for 1/f Phenomena, IEEE Trans. On Signal Processing, 45(2): 396-410, Feb. 1997.
[149] Lin Zhou; Leung Tsang; Jandhyala, V.; Chi-Te Chen, Studies on accuracy of numerical simulations of emission from rough ocean-like surfaces, IEEE Transactions on Geoscience and Remote Sensing, Volume: 39 Issue: 8 , Aug. 2001, pp 1757 -1763.
[150] Franceschetti, G; Iodice, A.; Riccio, D, Scattering from dielectric random fractal surfaces via method of moments, IEEE Transactions on Geoscience and Remote Sensing, Volume: 38 Issue: 4 Part: 1 , July 2000, pp 1644-1655.
[151] Franceschetti, G; Iodice, A.; Riccio, D.; Ruello, G, Scattering from fractal dielectric profiles: the extended boundary condition method, in Proceedings of IEEE 2000 International Conference on Geoscience and Remote Sensing Symposiun, IGARSS 2000. , Volume: 4 , 2000,pp 1727-1729 vol.4.
[152] Scowen, B.C.; Smith, S.L.; Vannan, M.A., Quantitative 3D modelling of the left ventrical from ultrasound images [ventrical read ventricle], in Proceedings of the 26th Euromicro Conference, 2000., Volume: 2 , 2000, pp 432 -439 vol.2.
[153] Onufriyenko, V.M.; Samolchev, P.A.; Slyusarova, T.I., Interaction of an electrostatic field with a dielectric body, Microwaves, 13th International Conference on Radar and Wireless Communications. 2000. MIKON-2000., Volume: 2 , 2000, pp 502 -505 vol.2.
[154] Berizzi, F.; Dalle Mese, E.; Pinelli, G, One-dimensional fractal model of the sea surface,in IEE Proceedings of Radar, Sonar and Navigation, Volume: 146 Issue: 1 , Feb. 1999, pp 55-64.
[155] Wang, X.; Yoshimura, N., Fractal phenomena. Dependence of hydrophobicity on surface appearance and structural features of SIR insulators, IEEE Transactions on [see also Electrical Insulation, IEEE Transactions on] Dielectrics and Electrical Insulation, Volume: 6 Issue: 6 ,Dec. 1999, pp 781 -791.
[156] Franceschetti, G; Iodice, A.; Migliaccio, M.; Riccio, D., Scattering from natural rough surfaces modeled by fractional Brownian motion two-dimensional processes, IEEE Transactions on Antennas and Propagation, Volume: 47 Issue: 9 , Sept. 1999, pp 1405 -1415.
[157] Berizzi, F.; Dalle-Mese, E., Fractal analysis of the signal scattered from the sea surface,IEEE Transactions on Antennas and Propagation, Volume: 47 Issue: 2 , Feb. 1999, pp 324-338.
[158] Guo Lixin; Wu Zhensen, Electromagnetic scattering from 2D band-limited fractal surface using Kirchhoff approximation, in Proceedings of (ICCEA '99) 1999 International Conference on Computational Electromagnetics and Its Applications, 1999, pp 456 -459.
[159] Franceschetti, G; Migliaccio, M.; Riccio, D., The validity of the Kirchhoff approximation for fractal surface scattering, Geoscience and Remote Sensing Symposium, in Proceedings of IEEE 1999 International Conference on IGARSS., Volume: 5 , 1999, pp 2407 -2409.
[160] Eliseev, M.V.; Isayeva, O.B.; Rozhnev, A.G.; Ryskin, N.M., Numerical simulation of electron field emission from fractal surface, in International University Conference Proceedings of Electronics and Radiophysics of Ultra-High Frequencies, 1999, pp 309 -312.
[161] Price, J.R.; Hayes, M.H., III, Fractal interpolation of images and volumes, in Conference Record of the Thirty-Second Asilomar Conference on Signals, Systems & Computers, 1998,Volume: 2, 1998, pp 1698-1702.
[162] Wang, X.; Kumagai, S.; Yoshimura, N., Fractal analysis on the recovery of contaminant properties of silicone rubber insulator against acid rain, in Proceedings of 1998 International Symposium on Electrical Insulating Materials, 1998, pp 619 -622.
[163] Dansereau, R.; Kinsner, W., Progressive transmission of images through fractal surface interpolation, in Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, 1998. , Volume: 1 , 1998, pp 277 -280.
[164] Berizzi, F.; Dalle Mese, E., Scattering analysis from fractal sea surfaces, in Proceedings of 1998 IEEE International Symposium on Geoscience and Remote Sensing, 1998. IGARSS '98. , Volume: 5 , 1998, pp 2483 -2486.
[165] Vemuri, B.C.; Mandal, C; Shang-Hong Lai, A fast Gibbs sampler for synthesizing constrained fractals, IEEE Transactions on Visualization and Computer Graphics, Volume: 3 Issue: 4 , Oct.-Dec. 1997, pp 337 -351.
[166] Zangari, G; Lambeth, D.N., Porous aluminum oxide templates for nanometer-sized cobalt arrays, IEEE Transactions on Magnetics, Volume: 33 Issue: 5 Part: 1 , Sept. 1997, pp3010-3012.
[167] Dansereau, R.; Kinsner, W., Image compression through fractal surface interpolation and wavelet compression, in Proceedings of IEEE Conference on WESCANEX 97:Communications, Power and Computing, 1997, pp 94 -99.
[168] Nai-Yu Wang; Vesecky, J.F., Active/passive microwave method for sea surface temperature estimation, in Proceedings of MTS/IEEE Conference on OCEANS '97, Volume: 2, 1997,pp 1155-1157.
[169] Nigmatullin, R.; Ryabov, Ya.; Polygalov, E.; Fewldman, Yu., The fractal nature of electrode polarization, in Proceedings of Seventh International Conference on Dielectric Materials, Measurements and Applications, (Conf. Publ. No. 430), 1996, pp 164 -167.
[170] Vemuri, B.C.; Mandal, C, A fast Gibbs sampler for synthesizing constrained fractals, in Proceedings of .Visualization '96., 1996, pp 29 -35.
[171] Heneghan, C; Lowen, S.B.; Teich, M.C., Two-dimensional fractional Brownian motion: wavelet analysis and synthesis, in Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation, 1996, pp 213 -217.
[172] Dansereau, R.; Kinsner, W., Perceptual image compression through fractal surface interpolation, in Proceedings of Canadian Conference on Electrical and Computer Engineering, 1996., Volume: 2 , 1996, pp 899 -902.
[173] Axelsson, S.R.J.; Johnsson, K.-G.; Tullsson, B.-E.; Kjellgren, J.; Carlstrom, A.,Comparison of measured and predicted scattering coefficients at 94 GHz, in Proceedings of International Geoscience and Remote Sensing Symposium (IGARSS '94) on Surface and Atmospheric Remote Sensing: Technologies, Data Analysis and Interpretation., Volume: 3 ,1994,pp 1631 -1634.
[174] Chen, S.S.; Keller, J.M.; Crownover, R.M., On the calculation of fractal features from images, IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume: 15 Issue: 10,Oct. 1993,pp1087-1090.
[175] Vemuri, B.C.; Radisavljevic, A., From global to local, a continuum of shape models with fractal priors, Proceedings of 1993 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '93), pp 307 -313.
[176] Chan, K.L., Fractal-based texture analysis, Singapore ICCS/ISITA '92 of 'Communications on the Move', 1990, pp 102 -106.
[177] Allinson, N.M.; Lawson, M., Accurate textural characterisation using fractal techniques,IEE Colloquium on Application of Fractal Techniques in Image Processing, , 1990, pp 6/1-6/6.
[178] Jaggard, D.L.; Sun, X., Scattering from bandlimited fractal fibers, IEEE Transactions on Antennas and Propagation, Volume: 37 Issue: 12 , Dec. 1989, pp 1591 -1597.
[179] Britton, D., Surface modeling algorithm for pyramid architectures, in Proceedings of 2nd Symposium on the Frontiers of Massively Parallel Computation, 1989, pp 321 -322.
[180] T. Blu and M. Unser, Wavelets, fractals and radial basis functions, IEEE Trans. On Signal Processing, vol. 50, no. 3, pp. 543-553, March 2002.
[181] K. Arakawa and E. Krotkov, Estimating of Fractal Dimension from Range Images of Natural Terrain, Technical Report CMU-CS-91-156, Carnegie Mellon University, School of Computer Science, 1991.
[ 182] J. P. Lewis, Is the Fractal Model Appropriate for Terrain?, in section 6.1 of paper [240].
[183] T. Gneiting and M. Schlather, Stochastic Models Which Separate Fractal Dimension and Hurst Effect, Society for Industrial and Applied Mathematics (SIAM) Review, 46(2), 1995,pp269-282.
[184] H. Xie, D. Chen, and X. Kong, Characterization on Three-Dimensional Surface Topography of Textured Cold-Rolled Steel Sheets, in Proc. of the First Asia Inter. Conf. on Trib, Tsinghua University, Beijing, pp 396-399, 1998.
[185] K. S. Pedersen and M. Nielsen, The Haustorff Dimension and Scale-Space Normalization of Natural Images, Journal of Visual Communication and Image Representation, 11, 266-277, 2000.
[186] J. Militky and V. Bajzik, Influence of Wool Content on Properties of Blended Fabrics,International Journal of Clothing Science and Technology, Volume 6, Issue 23, August 1994,pp. 32-36.
