基于图像灰度信息的自由曲面自组织重构的研究
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摘要
自由曲面的三维重构技术在制造工业、艺术设计及医疗整形等领域具有广泛的应用价值。从单幅图像的灰度信息重构物体形貌(Shape from Shading,SFS)已成为计算机视觉的一个重要分支,是实现自由曲面三维重构的手段之一。但传统的SFS方法重构精度低、普适性差,而且局限于理想的漫反射模型。因此,本文将系统理论中的自组织原理引入到SFS中,将图像中的每个象素视为具有决策能力的生命单元,以灰度图像为模板,在此模板引导下,模仿生物群体的自组织行为,实现自由曲面的三维重构。
本文首先对自由曲面自组织重构方法的可行性进行了研究。该方法将自由曲面视为由若干微观曲面组成的宏观曲面,并将每个微观曲面当作具有生命力的自组织单元。若微观曲面的形貌为已知,则在自组织系统的机制作用下,利用相邻自组织单元之间的短程通信以及决策能力,按照一定的演化规则,由微观曲面的形貌进行自组织迭代,逐渐重构出宏观的自由曲面。由于自组织系统具有从简单到复杂、从粗糙到细致的进化能力,因而基于自组织原理的自由曲面重构方法具有较强的抗噪性,能够消除微观曲中的一定误差。
本文提出了三种理想漫反射模型下的自由曲面自组织重构方法,即基于三角片化的自由曲面自组织重构方法、基于二次曲面拟合的自由曲面自组织重构方法和基于表面法线调整的自由曲面自组织重构方法。
基于三角片化的自由曲面自组织重构方法将图像中的每个象素视为自组织系统中的生命单元,每个生命单元与其相邻的两个单元组成一个三角片,该生命单元调整自己的状态,使其与邻域单元构成的三角片按朗伯反射模型(Lambertian reflectance model)满足原始灰度图像的要求。所有生命单元进行并行调整、协同处理,从而重构出自由曲面。
基于二次曲面拟合的自由曲面自组织重构方法在待重构的自由曲面上某点的邻域内,依据图像的灰度模板,按照朗伯反射模型拟合一个二次曲面,并将该二次曲面视为自由曲面在该点处的微观模型。将拟合所得的每个微观曲面视为具有生命力的自组织单元,在自组织系统的内在机制作用下,重构得到宏观曲面。
基于表面法线调整的自由曲面自组织重构方法改变了重构结果的表达方式,将自由曲面的表面法线视为生命单元。该方法首先对自由曲面的表面法线进行初始化,然后依据图像模板,按照自组织系统的内在演化规则,在灰度梯度约束、光滑约束、可积性约束和灰度约束的限制下,对自由曲面的表面法线进行调整,逐渐得到真实的表面法线。然后根据每个生命单元及其邻域内的表面法线拟合二次曲面,并将此二次曲面视为微观模型,再根据自组织系统,重构出宏观曲面。
为了提高SFS的普适能力,本文将自组织重构技术扩展到一般光照模型下。首先建立物体表面反射特性的测定装置,用来测量物体表面的反射特性。按照Phong光照模型,根据测定的反射特性参数,对物体表面的光照成分进行分离,得到漫反射成分和镜面反射成分,再利用其中的漫反射成分来进行自由曲面的重构。
实验结果表明,本文的自由曲面自组织重构方法具有较高的重构能力、较好的普适性,且可以实现一般光照模型下的自由曲面重构。该方法首次将自组织原理引入到SFS方法中,具有一定的理论价值;同时将SFS技术扩展到一般光照模型下,因而具有一定的实用价值。本文研究结果进一步完善后,可以应用于地貌航测或者月球地貌的重构、整形医疗中基于图像的三维头像或者胸像恢复、军事中移动机器人的精确导航。因此该方法能够应用于军事、医疗、艺术以及太空探测等领域,具有一定的学术价值和应用前景。
The three-dimension reconstruction technique of free-form surfaces has been widely used in many fields such as manufacturing industry, art design, medical treatment and plastic surgery. Shape from shading (SFS), an important branch in computer vision field, is one of reconstruction methods of free-form surface. In order to overcome some disadvantages of traditional SFS methods such as low reconstruction precision, limited compatibility and constrained application under Lambertian reflectance model, this dissertation studies and proposes a novel SFS method based on self-organization principle in system theory. This method takes the intensity image as a target template, treats each pixel of an image as a bion that possesses decision-making capacity, and simulates the self-organization behavior of biotic populations to reconstruct the free-form surfaces guided by the target template.