[187] G. Chan and A. T. A. Wood, Estimation of Fractal Dimension for A Class of Non-Gaussian Stationary Processes and Fields, Annals of Statistics, 32(3), 2004, pp 1222-1260.
[188] C. Traina Jr., A. Traina, L. Wu, and C. Faloutsos, Fast Feature Selection Using Fractal Dimension, in Proceedings of XV Brazilian Symposium on Databases (SBBD), Paraiba, Brazil, October, 2000.
[189] E. P. M. de Sousa, C. Traina Jr., and A. Traina, How to Use Fractal Dimension to Find Correlations Between Attributes, in Proceedings of KDD-Workshop on Fractals and Self-similarity in Data Mining: Issues and Approaches, 2002.
[190] J. -C. Liu, W. -L. Hwang, and M. -S. Chen, Estimation of 2D Noisy Fractional Brownian Motion and Its Applications Using Wavelets, IEEE Transactions on Image Processing, 9(8), pp 1407-1419, August 2000.
[191] B. Xie, S. Zhu, and G. Hu, Blind Fractal Signal Estimation for SCDMA Systems Over Multipath Fading Channels, In Proceedings of 2000 International Conferences on Communication Technology, (ICCT' 2000), Beijing, August, 21-25, 2000, pp 359-362.
[192] J. -C. Liu and W. -L. Hwang, Parameter Estimation and Denoising of 2-D Noisy Fractional Brownian Motion Using Non-Orthogonal Wavelets, in Proceedings of IEEE Symposium on Time Frequency and Time Scale Analysis, Pittsburg, October 1998.
[193] K. E. Timmermann and R. D. Nowak, Multiscale Modeling and Estimation of Poisson Processes with Application to Photon-Limited imaging, IEEE Transactions on Information Theory, 45(3), April 1999, pp 846-862.
[194] E. Lutton etc., Mixed IFS: Resolution of Inverse Problem Using Genetic Programming, Complex Systems, Vol. 9, 1995, pp 375-398.
[195] J. C. Hart, Implicit Representations of Rough Surfaces, Computer Graphics Forum, 16(2), June 1997.
[196] C. M. Wittenbrink, IFS Fractal Interpolation for 2D and 3D Visualization, In Proceedings of the 6th IEEE conference on Visualization '95, 1995, pp 77.
[197] W. O. Kochran, J. C. Hart, and P. J. Flynn, Similarity and Affinity Hashing: A Computer Vision Solution to the Inverse Problem of Linear Fractals, Fractals, 5 (Supplementary Issue), April 1997, pp 39-50.
[198] G. Vines, Signal Modeling with Iterated Function Systems, PhD Thesis, Georgia Institute of Technology, 1993.
[199] 陈守吉、张立明编著，《分形与图像压缩》，上海科技教育出版社。
[200] 肯尼思·法尔科内内，著，曾文曲、刘世耀 译，《分形几何——数学基础及其应用》，东北大学出版社，1991年8月。
[201] 肯尼思·法尔科内 著，曾文曲、王向阳、陆夷 译，《分形几何中的技巧》，东北大学出版社，1999年6月第1版，1999年6月第1次印刷。
[202] M. J. Turner, J. M. Blackledge, and R R. Andrews, Fractal Geometry in Digital Imaging, Academic Press 1998, 525 B Street, Suite 1900, San Diego, California 92101-4495, USA.
[203] R R. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, 1994.
[204] John C. Russ, Fractal Surfaces, Plenum Press, New York and London, 1994.
[205] Natalia Alexandrov and J. E. Dennis, Multilevel Algorithms for Nonlinear Optimization,NASA CR-194940 ICASE Report No. 94-53, Institute for Computer Applications in Science and Engineering Mail Stop 132C, NASA Langley Research Center Hampton, VA 23681-0001, June 1994, pp. 21.
[206] M. S. Gockenbach, A. J. Kearsley, and W. W. Symes, An Infeasible Point Method for Minimizing the Lennard-Jones Potential, Computational Optimization and Applications, 8(3),1997,pp 273-286.
[207] P. T. Boggs, J. W. Tolle, and A. J. Kearsley, A Truncated SQP Algorithm for Large Scale Nonlinear Programming Problems, In Susana Gomez and Jean-Pierre Hennart, editors, Advances in Optimization and Numerical Analysis: Proceedings of the Sixth Conference on Numerical Analysis and Optimization, pages 69-78, Dordrecht, 1994. Kluwer Academic Publishers.
[208] P. T. Boggs, J. W. Tolle, and A. J. Kearsley, On the Convergence of A Trust Region SQP Algorithm for Nonlinearly Constrained Optimization Problems, In J. Dolezal, editor, Proceedings of the 17th IFIP TC7 Conference on System Modeling and Optimization, pp1-14, London, 1995. Chapman.
[209] A. J. Kearsley, The Use of Optimization Techniques in the Solution of Partial Differential Equations from Science and Engineering, Technical Report and Ph.D. Thesis,Rice University, Department of Computational and Applied Mathematics, 1996.
[210] J. E. Dennis, M. EL-Alem, and K. Williamson, A Trust Region Approach to Nonlinear Systems of Equalities and Inequalities, SIAM. J. Optim., 9(2), 1999, pp. 291-315.
[211] J. E. Dennis, M. Heinkenschloss, and L. N. Vicente, Trust Region Interior-Point SQP Algorithms for A Class of Nonlinear Programming Problems, SIAM Journal on Control and Optimization, 36(5), Sep. 1998, pp 1750-1794.
[212] J. Marin and R. V. Sole, Macroevolutionary Algorithms: A New Optimization Method on Fitness Landscapes, IEEE Transactions on Evolutionary Computation, 3(4), Nov. 1999, pp272-286.
[213] A. Gupta, Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matriccs, IBM Research Report RC 22137 (99131), August 1, 2001.
[214] M. C. Turley and E. D. Ford, A Comparison on Consistency of Parameter Estimation Using Optimization Methods for a Mixture, NRCSE Technical Report Series (NRCSE-TRS) No. 050,July 17, 2000.
[215] R. Koch and W. Benzing, Multi-Dimensional Parameter Optimization for RSFQ Circuit Design, Ext. Abs. ISEC'97, pp 305-307, 1997.
[216] M. A. Branch, T. F. Coleman, and Y. Li, A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems, SIAM. Sci. Comput., Vol. 21,No. 1.pp 1-23, 1999.
[217] L. Gilles, C. Vogel, and B. Ellerbroek, A Multigrid Preconditioned Conjugate Gradient Method for Large Scale Wavefront Reconstruction, JOSA A, Vol. 19, Issue 9, pp 1817-1822,Sept. 2002.
[218] J. E. Dennis, Jr., and R. M. Lewis, A Comparison of Nonlinear Programming Approaches to An Elliptic Inverse Problem and A New Domain Decomposition Approach,Tech. Rep. TR94-33, Department of Computational and Applied Mathematics, Rice University, 1994.
[219] J. P. Hamalainen, CFD Coupled with Shape Optimization - A New Promising Tool in Paper Machine R&D, in Proceedings of 10th Conference of European Consortium for Mathematics in Industry, L. Arkeryd, H. Engl, A. Fasano, R. Mattheij, P. Neittaanmaki, H.Neunzert (eds.), B.G. Teubner, Stuttgart-Leipzig, 1999, pp. 171-178 (jointly with: J. Hamalainen).
[220] A. J. Kearsley, R. A. Tapia, and M. W. Trosset, The Solution of The Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method, Computational Statistics, Vol.13, 1998, 369-396.
[221] S. E. Minkoff, Implementation of The Conjugate Gradient Algorithm in DSO, Tech Report 94-31, Department of Computational and Applied Mathematics, Rice University,July 11, 1994.
[222] J. Dong, J. Shi, S. Wang, and Y. Xue, A Trust Region Algorithm for Equality-Constrained Optimization via A Reduced Dimension Approach, Journal of Computational and Applied Mathematics, 152(2003), pp 99-118.
[223] S. J. Oshcr and F. Santosa, Level Set Methods for Optimization Problems Involving Geometry and Constraints: I. Frequencies of a Two-Density Inhomogeneous Drum, Journal of Computational Physics 171, pp 272-288, 2001.
[224] S. Ta'asan, Differential Optimization Problems: Analysis of the Hessian, IMA, Optimization in Simulation-Based Models, January 9-16, 2000.
[225] S. Henn and K. Witsch, Iterative Multigrid Regularization Techniques for Image Maching, SIAM. Sci. Comput. Vol. 23, No. 4, pp 1077-1093, 2001.
[226] M. S. Gockenbach and A. J. Kearsley, Optimal Signal Sets for Non-Gaussian Detectors,SIAM Journal on Optimization, 9(2), 1999, pp 316-326.
[227] A. Takeda, Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems, In Proceedings of The Intrnational Conference on Complementarity 99, June 9-12, 1999, Madison, Wisconsin.
[228] C. A. Floudas and V. Visweswaran, Quadratic Optimization, in Handbook of Global Optimization (R.Horst and P.M. Pardalos, Editors), Kluwer Academic Publishers, pp. 217-270(1994).
[229] P. T. Boggs and J. W. Tolle, Sequential Quadratic Programming, Acta. Numerica. 1996,pp 1-52.
[230] S. Kruk and H. Wolkowicz, SQ2P, Sequential Quadratic Constrained Quadratic Programming, Research Report CORR 97-01, University of Waterloo, August 7, 1998.
[231] S. Kim and M. Kojima, Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations, Computational Optimization and Applications, 26(2), 2003, pp 143-154.
[232] S. J. Benson, Y. Ye, and X. Zhang, Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization, SIAM Journal on Optimization, 10(2), 2000, pp 443-461.
[233] V. Migallon, J. Penades, D. B. Szyld, Block Two-Stage Methods for Singular Systems and Markov Chains, Report 95-121, Dec. 1995. Also in Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications, Nijmegan, The Netherlands, June 13-15, 1996.
[234] Stan Z. Li, Markov Random Field Modeling in image Analysis, Springer Berlin Heidelberg New York, 2nd ed., 2001, ⅪⅩ, 323 p. 99 illus., Softcover, ISBN: 4-431-70309-8.
[235] 崔景泰(美国) 著，程正兴 译，白居宪 审校，《小波分析理论》，西安交通大学出版社，1995年1月第1版，1997年1月第2次印刷。
[236] 秦前清、杨宗凯 编著，《实用小波分析》，西安电子科技大学出版社，1994年1月第1版，1998年1月第4次印刷。
[237] C. Vogel, Regularization methods: An Applied Mathematician's Perspective, www.samsi.info/talks/inversc/Inverse-Vogel.pdf
[238] 齐尔旭，《分形及其计算机生成》，科学出版社，1994年11月，页130。
[239] Randal Barnes, Variogram Tutorial, Golden Software, Inc., www.goldensoftware.com/variogramTutorial.pdf.
[240] J. R Lewis, Generalized stochastic subdivision, ACM Transactions on Graphics, Vol. 3, July 1987, pp 167-190.
[241] J. Y. Yuan and P. Y. Yalamov, A Method for Constructing Diagonally Dominant Preconditioners based on Jacobi Rotations, Applied Mathematics and Computation, 2004.
[242] R. H. Riedi, Multifractal Processes, in "Long Range Dependence: Theory and Applications", eds. Doukhan, Oppenheim and Taqqu, Birkhauser, 2001.
[243] J. v. L. v. Pabst and H. Jense, Dynamic Terrain Generation Based on Multifractal Techniques, in Proceedings of the International Workshop on High Performance Computing for Computer Graphics and Visualisation, Swansea, 3-4 July 1995.
[244] 廖熠、赵荣椿，从明暗恢复形状方法综述，中国体视学第一届联合学术会议论文集，2000年8月，页310-315。
[245] 廖熠、赵荣椿，几类SFS典型算法分析与评价，中国图像图形学报，第六卷(A版)第10期，2001年10月，页953-961。
[246] 廖熠、赵荣椿，从明暗恢复形状问题中的一种分形约束方法探讨，信号处理，第十七卷第六期，2001年，页521-527。
[247] 廖熠、赵荣椿，一种基于小波分层模型的自然景物图像表面恢复算法，信号处理，第十七卷 (增刊)，2001年11月，395-399。
[248] 廖熠、赵荣椿，基于Hamilton系统理论的SFS模型分析，系统仿真学报，第十三 卷 (增刊)，2001年，页30-32。
[249] Yi Liao, Rong-chun Zhao, A New Relaxation Algorithm for Linearized SFS Problem, Chinese Journal of Electronics, accepted, Nov. 2002.
[250] Y. Liao and R. C. Zhao, "A Novel Method for Solving the Shape from Shading (SFS) Problem", in Proceedings of Second International Conference on Natural Computation (ICNC 2006), Ⅱ, Xi'an, China, Sep. 2006, pp 714-723.
[251] T. S. Pan and A. E. Yagle, "Numerical Study of Multigrid Implementations of Some Iterative Image Reconstruction Algorithms", IEEE Transactions on Medical Imaging, 10(4), 1991, pp 572-588.
[2] M. J. Brooks, Two Results Concerning Ambiguity in Shape from Shading, in Proceedings of the National Conference on Artificial Intelligence, American Association for Artificial Intelligence: Washington, D.C., U.S.A., 1983, pp26-39.
[3] J.Oliensis, Uniqueness in Shape from Shading, International Journal of Computer Vision, 6(2),1991,pp75—104.
[4] P. Dupuis and J. Oliensis, Shape from Shading: Provably Convergent Algorithms and Uniqueness Results, in Proceedings of 1994 European Conference on Computer Vision (ECCV'94), 1994, pp 259—268.
[5] R. Kozera, Uniqueness in Shape from Shading Revisited, Journal of Mathematical Imaging and Vision, 7, 1997, pp 123—138.
[6] G. Ulich, Provably Convergent Methods for the Linear and Nonlinear Shape from Shading Problem, Journal of Mathematical Imaging and vision, 9,1998, pp 69—82.
[7] J.Oliensis, Shape from Shading as a Partially Well-Constrained problem, CVGIP: Image Understanding, 54(2), 1991.9,pp 163—183.
[8] R. Zhang, P.-S.Tsai, J.E.Cryer and M.Shah, Shape from Shading : A Survey, IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 21(8), 1999.8, pp 690—705.
[9] R.T.Frankot and R.Chellappa, A Method for Enforcing Integrability in Shape from Shading Algorithms, IEEE Trans, on Pattern Analysis and Machine Intelligence (PAMI), 10(4), 1988.7,pp 439—451.
[10] T.-C. Pong, R.M.Haralick and L.GSharpiro, Shape from Shading Using the Facet Model,Pattern Recognition, 22(6), 1989, pp 683—695.
[11] K.M.Lee and C.-C. J. Kuo, Shape from Shading with a Linear Triangular Element Surface Model, IEEE Trans, on Pattern Analysis and Machine Intelligence (PAMI), 15(8), 1993.8, pp815—812.
[12] H. Saito and N.Tsunashima, Estimation of 3-D Parametric Models from Shading Image Using Genetic Algorithms, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 668—670.
[13] J.-W. Hsieh, H.-Y.M. Liao, M.-T. Ko and K.-C. Fan, Wavelet-Based Shape from Shading,Graphical Models and Image Processing, 57(4), 1995.7, pp 343—362.
[14] G.-Q. Wei and G. Hirzinger, Parametric Shape-from-Shading by Radial Basis Functions,IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 19(4), 1997.4, pp353—365.
[15] B.-H. Kim and R.-H. Park, Shape from Shading and Photometric Stereo Using Surface Approximation by Legendre Polynomials, Computer Vision and Image Understanding, 66(3), 1997. 6, pp 255—270.
[16] R. Szeliski, Fast Shape from Shading, CVGIP: Image Understanding, 53(2), 1991. 3, pp 129—153.
[17] O. E. Vega and Y. H. Yang, Shading Logic: A Heuristic Approach to Recover Shape from Shading, IEEE Trans. on Pattern Analysis and Machine Intelligence (PAMI), 15(6), 1993. 6, pp 592—597.
[18] S. I. Cho, H. Saito and S. Ozawa, Geometric Solution of Shape from Shading Problem, Korean-Japan Joint Workshop on Computer Vision (FCV'98), Feb. 2, 1998, pp 19-24.
[19] P. -S. Tsai & M. Shah, A Fast Linear Shape from Shading, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp 734—736.
[20] B. K. P. Horn, Height and Gradient from Shading, International Journal of Computer Vision, 5(1), 1990, pp 37—75.
[21] K. Ikeuchi and B. K. P. Horn, Numerical Shape from Shading and Occluding Boundaries, Artificial Intelligence, 17(1981) 141-184.
[22] K. Ikeuchi, Comment On "Numerical Shape from Shading and Occluding Boundaries", Artificial Intelligence, 59, 1993, pp 89—94.
[23] 刘辉、谈正，从遮挡边缘和局部阴影恢复表面形状，中国图像图形学报，3 (7)，1998．7， pp 588—590。
[24] K. Atsuta, M. Sanoworasil and S. Kondo, A New Method of Estimating Shape from Shading by using a Constraint at Zero-crossings of Image Brightness, in Proceedings of 9th International Conference on Pattern Recognition, vol. 2, 1988, pp 666-668.
[25] D. Lee, Algorithms for Shape from Shading and Occluding Boundaries, in Proceedings of Computer Society Conference on Computer Vision and Pattern Recognition, 1988, pp 478-485.
[26] M. Shao, T. Simchony, and R. Chcllappa, Direct analytical methods for solving Poisson equations in computer vision problems, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12 (5), May 1990, pp 435-446.
[27] R. T. Frankot and R. Chellappa, A method for enforcing integrability in shape from shading algorithms, IEEE Transactions on Pattern Analysis and Machine Intelligence, 10(4), July 1988, pp 439-451.
[28] Y. Choc and R. L. Kashyap, A 3-D Texture Model Of Natural Scene Image, in Proceedings of Twenty-Second Asilomar Conference on Signals, Systems and Computers, 1988, Vol 1, pp 463-467.
[29] M. A. Penna, A shape from shading analysis for a single perspective image of a polyhedron, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11(6), June 1989, pp 545-554.
[30] N. Shrikhande and G. Stockman, Surface orientation from a projected grid, IEEE Transactions on Pattern Analysis and Machine Intelligence, 11 (6), June 1989, pp 650-655.