This dissertation uses a novel SFS method based on self-organization principle to reconstruct surface. First the feasibility of this method is studied. The free-form surface to be reconstructed is regarded as a macro-surface which is composed of some micro-surface. By using the mechanism of self-organization system, each micro-surface is treated as a bion that possesses decision-making capacity, and uses its local communication and decision-making capacity to gradually realize the self-organizing reconstruction for the free-form macro-surface guided by the transition rule. Since self-organization system has the ability of evolution from simplicity to complexity, and from roughness to fineness, and it has antinoise capacity, this method can eliminate some error caused by inaccurate micro-surface.
Then based on self-organization principle, three SFS methods under idea Lambertian reflectance model are presented, namely self-organization freeform reconstruction method based on triangulation, self-organization freeform reconstruction method based on quadric surface, and self-organization freeform reconstruction method based on adjusting needle map.
In self-organization freeform reconstruction method based on triangulation, each pixel of an image is taken as a bion of self-organization system, and each bion and its two neighbors constitute a triangular surface patch, then this bion adjusts its state in order that the triangle element satisfies the Lambertian reflectance model. All bion can parallelly operate and cooperate with its neighbors, and gradually reconstruct the free-form surface.
In self-organization freeform reconstruction method based on quadric surface, the surface to be reconstructed can be divided into a union of micro-surface. According to the intensity target template of image, each micro-surface is approximated by a quadric surface under Lambertian reflectance map. Then each approximated micro-surface is treated as a vital self-organization unit, and all units reconstruct the macro-surface under the internal machanism of self-organization system.
The reconstructed results are expressed as surface normal in self-organization freeform reconstruction method based on adjusting needle map. In self-organization system, each surface normal is treated as a bion. At first all surface normals are initialed, then guided by the image template, surface normals are parallelly and gradually adjusted by a procedure which includes three constraints: smooth constraint, intensity gradient constraint and intensity constraint. And then micro-surface is approximated by a quadric surface from each surface normal and its neighbors, in the same way, the macro-surface can be reconstructed from the known micro-surface.
In order to improve the compatibility of SFS, the presented SFS technique is extended to general reflectance model. This study develops a measuring apparatus for the reflection model parameters, and then uses the parameters to separate reflection components from grayscale image, and then reconstructs free-form surface from the diffuse component.
The experiment results demonstrate this SFS approach has better precision and compatibility, and can be used under general reflectance model. This method introduces self-organization principle to SFS method for the first time, and extends its application to general reflection model, so it has estimable theory value. After being further improved, the results of this dissertation can be applied to many fields, such as aerial survey of relief of Earth’s or Moon’s surface, reconstruction of 3D head skeleton or breast from image in medical aesthetics, automatic navigation of mobile military robot, so it can be applied to military, arts, medical treatments, space exploration and so on, and this method is valuable for academic research and application.
本文首先对自由曲面自组织重构方法的可行性进行了研究。该方法将自由曲面视为由若干微观曲面组成的宏观曲面,并将每个微观曲面当作具有生命力的自组织单元。若微观曲面的形貌为已知,则在自组织系统的机制作用下,利用相邻自组织单元之间的短程通信以及决策能力,按照一定的演化规则,由微观曲面的形貌进行自组织迭代,逐渐重构出宏观的自由曲面。由于自组织系统具有从简单到复杂、从粗糙到细致的进化能力,因而基于自组织原理的自由曲面重构方法具有较强的抗噪性,能够消除微观曲中的一定误差。
本文提出了三种理想漫反射模型下的自由曲面自组织重构方法,即基于三角片化的自由曲面自组织重构方法、基于二次曲面拟合的自由曲面自组织重构方法和基于表面法线调整的自由曲面自组织重构方法。
基于三角片化的自由曲面自组织重构方法将图像中的每个象素视为自组织系统中的生命单元,每个生命单元与其相邻的两个单元组成一个三角片,该生命单元调整自己的状态,使其与邻域单元构成的三角片按朗伯反射模型(Lambertian reflectance model)满足原始灰度图像的要求。所有生命单元进行并行调整、协同处理,从而重构出自由曲面。
基于二次曲面拟合的自由曲面自组织重构方法在待重构的自由曲面上某点的邻域内,依据图像的灰度模板,按照朗伯反射模型拟合一个二次曲面,并将该二次曲面视为自由曲面在该点处的微观模型。将拟合所得的每个微观曲面视为具有生命力的自组织单元,在自组织系统的内在机制作用下,重构得到宏观曲面。
基于表面法线调整的自由曲面自组织重构方法改变了重构结果的表达方式,将自由曲面的表面法线视为生命单元。该方法首先对自由曲面的表面法线进行初始化,然后依据图像模板,按照自组织系统的内在演化规则,在灰度梯度约束、光滑约束、可积性约束和灰度约束的限制下,对自由曲面的表面法线进行调整,逐渐得到真实的表面法线。然后根据每个生命单元及其邻域内的表面法线拟合二次曲面,并将此二次曲面视为微观模型,再根据自组织系统,重构出宏观曲面。
为了提高SFS的普适能力,本文将自组织重构技术扩展到一般光照模型下。首先建立物体表面反射特性的测定装置,用来测量物体表面的反射特性。按照Phong光照模型,根据测定的反射特性参数,对物体表面的光照成分进行分离,得到漫反射成分和镜面反射成分,再利用其中的漫反射成分来进行自由曲面的重构。
实验结果表明,本文的自由曲面自组织重构方法具有较高的重构能力、较好的普适性,且可以实现一般光照模型下的自由曲面重构。该方法首次将自组织原理引入到SFS方法中,具有一定的理论价值;同时将SFS技术扩展到一般光照模型下,因而具有一定的实用价值。本文研究结果进一步完善后,可以应用于地貌航测或者月球地貌的重构、整形医疗中基于图像的三维头像或者胸像恢复、军事中移动机器人的精确导航。因此该方法能够应用于军事、医疗、艺术以及太空探测等领域,具有一定的学术价值和应用前景。
The three-dimension reconstruction technique of free-form surfaces has been widely used in many fields such as manufacturing industry, art design, medical treatment and plastic surgery. Shape from shading (SFS), an important branch in computer vision field, is one of reconstruction methods of free-form surface. In order to overcome some disadvantages of traditional SFS methods such as low reconstruction precision, limited compatibility and constrained application under Lambertian reflectance model, this dissertation studies and proposes a novel SFS method based on self-organization principle in system theory. This method takes the intensity image as a target template, treats each pixel of an image as a bion that possesses decision-making capacity, and simulates the self-organization behavior of biotic populations to reconstruct the free-form surfaces guided by the target template.
This dissertation uses a novel SFS method based on self-organization principle to reconstruct surface. First the feasibility of this method is studied. The free-form surface to be reconstructed is regarded as a macro-surface which is composed of some micro-surface. By using the mechanism of self-organization system, each micro-surface is treated as a bion that possesses decision-making capacity, and uses its local communication and decision-making capacity to gradually realize the self-organizing reconstruction for the free-form macro-surface guided by the transition rule. Since self-organization system has the ability of evolution from simplicity to complexity, and from roughness to fineness, and it has antinoise capacity, this method can eliminate some error caused by inaccurate micro-surface.