[31] K. Hartt and M. Carlotto, A method for shape-from-shading using multiple images acquired under different viewing and lighting conditions, in Proceedings of IEEE Computer Society Conference on ,Computer Vision and Pattern Recognition, 1989, pp 53 -60.
[32] Y.-S. Choi, S.-C. Chung and J.-S. Choi, Reinforced Shape From Shading Using Multigrid Techniques, in Proceedings of the 1988 IEEE International Conference on Systems, Man, and Cybernetics, 1988(2), pp 766 -770.
[33] G. Ron and S. Peleg, Nonlinear multiresolution: a shape-from-shading example, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(12), Dec. 1990, pp 1206-1210.
[34] D. Forsyth and A. Zisserman, Mutual illumination, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1989, pp 466 -473.
[35] M. J. Korsten and Z. Houkes, Parametric descriptions and estimation, a synergetic approach to resolving shape from shading and motion, in Proceedings of Third International Conference on Image Processing and its Applications, 1989, pp 5 -9.
[36] Q. Zheng and R. Chellappa, Estimation of surface topography from stereo SAR images, in Proceedings of International Conference on Acoustics, Speech, and Signal Processing,1989(3),pp 1614-1617.
[37] J. Thomas, W. Kober and F. Leberl, Multiple-image Sar Shape From Shading, in Proceedings of 12th International Geoscience and Remote Sensing Symposium, Canadian Symposium on Remote Sensing, 1989(2), pp 592 -596.
[38] Y. Iwahori, H. Sugie and N. Ishii, Reconstructing shape from shading images under point light source illumination, in Proceedings of 10th International Conference on Pattern Recognition, 1990(1), pp 83 -87.
[39] J. J. Clark and A. L. Yuille, Shape from shading via the fusion of specular and Lambertian image components, in Proceedings of 10th International Conference on Pattern Recognition,1990(1),pp88-92.
[40] B. Guindon, Development Of A Shape-from-shading Technique For The Extraction Of Topographic Modem From Individual Spaceborne Sar Images, 12th International Canadian Symposium on Remote Sensing, Geoscience and Remote Sensing Symposium, 1989(2), pp597 -602.
[41] B. Guindon, Development of A Shape-from-Shading Technique for the Extraction of Topographic Models from Individual Spaceborne SAR Images, IEEE Trans. Geoscience and Remote Sensing, vol. 28 no. 4, pp. 654-661.
[42] P. K. Bora, Y. V. Venkatesh, and K. R. Ramakrishnan, Shape from shading using discrete polynomials, ACE '90. Proceedings of XVI Annual Convention and Exhibition of the IEEE In India, 1990, pp 260-264.
[43] Q.Zheng and R.Chellappa, Estimation of Illuminant Direction, Albedo, and Shape from Shading, IEEE Transactions on Pattern Analysis and Machine Intelligence, 13(7), July 1991,pp 680-702.
[44] R. -X. Li and S. Pai, Improvement Of Bathymetric Data Bases By Shape From Shading Technique Using Side-scan Sonar Images, in Proceedings of Ocean Technologies and Opportunities in the Pacific for the 90's (OCEANS '91), 1991(1), pp 320 -324.
[45] B. Kim and P. Burger, Depth and Shape from Shading Using the Photometric Stereo Method,in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991, pp 416—427.
[46] S. Banerjee, P. S. Sastry, and Y. V. Venkatesh, Surface reconstruction from disparate shading: an integration of shape-from-shading and stereopsis, in Proceedings of 11th International Conference on Pattern Recognition (Conference A: Computer Vision and Applications),1992(1),pp 141 -144.
[47] K. M. Lee and C.-C. J. Kuo, Shape from shading with a linear triangular element surface model, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(8), Aug. 1993,pp815-822.
[48] P.Dupuis and J.Oliensis, Direct Method for Reconstructing Shape from Shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp 453-458.
[49] M.Bichsel and A.P.Pentland, A Simple Algorithm for Shape from Shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp459—465.
[50] B. V. Funt and M. S. Drew, Color space analysis of mutual illumination, IEEE Transactions on Pattern Analysis and Machine Intelligence, 15(12), Dec. 1993, pp 1319 -1326.
[51] W.-S. Ching, P.-S. Toll, and W.-L. Goh, Concurrent acquisition and processing of multi-spectral shadow information for 3D computer vision, in Proceedings of the International Conference on Industrial Electronics, Control, and Instrumentation, 1993(3), pp1736-1741.
[52] J. E. Crycr, P.-S. Tsai, and M. Shah, Integration of shape from X modules: combining stereo and shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1993, pp 720 -721.
[53] D. R. Hougen and N. Ahuia, Adaptive polynomial modelling of the reflectance map for shape estimation from stereo and shading, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 991 -994.
[54] M. S. Langer and S. W. Zucker, Diffuse shading, visibility fields, and the geometry of ambient light, in Proceedings of Fourth International Conference on Computer Vision, April 1993,pp 138-147.
[55] H. Schultz, Retrieving shape information from multiple images of a specular surface, IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(2), Feb. 1994, pp 195 -201.
[56] A. P. R. Cooper, A Simple Shape-From-Shading Algorithm Applied to Images of Ice-Covered Terrain, IEEE Transactions on Geoscienee and Remote Sensing, 32(6), Nov. 1994, pp 1196-1198.
[57] A. G. Jones and C. J. Taylor, Automated interpretation of SEM images, in Proceedings of IEEE Region 10's Ninth Annual International Conference on Theme of Frontiers of Computer Technology, 1994(2), pp 872 -876.
[58] W. P. Cheung, C. K. Lee, and K. C. Li, Surface reconstruction by integrating stereo vision with shading, in Proceedings of the 20th International Conference on Industrial Electronics, Control and Instrumentation, 1994(2), pp 968 -971.
[59] T. Wada, H. Ukida, and T. Matsuyama, Shape from shading with interreflections under proximal light source-3D shape reconstruction of unfolded book surface from a scanner image, in Proceedings of the Fifth International Conference on Computer Vision, 1995, pp 66-71.
[60] M. Jones and J. P. Oakley, A new shape representation for fast 3D reconstruction from multiple 2D perspective images, in Proceedings of IEE Colloquium on New Developments in 3D Image Capture and Application, 1995, pp 4/1 -4/3.
[61] Y. Numagami, Y. Kajiwara, O. Nakamura, and T. Minami, Reconstruction of the 3-D shape of an object from a 2-D intensity image, in Proceedings of Canadian Conference on Electrical and Computer Engineering, 1995(2), pp 1188 -1191.
[62] G.-Q. Wei and G. Hirzinger, Parametric shape-from-shading by radial basis functions, IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(4), April 1997, pp 353 -365.
[63] A.J.Stewart and M. S. Langer, Towards accurate recovery of shape from shading under diffuse lighting, in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1996, pp 411 -418.
[64] K. Deguchi and T. Okatani, On identification of singular points using photometric invariants for global shape from shading problem, in Proceedings of the Fourteenth International Conference on Pattern Recognition, 1998(2), pp 1787 -1790.
[65] C.-K. Huang, C. Pai, and W.-T. Chang, Shape from shading using Ritz method with tent basis,in Proceedings of the 13th International Conference on Pattern Recognition, 1996(1), pp 398-402.
[66] J. Y. Zheng, H. Kakinoki, K. Tanaka, and N. Abe, Computing 3D models of rotating objects from moving shading, in Proceedings of the 13th International Conference on Pattern Recognition, 1996(1), pp 800 -804.
[67] A. Goller, Concurrent radar image shape-from-shading on high-performance computers, in Proceedings of the 13th International Conference on Pattern Recognition, 1996(3), pp 589-593.
[68] R. Lengagne, J.-P. Tarel, and O. Monga, From 2D images to 3D face geometry, in Proceedings of the Second International Conference on Automatic Face and Gesture Recognition, 1996, pp 301 -306.
[69] C. R. Guarino, SAR interferometry: a novel method for enhancing elevation maps by combining interferometry with shape-from-shading, in Proceedings of International Conference on Image Processing, 1996(1), pp 45 -48.
[70] P. L. Worthington and E. R. Hancock, Shape from Shading using Robust Statistics, in Proceedings of 13th International Conference on Digital Signal Processing, 1997(2), pp 1145-1148.
[71] T.-E. Kim, S.-H. Lee, S.-H. Ryn, and J.-S. Choi, Shape recovery of hybrid reflectance surface using neural network, in Proceedings of International Conference on Image Processing,1997(3),pp416-419.
[72] N. Barnes and Z.-Q. Liu, A knowledge based approach to shape from shading, in Proceedings of IEEE International Conference on Intelligent Processing Systems, 1997(2), pp 1390 -1394.
[73] J. Ben-Arie and D. Nandy, A neural network approach for reconstructing surface shape from shading, in Proceedings of 1998 International Conference on Image Processing, 1998(2), pp972 -976.
[74] A. Z. Kouzani, F. He, and K. Sammut, Example-based shape from shading: 3D heads form 2D face images, in Proceedings of 1998 IEEE International Conference on Systems, Man,and Cybernetics, 1998(4), pp 4092 -4097.
[75] S. M. Yamany and A. A. Farag, A system for human jaw modeling using intra-oral images, in Proceedings of the 20th Annual IEEE International Conference on Engineering in Medicine and Biology Society, 1998(2), pp 563 -566.