Then based on self-organization principle, three SFS methods under idea Lambertian reflectance model are presented, namely self-organization freeform reconstruction method based on triangulation, self-organization freeform reconstruction method based on quadric surface, and self-organization freeform reconstruction method based on adjusting needle map.
In self-organization freeform reconstruction method based on triangulation, each pixel of an image is taken as a bion of self-organization system, and each bion and its two neighbors constitute a triangular surface patch, then this bion adjusts its state in order that the triangle element satisfies the Lambertian reflectance model. All bion can parallelly operate and cooperate with its neighbors, and gradually reconstruct the free-form surface.
In self-organization freeform reconstruction method based on quadric surface, the surface to be reconstructed can be divided into a union of micro-surface. According to the intensity target template of image, each micro-surface is approximated by a quadric surface under Lambertian reflectance map. Then each approximated micro-surface is treated as a vital self-organization unit, and all units reconstruct the macro-surface under the internal machanism of self-organization system.
The reconstructed results are expressed as surface normal in self-organization freeform reconstruction method based on adjusting needle map. In self-organization system, each surface normal is treated as a bion. At first all surface normals are initialed, then guided by the image template, surface normals are parallelly and gradually adjusted by a procedure which includes three constraints: smooth constraint, intensity gradient constraint and intensity constraint. And then micro-surface is approximated by a quadric surface from each surface normal and its neighbors, in the same way, the macro-surface can be reconstructed from the known micro-surface.
In order to improve the compatibility of SFS, the presented SFS technique is extended to general reflectance model. This study develops a measuring apparatus for the reflection model parameters, and then uses the parameters to separate reflection components from grayscale image, and then reconstructs free-form surface from the diffuse component.
The experiment results demonstrate this SFS approach has better precision and compatibility, and can be used under general reflectance model. This method introduces self-organization principle to SFS method for the first time, and extends its application to general reflection model, so it has estimable theory value. After being further improved, the results of this dissertation can be applied to many fields, such as aerial survey of relief of Earth’s or Moon’s surface, reconstruction of 3D head skeleton or breast from image in medical aesthetics, automatic navigation of mobile military robot, so it can be applied to military, arts, medical treatments, space exploration and so on, and this method is valuable for academic research and application.
引文
[1]朱心雄,自由曲线曲面造型技术,第一版,北京:科学出版社,2000
[2]单东日,柯映林,刘云峰.反求工程中复杂曲面测量规划研究.中国机械工程,2003,14(1): 9~12
[3]孙家广,陈玉健,辜凯宁.计算机辅助几何造型技术.北京:清华大学出版社,1990. 126~165
[4]王宗彦.基于ICT和RP&M技术的产品快速反求系统研究.华北工学院学报,1999,20(4):294~297
[5]邢渊,周雄辉,阮雪榆.集成反向工程系统研究.机械工程学报,1998(3):1~6
[6]徐琳,袁保宗,高文.真实感人脸建模研究的进展与展望.软件学报,2003, 14(4): 804~810
[7]董兰芳,王洵,陈意云.真实感虚拟人脸的实现和应用.小型微型计算机系统,2002, 23(1): 90~92
[8]张青山,陈国良.具有真实感的三维人脸动画.软件学报,2003,14(3): 643~650
[9]王运赣.快速成形技术.武汉:华中理工大学出版社, 1999. 1~10
[10] Horn B K P. Shape From Shading: A method for obtaining the shape of a smooth opaque object from one view: [PhD thesis], MIT, 1970.
[11] Marr D. Vision. W. H. Freeman and Company, San Francisco.中译本:视觉计算理论.姚国正,刘磊,汪云九译,北京:科学出版社,1988. 6~37
[12] Mishra D K, Chandwani M. CCD camera based automatic dimension measurement and reproduction of 3-D objects. TENCON '93. Proceedings. Computer, Communication, Control and Power Engineering.1993 IEEE Region 10 Conference on Issue 0, Part 40000,19-21 Oct. 1993,4: 530~533
[13] Wang J G, Li Y F. 3D object modeling using a binocular vision system. Instrumentation and Measurement Technology Conference, 1999. IMTC/99. Proceedings of the 16th IEEE Volume 2, 24-26 May 1999, 2: 684~689
[14] Tsai R Y. A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lens. IEEE Journal of Robotics Automation. 1987, RA-3(4): 323~344
[15] Wei Guoqing, Ma Songde. Implicit and explicit camera calibration: theory andexperiments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, 16(5): 469~480
[16] Ma Songde. A self-calibration technique for active vision systems. Robotics and Automation, IEEE Transactions, 1996, 12(1): 114~120
[17] Hemayed E E. A survey of camera self-calibration. Proceedings. IEEE Conference on Advanced Video and Signal Based Surveillance, 2003. 21-22 2003(7): 351~357
[18]章毓晋.图像理解与计算机视觉.第一版.北京:清华大学出版社,2000
[19] Cryer James Edwin, Tsai Ping-Sing, Shah Mubarak. Integration of shape from X modules: Combining stereo and shading. IEEE computer society conference on: proceeding of computer vision and pattern recognition, 1993(15-17):720~721
[20] Weinshall Daphna. Qualitative depth and shape from stereo - in agreement with psychophysical evidence. ACM Technical report: AIM-1007, 1987
[21] Woodham R J. Photometric stereo: a reflectance map technique for determing surface orientation from a single view. Proc. SPIE, 1978, 155:136~143
[22] Nayar S K, Ikeuchi K, Kanade T. Extracting shape from reflectance of hybrid surfaces by photometric sampling. Image understanding workshop, 1989: 563~583
[23] Nayar S K, Gong Y. Colored interreflection and shape recovery. DARPA Image understanding workshop, 1992
[24] Christensen P H, Shapiro L G. Three dimensional shape from color photometric stereo. International Journal of Computer Vision, 1994, 13(2), p 213~217
[25] Boufama Boubakeur, Weinshall Daphna, Werman Mike. Shape from motion algorithms: a comparative analysis of scaled orthography and perspective. Proceedings of the third European conference on Computer vision, Stocklholm, Sweden, 1994(1): 199~204
[26] Barron J L, Fleet D J, Beauchemin S. Performance of optical flow techniques. International Journal of Computer Vision, 1994, 12(1):43~77
[27] Aloimonos Y, Swain M J. Shape from texture. Biological Cybernetics, 1988, 58(5):345~360
[28] Bajcsy R K, Lieberman L I. Texture gradient as a depth cue. Computer Graphics and Image Processing, 1976, 5(1):52~67
[29] Blostein D, Ahuja N. Shape from texture: Integrating texture-element extraction and surface estimation. IEEE Transaction on Pattern Analysis and MachineIntelligence, 1989, 11(12):1233~1251
[30] Clerc M, Mallat S. The texture gradient equation for recovering shape from texture. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2002, 24(4): 536~549
[31] Weik S A. A passive full body scanner using shape from silhouettes. Proc. International Conference on Pattern Recognition, 2000:1750~1753
[32]唐挺,李鹏程.基于轮廓的运动目标视觉分析的研究.四川理工学院学报, 2006(4):33~36
[33] Laurentini A. How far 3-D shapes can be understood from 2-D silhouettes. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1995, 17 (2): 188~195
[34] Laurentini A. The visual Hull concept for silhouette based image understanding. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1994, 16(2):150~162
[35] Gelli Daniele, Vitulano Domenico. Surface recovery by self shading projection. Signal Processing, 2004, 84(3):467~473
[36] Tankus Ariel, Sochen Nir, Yeshurun Yehezkel. A new perspective on shape from shading. Proceedings of the IEEE International Conference on Computer Vision, 2003(2):862~869
[37] Oliensis J. Uniqueness in shape from shading. International Journal of Computer Vision, 1991, 6(2):75~104