[76] B. L. Craine, E. R. Craine, C. J. O'Toole, and Q. Ji, Digital imaging colposcopy: corrected area measurements using shape-from-shading, IEEE Transactions on Medical Imaging, 17(6),Dec. 1998, pp 1003-1010.
[77] D. Samaras and D. Metaxas, Coupled Lighting Direction and Shape Estimation from Single Images, in Proceedings of the Seventh IEEE International Conference on Computer Vision,1999(2),pp868-874.
[78] R. C. Wilson and E. R. Hancock, A radar reflectance model for terrain analysis using shape from shading, IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(8), Aug.1999,pp690-706.
[79] S.-Y. Cho and T. W. S. Chow, Shape Recovery from Shading.by a New Neural-Based Reflectance Model, IEEE Transactions on Neural Networks, 10(6), Nov. 1999, pp 1536-1541.
[80] W. Y. Zhao and R. Chellappa, SFS Based View Synthesis for Robust Face Recognition, in Proceedings of the Fourth IEEE International Conference on Automatic Face and Gesture Recognition, 2000, pp 285 -292.
[81] A. G. Bors, E. R. Hancock, and R. C. Wilson, 3-D Terrain from Synthetic Aperture Radar Images, in Proceedings of 2000 IEEE Workshop on Computer Vision Beyond the Visible Spectrum: Methods and Applications, 2000, pp 63 -72.
[82] A. G. Bors, E. R. Hancock, and R. C. Wilson, A Bayesian Framework for Radar Shape-from-shading, in Proceedings of 2000 IEEE Conference on Computer Vision and Pattern Recognition, 2000(1), pp 262 -268.
[83] J. R. A. Torreao, Shape from shading and intensity gradient, in Proceedings of XIII Brazilian Symposium on Computer Graphics and Image Processing, 2000, pp 7-14.
[84] C. H. Q. Forster, C. L. Tozzi, Towards 3D Reconstruction of Endoscope hnages Using Shape from Shading, in Proceedings of ⅩⅢ Brazilian Symposium on Computer Graphics and Image Processing, 2000, pp 90-96.
[85] A. Ortiz and G. Oliver, Shape from shading for multiple albedo images, in Proceedings of 15th International Conference on Pattern Recognition, 2000(1), pp 786-789.
[86] K. M. Lee and C. -C. J. Kuo, Shape from Shading with a Generalized Reflectance Map Model, Computer Vision and Image Understanding, 67(2), 1997. 8, pp 143—160.
[87] S. Pankanti and A. K. Jain, On Integration of Vision Modules, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994(1), pp 316—322.
[88] M. G. -H. Mostafa, S. M. Yamany and A. A. Farag, Integrating Shape from Shading and Range Data Using Neural Networks, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999(1), pp 15—20.
[89] M. S. Lee and G. Medioni, Grouping., -, →, θ, into Regions, Curves, and Junctions, Computer Vision and Image Understanding, 76(1), Oct. 1999, pp 54—69.
[90] D. Nandy and J. B. -Arie, Shape from Recognition and Learning: Recovery of 3-D Face Shapes, IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999(1), pp 2—7.
[91] K. M. Lee and C. -C. J. Kuo, Shape from Shading with Perspective Projetion, CVGIP: Image Understanding, 59(2), Mar. 1994, pp 202—212.
[92] 蔚艳、杨振华、王成道，多方法相融合的复杂物体深度信息的恢复，中国图像图形学报，4 (A4)，April 1999，pp 285—288。
[93] L. B. Wolff, S. K. Nayar and M. Oren, Improved Diffuse Reflection Models for Computer Vision, international Journal of Computer Vision, 30(1): 55～71, 1998.
[94] A. M. Bruckstein, On Shape from Shading, Computer Vision, Graphics and image Processing (CVGIP), 44, 1988, pp 139-154.
[95] R. Kimmel and A. M. Bruckstein, Tracking Level Sets by Level Stes: A Method for Solving the Shape from Shading Problem, Computer Vision and Image Understanding (CVIU), 62(2), July 1995, pp 47-58.
[96] R. Kimmel and A. M. Bruckstein, Global Shape from Shading, Computer Vision and Image Understanding (CVIU), 62(3), Nov. 1995, pp 360-369.
[97] I. Shimshoni, R. Kimmel and A. M. Bruckstein, Dialogue: Global Shape from Shading, Computer Vision and Image Understanding (CVIU), 64(1), July 1996, pp 188-189.
[98] E. Rouy and A. Tourin, A Viscosity Solutions Approach to Shape-from-Shading, SIAM Journal of Numerical Analysis, 29(3), June 1992, pp 867-884.
[99] S. Osher, A Level Set Formulation for the Solution of the Diricblet Problem for Hamilton-Jacobi Equations, SIAM J. Math. Anal. 24(5), Sept. 1993, pp 1145-1152.
[100] A. P. Pentland, Local Shading Analysis, IEEE Transactions on Pattern Analysis and Machine Inteligence (PAMI), 6(2), Mar. 1984, pp 170-187.
[101] C.-H Lee and A.Rosenfeld, Impoved Methods of Estimating Shape from Shading Using the Light Source Coordinate System, Artificial Inteligence, 26, 1985, pp 125-143.
[102] A. Pentland, Shape Information from Shading: A Theory about Human Perception, in Proceedings of Internationall Conference on Computer Vision,1988, pp 404-413.
[103] J. E. Cryer, P.-S. Tsai, and M. Shah, Integration of Shape from Shading and Stereo, Pattern Recognition, 28(7), 1995, pp 1033-1043.
[104] Tutorial for Green's Functions: Introduction to Green's Functions, http://www.boulder.nist.gov/div853/greenfn/tutorial.html.
[105] W.-J. Zhang and Y.-H. Zhou, An improved method for shape from shading, in Proceedings of the 9th International Conference on Pattern Recognition, 1988(2), pp 1106-1108.
[106] T. Simchony, R. Chellappa, and Z. Lichtenstein, Pyramid implementation of optimal-step conjugate-search algorithms for some low-level vision problems, IEEE Transactions on Systems, Man and Cybernetics, 19(6), Nov.-Dec. 1989, pp 1408 -1425.
[107] S. Peleg and G. Ron, Nonlinear Multiresolution: A Shape-from-Shading Example, IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(12), Dec. 1990, pp 1206-1210.
[108] D. Keren and M. Werman, Variations on regularization, in Proceedings of the 10th International Conference on Pattern Recognition, 1990(1), pp 93 -98.
[109] J. Thomas and W. Kober, Using a Range Constraints In Terrain Reconstruction Using Multiple Image Sar Shape-from-shading, in Proceedings of the 10th Annual International Geosciencc and Remote Sensing Symposium on Remote Sensing Science for the Nineties,1990,pp 1439-1439.
[110] Y. G. Leclerc and A. F. Bobick, The direct computation of height from shading, in Proceedings of 1991 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1991, pp 552 -558.
[111] T. A. Mancini and L. B. Wolff, 3 D shape and light source location from depth and reflectance, in Proceedings of 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp 707 -709.
[112] J.-Y. Herve and Y. Aloinionos, Exploratory active vision: theory, in Proceedings of 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1992, pp10-15.
[113] K. Ikeuchi, Numerical Shape from Shading and Occluding Contours in a Single View,Artificial Intelligence Lab., MIT, Cambridge, AI Memo 566, 1980.
[114] R. Zhang, P.-S. Tsai, J. E. Cryer, and M. Shah, Shape-from-shading: a survey, IEEE Transactions on Pattern Analysis and Machine Intelligence, 21(8), Aug. 1999, pp 690 -706.
[115] R. Zhang and M. Shah, Height Recovery from Intensity Gradient, in Proceedings of 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994,pp508-513.
[116] D. Suter, Motion estimation and vector splines, in Proceedings of 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 939 -942.
[117] D. R. Hougen and N. Ahuja, Adaptive Polynomial Modelling of the Reflectance Map for Shape Estimation from Stereo and Shading, in Proceedings of 1994 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1994, pp 991 -994.
[118] S. Bakshi and Y.-H. Yang, Shape from shading for non-Lambertian surfaces, in Proceedings of 1994 IEEE International Conference Image Processing, 1994(2), pp 130 -134.
[119] Y. Sato and K. Ikeuchi, Reflectance analysis under solar illumination, in Proceedings of the Workshop on Physics-Based Modeling in Computer Vision, 1995, pp 180 -187.
[120] Y.-L. Tian and H. T. Tsui, Shape from shading for non-Lambertian surfaces from one color image, in Proceedings of the 13th International Conference on Pattern Recognition,1996(1),pp258-262.
[121] S.-H. Lai and B.-C. Vemuri, Physically based adaptive preconditioning for early vision,IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(6), June 1997, pp 594-607.
[122] A. Yuille, M. Ferraro, and T. Zhang, Surface shape from warping, in Proceedings of 1997 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1997,pp846-851.
[123] E. Kobayashi, T. Fukuda, K. Shimojima, and T. Takusagawa, Shape reconstruction system integrating stereo vision and shape-from-shading-shape reconstruction using pair improvement method, in Proceedings of 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems, 1998(3), pp 1847 -1852.
[124] R. Zhang and M. Shah, Shape from Intensity Gradient, IEEE Transactions on Systems,Man and Cybernetics, Part A, 29(3), May 1999, pp 318 -325.