[38] Ragheb Hossein, Hancock Edwin R. Darboux smoothing for shape from shading. Pattern Recognition Letters, 2003, 24(1-3):579~595
[39] Ascher Uri M, Carter Paul M. Multigrid method for shape from shading. SIAM Journal on Numerical Analysis, 1993, 30(1):102~115
[40] Ikeda Osamu. A robust shape from shading algorithm using two images and control of boundary conditions. IEEE International conference on image processing, 2003(1): 405~408
[41] Oliensis J. Shape from shading as a partially well constrained problem. CVGIP: Image understanding, 1991, 54(2):163~183
[42] Saxberg Bror V H. Existence and uniqueness for shape from shading around critical points: Theory and an algorithm. International Journal of Robotics Research, 1992, 11(3):202~224
[43] Barnes Nick, Liu Zhiqing. Knowledge-based shape from shading. International Journal of Pattern Recognition and Artificial Intelligence, 1999, 13(1):1~23
[44] Zhong Sheng, Shi Qingyun, Cheng Minte. Fast shape from shading based on wavelet transform. Proceedings of SPIE: The International Society for Optical Engineering, 1994(2242):169~178
[45] Ramachandran V S. Perceiving shape from shading. Scientific America, 1988(159): 76~83
[46] Hayakawa Hideki , Nishida Shin'ya, Wada Yasuhiro, Kawato Mitsuo. Computational model for shape estimation by integration of shading and edge information. Neural Networks, 1994, 7(8):1193~1209
[47] Oren M, Nayar S K. Diffuse reflectance from rough surfaces. IEEE Proc. Computer Vision and Pattern Recognition, 1993: 763~764
[48] Forsyth D, Zisserman A. Mutual illumination. IEEE Proc. Computer Vision and Pattern Recognition, 1989: 466~473
[49] Prados Emmanuel, Faugeras Olivier, Camilli Fabio. Shape from shading: a well-posed problem? INRIA Research Report, No.RR-5297, August 2004.
[50] Zhang R, Tsai P S, Cryer J E, Shah M. Shape from shading: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(8):690~706
[51]郭东明,乌秀春,王晓明等.反求工程中基于图像灰度信息的三维曲面重构.机械工程学报, 2003, 39(1):47~50
[52] Horn B K P. Height and gradient from shading. International Journal of Computer Vision, 1989:37~75
[53] Ikeuchi K, Horn B K P. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 1981, 17(1-3): 141~184
[54] Camilli F, Grune L. Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. SIAM Journal on Numerical Analysis, 2000, 38(5):1540~1560
[55] Frankot R T, Chellappa R. A method for enforcing integrability in shape from shading algorithms. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1988(10): 439~451
[56] Christophe S. A survey of shading and reflectance models. Computer Graphics Forum 1994, 13(2): 121~131
[57] Pentland A P. Local shading analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6(2):170~187
[58] Lee C H, Rosenfeld A. Improved methods of estimating shape from shading using the light source coordinate system. Artificial Intelligence, 1985, 26: 125~143
[59] Lee K M , Kuo C C J. Shape from shading with a linear triangular element surface model. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1993, 15(8): 815~822
[60] Collings Simon. Single image shape from shading. [PhD Thesis], Computer science department, University of Western Australia, Sep.,2001
[61] Collings Simon, Kozera Ryszard, Noakes Lyle. A Piecewise quadratic approach to single image shape from shading. In Proc. 16th Int. Conf. Pattern Recognition ICPR'02, Quebec, Canada, 2002, (4): 126~129
[62] Prados E, Faugeras O, Rouy E. Shape from shading and viscosity solutions. In Proceedings of the 7th European Conference on Computer Vision, Copenhagen, Denmark, 2002(2): 790~804
[63] Prados E, Faugeras O. "Perspective shape from shading" and viscosity solutions. In Proceedings of the Ninth IEEE International Conference on Computer Vision, 2003. 826~831
[64] Rouy E, Tourin A. A viscosity solutions approach to shape from shading. SIAM Journal of Numerical Analysis, 1992, 29(3):867~884
[65] Lions P L, Rouy E, Tourin A. Shape-from-shading, viscosity solutions and edges. Numerical Math., 1993, 64:323~353
[66] Kimia B B, Kimmel R, Siddiqqi K, Bruckstein A M. Shape from shading: Level set propagation and viscosity solutions. International Journal of Computer Vision, 1995, (16):107~133.