[125] P. L. Worthington and E. R. Hancock, Data-driven Shape-from-Shading using Curvature Consistency, in Proceedings of 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 1999(1), pp 288 -293.
[126] H. Lange, Advances in the cooperation of shape from shading and stereo vision, in Proceedings of the Second International Conference on 3-D Digital Imaging and Modeling,1999, pp46-58.
[127] N. J. Ferrier and R. W. Brockett, Reconstructing the Shape of a Deformable Membrane form Image Data, The International Journal of Robotics Research, 19(9), Sept. 2000, pp795-816.
[128] S.-Y. Cho and T. W. W. Chow, Shape and Surface Measurement Technology by an Improved Shape-From-Shading Neural Algorithm, IEEE Transactions on Industrial Electronics, 47(1), Feb. 2000, pp 225 -230.
[129] A. G. Bors, E. R. Hancock, and R. C. Wilson, Terrain Modeling in Synthetic Aperture Radar Images using Shape-from-Shading, in Proceedings of the 15th International Conference on Pattern Recognition, 2000(1), pp 798 -801.
[130] D. Weinshall, Local Shape Approximation from Shading, Journal of Mathematical Imaging and Vision, 4(2), April 1994, pp 119—138.
[131] D. Baskent and B. Barshan, Surface Profile Determination form Multiple Sonar Data Using Morphological Processing, the International Journal of Robotics Research, 18(8),August 1999,pp788-808.
[132] A. Pentland, Fractal-Based Description of Natural Scenes, IEEE Trans. On Pattern Analysis and Machine Intelligence, 6(6), Nov. 1984, pp 661-674.
[133] P. Kube and A. Pentland, On the Imaging of Fractal Surfaces, IEEE Trans. On Pattern Analysis and Machine Intelligence, 10(5), Sept. 1988, pp 704-707.
[134] R. Szeliski and D. Terzopoulos, From Splines to Fractals, Computer Graphics, 23(3),July 1989,pp51-60.
[135] S. J. Lee, P. Y. Wu, and K. T. Sun, Fractal Image Compression Using Neural Networks,in Proc. of International Joint Conference on Neural Networks (IJCNN'98), pp. 613-618,Anchorage, Alaska.
[136] P. W. Fieguth and A. S. Willsky, Fractal Estimation Using Models on Multiscale Trees, IEEE Trans. On Signal Processing, 44(5), May 1996, pp 1297-1300.
[137] Y. Zhou, P.C. Yip, and H. Leung, On the Efficient Prediction of Fractal Signals, IEEE Trans. On Signal Processing, 45(7), July 1997, pp 1865-1997.
[138] G. W. Wornell, A Karhunen-Loeve-like Expression for 1/f Processes via Wavelets, IEEE Trans. On Information Theory, 36(4), July 1990, pp 859-861.
[139] A. H. Tewlik, Correlation Structure of the Discrete Wavelet Coefficients of Fractional Brownian Motion, IEEE Trans. On Information Theory, 38(2), Mar. 1992, pp 904-909.
[140] A. M. Sabatini, Wavelet-Based Estimation of 1/f-Type Signal Parameters: Confidence Intervals Using the Bootstrap, IEEE Trans. On Signal Processing, 47(12), Dec. 1999, pp3406-3409.
[141] P. Flandrin, Wavelet Analysis and Synthesis of Fractional Brownian Motion, IEEE Trans.On Information Theory, 38(2), Mar. 1992, pp 910-917.
[142] G. W. Wornell and A. V. Oppenheim, Estimation of Fractal Signals from Nosy Measurments Using Wavelets, IEEE Trans. On Signal Processing, 40(3): 611-623, Mar. 1992.
[143] W.-L. Wang, Estimation of Fractional Brownian Motion Embedded in a Noisy Environment Using Nonorthogonal Wavelets, IEEE Trans. On Signal Processing, 47(8):2211-2219, August 1999.
[144] Z. Han and T. S. Denney, A New Method for Fractional Brownian Motion Interpolation,IEEE Trans. On Signal Processing, 47(11): 3159-3164, Nov. 1999.
[145] L. M. Kaplan and C.-C. J. Kuo, Fractal Estimation from Noisy Data via Discrete Fractional Gaussian Noise (DFGN) and the Haar Basis, IEEE Trans. On Signal Processing,41(12): 3554-3562, Dec. 1993.
[146] L. M. Kaplan, Extended Fractal Analysis for Texture Classification and Segmentation,IEEE Trans. On Image Processing, 8(11): 1572-1585, Nov. 1999.
[147] L. M. Kaplan and C.-C. J. Kuo, An Improved Method for 2-D Self-Similar Image Synthesis, On Image Processing, 5(5): 754-760, May 1996.
[148] B. Yazici and R. L. Kashyap, A Class of Second-Order Stationary Self-Similar Processes for 1/f Phenomena, IEEE Trans. On Signal Processing, 45(2): 396-410, Feb. 1997.
[149] Lin Zhou; Leung Tsang; Jandhyala, V.; Chi-Te Chen, Studies on accuracy of numerical simulations of emission from rough ocean-like surfaces, IEEE Transactions on Geoscience and Remote Sensing, Volume: 39 Issue: 8 , Aug. 2001, pp 1757 -1763.
[150] Franceschetti, G; Iodice, A.; Riccio, D, Scattering from dielectric random fractal surfaces via method of moments, IEEE Transactions on Geoscience and Remote Sensing, Volume: 38 Issue: 4 Part: 1 , July 2000, pp 1644-1655.
[151] Franceschetti, G; Iodice, A.; Riccio, D.; Ruello, G, Scattering from fractal dielectric profiles: the extended boundary condition method, in Proceedings of IEEE 2000 International Conference on Geoscience and Remote Sensing Symposiun, IGARSS 2000. , Volume: 4 , 2000,pp 1727-1729 vol.4.
[152] Scowen, B.C.; Smith, S.L.; Vannan, M.A., Quantitative 3D modelling of the left ventrical from ultrasound images [ventrical read ventricle], in Proceedings of the 26th Euromicro Conference, 2000., Volume: 2 , 2000, pp 432 -439 vol.2.
[153] Onufriyenko, V.M.; Samolchev, P.A.; Slyusarova, T.I., Interaction of an electrostatic field with a dielectric body, Microwaves, 13th International Conference on Radar and Wireless Communications. 2000. MIKON-2000., Volume: 2 , 2000, pp 502 -505 vol.2.
[154] Berizzi, F.; Dalle Mese, E.; Pinelli, G, One-dimensional fractal model of the sea surface,in IEE Proceedings of Radar, Sonar and Navigation, Volume: 146 Issue: 1 , Feb. 1999, pp 55-64.
[155] Wang, X.; Yoshimura, N., Fractal phenomena. Dependence of hydrophobicity on surface appearance and structural features of SIR insulators, IEEE Transactions on [see also Electrical Insulation, IEEE Transactions on] Dielectrics and Electrical Insulation, Volume: 6 Issue: 6 ,Dec. 1999, pp 781 -791.
[156] Franceschetti, G; Iodice, A.; Migliaccio, M.; Riccio, D., Scattering from natural rough surfaces modeled by fractional Brownian motion two-dimensional processes, IEEE Transactions on Antennas and Propagation, Volume: 47 Issue: 9 , Sept. 1999, pp 1405 -1415.
[157] Berizzi, F.; Dalle-Mese, E., Fractal analysis of the signal scattered from the sea surface,IEEE Transactions on Antennas and Propagation, Volume: 47 Issue: 2 , Feb. 1999, pp 324-338.
[158] Guo Lixin; Wu Zhensen, Electromagnetic scattering from 2D band-limited fractal surface using Kirchhoff approximation, in Proceedings of (ICCEA '99) 1999 International Conference on Computational Electromagnetics and Its Applications, 1999, pp 456 -459.
[159] Franceschetti, G; Migliaccio, M.; Riccio, D., The validity of the Kirchhoff approximation for fractal surface scattering, Geoscience and Remote Sensing Symposium, in Proceedings of IEEE 1999 International Conference on IGARSS., Volume: 5 , 1999, pp 2407 -2409.
[160] Eliseev, M.V.; Isayeva, O.B.; Rozhnev, A.G.; Ryskin, N.M., Numerical simulation of electron field emission from fractal surface, in International University Conference Proceedings of Electronics and Radiophysics of Ultra-High Frequencies, 1999, pp 309 -312.
[161] Price, J.R.; Hayes, M.H., III, Fractal interpolation of images and volumes, in Conference Record of the Thirty-Second Asilomar Conference on Signals, Systems & Computers, 1998,Volume: 2, 1998, pp 1698-1702.
[162] Wang, X.; Kumagai, S.; Yoshimura, N., Fractal analysis on the recovery of contaminant properties of silicone rubber insulator against acid rain, in Proceedings of 1998 International Symposium on Electrical Insulating Materials, 1998, pp 619 -622.
[163] Dansereau, R.; Kinsner, W., Progressive transmission of images through fractal surface interpolation, in Proceedings of IEEE Canadian Conference on Electrical and Computer Engineering, 1998. , Volume: 1 , 1998, pp 277 -280.
[164] Berizzi, F.; Dalle Mese, E., Scattering analysis from fractal sea surfaces, in Proceedings of 1998 IEEE International Symposium on Geoscience and Remote Sensing, 1998. IGARSS '98. , Volume: 5 , 1998, pp 2483 -2486.
[165] Vemuri, B.C.; Mandal, C; Shang-Hong Lai, A fast Gibbs sampler for synthesizing constrained fractals, IEEE Transactions on Visualization and Computer Graphics, Volume: 3 Issue: 4 , Oct.-Dec. 1997, pp 337 -351.
[166] Zangari, G; Lambeth, D.N., Porous aluminum oxide templates for nanometer-sized cobalt arrays, IEEE Transactions on Magnetics, Volume: 33 Issue: 5 Part: 1 , Sept. 1997, pp3010-3012.
[167] Dansereau, R.; Kinsner, W., Image compression through fractal surface interpolation and wavelet compression, in Proceedings of IEEE Conference on WESCANEX 97:Communications, Power and Computing, 1997, pp 94 -99.
[168] Nai-Yu Wang; Vesecky, J.F., Active/passive microwave method for sea surface temperature estimation, in Proceedings of MTS/IEEE Conference on OCEANS '97, Volume: 2, 1997,pp 1155-1157.
[169] Nigmatullin, R.; Ryabov, Ya.; Polygalov, E.; Fewldman, Yu., The fractal nature of electrode polarization, in Proceedings of Seventh International Conference on Dielectric Materials, Measurements and Applications, (Conf. Publ. No. 430), 1996, pp 164 -167.
[170] Vemuri, B.C.; Mandal, C, A fast Gibbs sampler for synthesizing constrained fractals, in Proceedings of .Visualization '96., 1996, pp 29 -35.
[171] Heneghan, C; Lowen, S.B.; Teich, M.C., Two-dimensional fractional Brownian motion: wavelet analysis and synthesis, in Proceedings of the IEEE Southwest Symposium on Image Analysis and Interpretation, 1996, pp 213 -217.
[172] Dansereau, R.; Kinsner, W., Perceptual image compression through fractal surface interpolation, in Proceedings of Canadian Conference on Electrical and Computer Engineering, 1996., Volume: 2 , 1996, pp 899 -902.
[173] Axelsson, S.R.J.; Johnsson, K.-G.; Tullsson, B.-E.; Kjellgren, J.; Carlstrom, A.,Comparison of measured and predicted scattering coefficients at 94 GHz, in Proceedings of International Geoscience and Remote Sensing Symposium (IGARSS '94) on Surface and Atmospheric Remote Sensing: Technologies, Data Analysis and Interpretation., Volume: 3 ,1994,pp 1631 -1634.
[174] Chen, S.S.; Keller, J.M.; Crownover, R.M., On the calculation of fractal features from images, IEEE Transactions on Pattern Analysis and Machine Intelligence, Volume: 15 Issue: 10,Oct. 1993,pp1087-1090.
[175] Vemuri, B.C.; Radisavljevic, A., From global to local, a continuum of shape models with fractal priors, Proceedings of 1993 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR '93), pp 307 -313.
[176] Chan, K.L., Fractal-based texture analysis, Singapore ICCS/ISITA '92 of 'Communications on the Move', 1990, pp 102 -106.
[177] Allinson, N.M.; Lawson, M., Accurate textural characterisation using fractal techniques,IEE Colloquium on Application of Fractal Techniques in Image Processing, , 1990, pp 6/1-6/6.
[178] Jaggard, D.L.; Sun, X., Scattering from bandlimited fractal fibers, IEEE Transactions on Antennas and Propagation, Volume: 37 Issue: 12 , Dec. 1989, pp 1591 -1597.
[179] Britton, D., Surface modeling algorithm for pyramid architectures, in Proceedings of 2nd Symposium on the Frontiers of Massively Parallel Computation, 1989, pp 321 -322.
[180] T. Blu and M. Unser, Wavelets, fractals and radial basis functions, IEEE Trans. On Signal Processing, vol. 50, no. 3, pp. 543-553, March 2002.
[181] K. Arakawa and E. Krotkov, Estimating of Fractal Dimension from Range Images of Natural Terrain, Technical Report CMU-CS-91-156, Carnegie Mellon University, School of Computer Science, 1991.
[ 182] J. P. Lewis, Is the Fractal Model Appropriate for Terrain?, in section 6.1 of paper [240].
[183] T. Gneiting and M. Schlather, Stochastic Models Which Separate Fractal Dimension and Hurst Effect, Society for Industrial and Applied Mathematics (SIAM) Review, 46(2), 1995,pp269-282.
[184] H. Xie, D. Chen, and X. Kong, Characterization on Three-Dimensional Surface Topography of Textured Cold-Rolled Steel Sheets, in Proc. of the First Asia Inter. Conf. on Trib, Tsinghua University, Beijing, pp 396-399, 1998.
[185] K. S. Pedersen and M. Nielsen, The Haustorff Dimension and Scale-Space Normalization of Natural Images, Journal of Visual Communication and Image Representation, 11, 266-277, 2000.
[186] J. Militky and V. Bajzik, Influence of Wool Content on Properties of Blended Fabrics,International Journal of Clothing Science and Technology, Volume 6, Issue 23, August 1994,pp. 32-36.
[187] G. Chan and A. T. A. Wood, Estimation of Fractal Dimension for A Class of Non-Gaussian Stationary Processes and Fields, Annals of Statistics, 32(3), 2004, pp 1222-1260.
[188] C. Traina Jr., A. Traina, L. Wu, and C. Faloutsos, Fast Feature Selection Using Fractal Dimension, in Proceedings of XV Brazilian Symposium on Databases (SBBD), Paraiba, Brazil, October, 2000.
[189] E. P. M. de Sousa, C. Traina Jr., and A. Traina, How to Use Fractal Dimension to Find Correlations Between Attributes, in Proceedings of KDD-Workshop on Fractals and Self-similarity in Data Mining: Issues and Approaches, 2002.
[190] J. -C. Liu, W. -L. Hwang, and M. -S. Chen, Estimation of 2D Noisy Fractional Brownian Motion and Its Applications Using Wavelets, IEEE Transactions on Image Processing, 9(8), pp 1407-1419, August 2000.
[191] B. Xie, S. Zhu, and G. Hu, Blind Fractal Signal Estimation for SCDMA Systems Over Multipath Fading Channels, In Proceedings of 2000 International Conferences on Communication Technology, (ICCT' 2000), Beijing, August, 21-25, 2000, pp 359-362.
[192] J. -C. Liu and W. -L. Hwang, Parameter Estimation and Denoising of 2-D Noisy Fractional Brownian Motion Using Non-Orthogonal Wavelets, in Proceedings of IEEE Symposium on Time Frequency and Time Scale Analysis, Pittsburg, October 1998.
[193] K. E. Timmermann and R. D. Nowak, Multiscale Modeling and Estimation of Poisson Processes with Application to Photon-Limited imaging, IEEE Transactions on Information Theory, 45(3), April 1999, pp 846-862.
[194] E. Lutton etc., Mixed IFS: Resolution of Inverse Problem Using Genetic Programming, Complex Systems, Vol. 9, 1995, pp 375-398.
[195] J. C. Hart, Implicit Representations of Rough Surfaces, Computer Graphics Forum, 16(2), June 1997.
[196] C. M. Wittenbrink, IFS Fractal Interpolation for 2D and 3D Visualization, In Proceedings of the 6th IEEE conference on Visualization '95, 1995, pp 77.
[197] W. O. Kochran, J. C. Hart, and P. J. Flynn, Similarity and Affinity Hashing: A Computer Vision Solution to the Inverse Problem of Linear Fractals, Fractals, 5 (Supplementary Issue), April 1997, pp 39-50.
[198] G. Vines, Signal Modeling with Iterated Function Systems, PhD Thesis, Georgia Institute of Technology, 1993.
[199] 陈守吉、张立明编著，《分形与图像压缩》，上海科技教育出版社。
[200] 肯尼思·法尔科内内，著，曾文曲、刘世耀 译，《分形几何——数学基础及其应用》，东北大学出版社，1991年8月。
[201] 肯尼思·法尔科内 著，曾文曲、王向阳、陆夷 译，《分形几何中的技巧》，东北大学出版社，1999年6月第1版，1999年6月第1次印刷。
[202] M. J. Turner, J. M. Blackledge, and R R. Andrews, Fractal Geometry in Digital Imaging, Academic Press 1998, 525 B Street, Suite 1900, San Diego, California 92101-4495, USA.
[203] R R. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, 1994.
[204] John C. Russ, Fractal Surfaces, Plenum Press, New York and London, 1994.
[205] Natalia Alexandrov and J. E. Dennis, Multilevel Algorithms for Nonlinear Optimization,NASA CR-194940 ICASE Report No. 94-53, Institute for Computer Applications in Science and Engineering Mail Stop 132C, NASA Langley Research Center Hampton, VA 23681-0001, June 1994, pp. 21.
[206] M. S. Gockenbach, A. J. Kearsley, and W. W. Symes, An Infeasible Point Method for Minimizing the Lennard-Jones Potential, Computational Optimization and Applications, 8(3),1997,pp 273-286.
[207] P. T. Boggs, J. W. Tolle, and A. J. Kearsley, A Truncated SQP Algorithm for Large Scale Nonlinear Programming Problems, In Susana Gomez and Jean-Pierre Hennart, editors, Advances in Optimization and Numerical Analysis: Proceedings of the Sixth Conference on Numerical Analysis and Optimization, pages 69-78, Dordrecht, 1994. Kluwer Academic Publishers.