[67] Kimmel R, Bruckstein A M. Tracking level sets by level sets: A method for solving the shape from shading problem. Computer Vision and Image Understanding, 1995, 62(2):47~48.
[68] Dupuis P, Oliensis J. Direct method for reconstructing shape from shading. IEEE Proc. Computer Vision and Pattern Recognition, 1992. 453~458
[69] Ishii H, Ramaswamy M. Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Communications in Partial DifferentialEquations, 1995(20):2187~2213
[70] Saito H, Usami K. Shape from shading using genetic algorithm. JECON’93, 1993:1620~1625
[71] Crouzil A, Descombes X, Durou J D. A multiresolution approach for shape from shading coupling deterministic and stochastic optimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(11):1416~1421
[72]杨敬安.基于照明参数与反射系数的分层SFS算法.自动化学报, 1999, 25(6): 735~742
[73] Hsieh J W, Liao M H Y, Ko M T, FanK C. Wavelet-based shape from shading. CVGIP: Graphical Models and Image Processing, 1995, (57):343~362
[74] Hsieh J W, Liao M H Y, FanK C, Ko M T. Wavelet-based shape from shading. Images & Recognition, 1994, 2(6):125~129
[75] Jiang Guang-Shan, Peng Danping. Weighted ENO Schemes for Hamilton-Jacobi Equations. SIAM Journal on Scientific Computing, 2000, 21(6):2126~2143
[76] Bichsel M, Pentland A P. A simple algorithm for shape from shading. IEEE Proc. Computer Vision and Pattern Recognition, 1992: 459~465
[77] Durou J D, Piau D. Ambiguous Shape from shading with critical points. Journal of Mathematical Imaging and Vision, 2000, 12(2):99~108
[78] Cheung W P, Lee C K, Li K C. Direct shape from shading with improved rate of convergence. Pattern Recognition, 1997, 30(3):353~365
[79] Pentland A P. Shape Information from Shading: A theory about human perception. Proc. Int'l Conf. Computer Vision, 1988: 404~413
[80] Tsai P S, Shah M. Shape from shading using linear approximation. Image and Vision Computing Journal, 1994, 12(8):487~488
[81]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,2001, 17(6):521~527
[82]赵歆波,张定华,Petrou M等.基于分形的从明暗恢复形状算法研究.中国图像图形学报. 2002, 7(5): 440~444
[83]乌秀春,郭东明,王晓明等.由灰度图像重构曲面三维形状算法研究与实现.大连理工大学学报,2002, 42(6):701~705
[84] Durou J D, Falcone M, Sagona M. A survey of numerical methods for shape from shading. Technical report, IRIT, 2004
[85] Zhang R, Tsai P S, Cryer J E, Shah M. A survey analysis of shape from shading technique. Technical report, Computer Science Department, University of Central Florida, 2000.
[86]俞鸿波,赵荣椿,王兵.基于阴影的三维表面重构技术的概述.计算机工程与技术,2004(10): 30~33
[87] Nicolis G, Prigogine I. Self-organization in non-equilibrium systems. John Wiley & Sons, 1977.中译本:非平衡系统的自组织,徐锡申等译.北京:科学出版社,1986:475~524.
[88] Haken H. Information and self-organization. Springer, 1987.中译本:信息与自组织,宁存政等译.成都:四川教育出版社,1988,6:1~70.
[89]师汉民.从“他组织”走向自组织——关于制造这里的沉思.中国机械工程,2000,11(1-2):80~85
[90] Prigogine, Stengers I. Order out of chaos, Bantam Books, Inc. 1984.中译本:从混沌到有序.曾庆宏,沈小峰译.上海:上海译文出版社,1987,8:174~258.