[208] P. T. Boggs, J. W. Tolle, and A. J. Kearsley, On the Convergence of A Trust Region SQP Algorithm for Nonlinearly Constrained Optimization Problems, In J. Dolezal, editor, Proceedings of the 17th IFIP TC7 Conference on System Modeling and Optimization, pp1-14, London, 1995. Chapman.
[209] A. J. Kearsley, The Use of Optimization Techniques in the Solution of Partial Differential Equations from Science and Engineering, Technical Report and Ph.D. Thesis,Rice University, Department of Computational and Applied Mathematics, 1996.
[210] J. E. Dennis, M. EL-Alem, and K. Williamson, A Trust Region Approach to Nonlinear Systems of Equalities and Inequalities, SIAM. J. Optim., 9(2), 1999, pp. 291-315.
[211] J. E. Dennis, M. Heinkenschloss, and L. N. Vicente, Trust Region Interior-Point SQP Algorithms for A Class of Nonlinear Programming Problems, SIAM Journal on Control and Optimization, 36(5), Sep. 1998, pp 1750-1794.
[212] J. Marin and R. V. Sole, Macroevolutionary Algorithms: A New Optimization Method on Fitness Landscapes, IEEE Transactions on Evolutionary Computation, 3(4), Nov. 1999, pp272-286.
[213] A. Gupta, Improved Symbolic and Numerical Factorization Algorithms for Unsymmetric Sparse Matriccs, IBM Research Report RC 22137 (99131), August 1, 2001.
[214] M. C. Turley and E. D. Ford, A Comparison on Consistency of Parameter Estimation Using Optimization Methods for a Mixture, NRCSE Technical Report Series (NRCSE-TRS) No. 050,July 17, 2000.
[215] R. Koch and W. Benzing, Multi-Dimensional Parameter Optimization for RSFQ Circuit Design, Ext. Abs. ISEC'97, pp 305-307, 1997.
[216] M. A. Branch, T. F. Coleman, and Y. Li, A Subspace, Interior, and Conjugate Gradient Method for Large-Scale Bound-Constrained Minimization Problems, SIAM. Sci. Comput., Vol. 21,No. 1.pp 1-23, 1999.
[217] L. Gilles, C. Vogel, and B. Ellerbroek, A Multigrid Preconditioned Conjugate Gradient Method for Large Scale Wavefront Reconstruction, JOSA A, Vol. 19, Issue 9, pp 1817-1822,Sept. 2002.
[218] J. E. Dennis, Jr., and R. M. Lewis, A Comparison of Nonlinear Programming Approaches to An Elliptic Inverse Problem and A New Domain Decomposition Approach,Tech. Rep. TR94-33, Department of Computational and Applied Mathematics, Rice University, 1994.
[219] J. P. Hamalainen, CFD Coupled with Shape Optimization - A New Promising Tool in Paper Machine R&D, in Proceedings of 10th Conference of European Consortium for Mathematics in Industry, L. Arkeryd, H. Engl, A. Fasano, R. Mattheij, P. Neittaanmaki, H.Neunzert (eds.), B.G. Teubner, Stuttgart-Leipzig, 1999, pp. 171-178 (jointly with: J. Hamalainen).
[220] A. J. Kearsley, R. A. Tapia, and M. W. Trosset, The Solution of The Metric STRESS and SSTRESS Problems in Multidimensional Scaling Using Newton's Method, Computational Statistics, Vol.13, 1998, 369-396.
[221] S. E. Minkoff, Implementation of The Conjugate Gradient Algorithm in DSO, Tech Report 94-31, Department of Computational and Applied Mathematics, Rice University,July 11, 1994.
[222] J. Dong, J. Shi, S. Wang, and Y. Xue, A Trust Region Algorithm for Equality-Constrained Optimization via A Reduced Dimension Approach, Journal of Computational and Applied Mathematics, 152(2003), pp 99-118.
[223] S. J. Oshcr and F. Santosa, Level Set Methods for Optimization Problems Involving Geometry and Constraints: I. Frequencies of a Two-Density Inhomogeneous Drum, Journal of Computational Physics 171, pp 272-288, 2001.
[224] S. Ta'asan, Differential Optimization Problems: Analysis of the Hessian, IMA, Optimization in Simulation-Based Models, January 9-16, 2000.
[225] S. Henn and K. Witsch, Iterative Multigrid Regularization Techniques for Image Maching, SIAM. Sci. Comput. Vol. 23, No. 4, pp 1077-1093, 2001.
[226] M. S. Gockenbach and A. J. Kearsley, Optimal Signal Sets for Non-Gaussian Detectors,SIAM Journal on Optimization, 9(2), 1999, pp 316-326.
[227] A. Takeda, Successive Convex Relaxation Methods for Nonconvex Quadratic Optimization Problems, In Proceedings of The Intrnational Conference on Complementarity 99, June 9-12, 1999, Madison, Wisconsin.
[228] C. A. Floudas and V. Visweswaran, Quadratic Optimization, in Handbook of Global Optimization (R.Horst and P.M. Pardalos, Editors), Kluwer Academic Publishers, pp. 217-270(1994).
[229] P. T. Boggs and J. W. Tolle, Sequential Quadratic Programming, Acta. Numerica. 1996,pp 1-52.
[230] S. Kruk and H. Wolkowicz, SQ2P, Sequential Quadratic Constrained Quadratic Programming, Research Report CORR 97-01, University of Waterloo, August 7, 1998.
[231] S. Kim and M. Kojima, Exact Solutions of Some Nonconvex Quadratic Optimization Problems via SDP and SOCP Relaxations, Computational Optimization and Applications, 26(2), 2003, pp 143-154.
[232] S. J. Benson, Y. Ye, and X. Zhang, Solving Large-Scale Sparse Semidefinite Programs for Combinatorial Optimization, SIAM Journal on Optimization, 10(2), 2000, pp 443-461.
[233] V. Migallon, J. Penades, D. B. Szyld, Block Two-Stage Methods for Singular Systems and Markov Chains, Report 95-121, Dec. 1995. Also in Proceedings of the Conference on Algebraic Multilevel Iteration Methods with Applications, Nijmegan, The Netherlands, June 13-15, 1996.
[234] Stan Z. Li, Markov Random Field Modeling in image Analysis, Springer Berlin Heidelberg New York, 2nd ed., 2001, ⅪⅩ, 323 p. 99 illus., Softcover, ISBN: 4-431-70309-8.
[235] 崔景泰(美国) 著，程正兴 译，白居宪 审校，《小波分析理论》，西安交通大学出版社，1995年1月第1版，1997年1月第2次印刷。
[236] 秦前清、杨宗凯 编著，《实用小波分析》，西安电子科技大学出版社，1994年1月第1版，1998年1月第4次印刷。
[237] C. Vogel, Regularization methods: An Applied Mathematician's Perspective, www.samsi.info/talks/inversc/Inverse-Vogel.pdf
[238] 齐尔旭，《分形及其计算机生成》，科学出版社，1994年11月，页130。
[239] Randal Barnes, Variogram Tutorial, Golden Software, Inc., www.goldensoftware.com/variogramTutorial.pdf.
[240] J. R Lewis, Generalized stochastic subdivision, ACM Transactions on Graphics, Vol. 3, July 1987, pp 167-190.
[241] J. Y. Yuan and P. Y. Yalamov, A Method for Constructing Diagonally Dominant Preconditioners based on Jacobi Rotations, Applied Mathematics and Computation, 2004.
[242] R. H. Riedi, Multifractal Processes, in "Long Range Dependence: Theory and Applications", eds. Doukhan, Oppenheim and Taqqu, Birkhauser, 2001.
[243] J. v. L. v. Pabst and H. Jense, Dynamic Terrain Generation Based on Multifractal Techniques, in Proceedings of the International Workshop on High Performance Computing for Computer Graphics and Visualisation, Swansea, 3-4 July 1995.
[244] 廖熠、赵荣椿，从明暗恢复形状方法综述，中国体视学第一届联合学术会议论文集，2000年8月，页310-315。
[245] 廖熠、赵荣椿，几类SFS典型算法分析与评价，中国图像图形学报，第六卷(A版)第10期，2001年10月，页953-961。
[246] 廖熠、赵荣椿，从明暗恢复形状问题中的一种分形约束方法探讨，信号处理，第十七卷第六期，2001年，页521-527。
[247] 廖熠、赵荣椿，一种基于小波分层模型的自然景物图像表面恢复算法，信号处理，第十七卷 (增刊)，2001年11月，395-399。
[248] 廖熠、赵荣椿，基于Hamilton系统理论的SFS模型分析，系统仿真学报，第十三 卷 (增刊)，2001年，页30-32。
[249] Yi Liao, Rong-chun Zhao, A New Relaxation Algorithm for Linearized SFS Problem, Chinese Journal of Electronics, accepted, Nov. 2002.
[250] Y. Liao and R. C. Zhao, "A Novel Method for Solving the Shape from Shading (SFS) Problem", in Proceedings of Second International Conference on Natural Computation (ICNC 2006), Ⅱ, Xi'an, China, Sep. 2006, pp 714-723.
[251] T. S. Pan and A. E. Yagle, "Numerical Study of Multigrid Implementations of Some Iterative Image Reconstruction Algorithms", IEEE Transactions on Medical Imaging, 10(4), 1991, pp 572-588.