[91] J.von Neumann. Theory of self-reproducing automata. Edited an completed by Burks A W, University Of Illinois Press, Champaign,Ⅱ, 1996
[92]谢惠民.复杂性与动力系统.上海:上海科技教育出版社,1994
[93]吴彤.生长的旋律——自组织演化的科学.济南:山东教育出版社,1996
[94] Stephen Wolfram. Cellular automata and complexity. Addison-Wesley Company, 1994:1~69.
[95] Gotts Nicholas Mark, Callahan Paul B. Emergent structure in spare field of conway’s“game of life”. Artificial Live VI, Proceedings of Sixth International Conference on Artificial Life, A Bradford Book, The MIT Press, 1998, 104~113.
[96] Packard N, Wolfram S. Two-dimensional cellular automata. J. Stat. Phys., 1985, (38): 901
[97] Flocchini P, Geurts F, Mingarelli A, Santoro N. Convergence and aperiodicity in fuzzy cellular automata: revisiting rule 90. Physica D: Nonlinear Phenomena, 2000, 142(1-2): 20~28
[98] Bruss A R. The Eikonal Equation: Some results applicable to computer vision. Journal of Math. Physics, 1982, 23(5): 890~896.
[99] Horn Berthold K P, Brooks Michael J. The variational approach to shape from shading. Computer vision, graphics, and image processing, 1986, 33:174~208
[100] Ulich Gabriele. A new variational technique for shape from shading. Lecture Notes in Control and Information Sciences,ICAOS, 1996, 219: 253~259
[101] Marquardt D W. An algorithm for least-squares estimation of nonlinear parameters. JSIAM , 1963, 11(2):431~441
[102] Oren M, Nayar S K. Generalization of Lambert’s reflectance model. In Proceedings of SIGGRAPH 94, Computer Graphics Proceedings, Annual Conference Series, 1994, 239~246.
[103] Smith W A P, Hancock E R. Recovering facial shape using a statistical model of surface normal direction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(12):1914~1930
[104] Smith W A P, Hancock E R. Recovering facial shape using a statistical surface normal model. In Proc. ICIP, 2005, 2:113~116
[105] Worthington P L, Hancock E R. Modeling needle-map consistency with novel constraints. Computer Analysis of Images and Patterns, 1999, 1689:498~507
[106] Worthington P L, Hancock E R. Needle map recovery using robust regularizers. Image and Vision Computing, 1999, 17(8):545~557
[107] Worthington P L, Hancock E R. New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(12):1250~1267
[108] Zheng Q, Chellappa R. Estimation of illuminant direction, albedo, and shape from shading. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1991, 13(7): 680~702
[109] Smith G D J, Bors A G. Height estimation from vector fields of surface normals. Proc. 14th Intel. Conference on Digital Signal Processing, Santorini, Greece, vol. II, 2002: 1031~1034.
[110] Daniel P, Durou J D. From deterministic to stochastic methods for shape from shading. In Proceedings of the 4th Asian Conference on Computer Vision, Taipei, Taiwan, January 2000, 187~192
[111] Falcone M, Sagona M. An algorithm for the global solution of the shape from shading model. In Proceedings of the 9th International Conference on Image Analysis and Processing, volume I, Florence, Italy, September 1997, 596~603
[112]彭群生.计算机真实感图形的算法基础.北京:科学出版社, 1999
[113] Westin Stephen H, Li Hongsong, Torrance Kenneth E. A field guide to BRDF models. Technical report, PCG-04-1,Cornell University, Jan., 2004
[114]程路.高等光学.北京:科学出版社,2000
[115] Ditteon Richard.詹涵菁译,现代几何光学,长沙:湖南大学出版社,2004
[116] Oren M, Nayar S K. Generalization of Lambert’s reflectance model. In Proceedings of SIGGRAPH 94, Computer Graphics Proceedings, Annual Conference Series, 1994, 239~246.
[117] Phong B T. Illumination for computer generated pictures. Communications of the ACM, 1975, 18(6): 311~317.
[118] Blinn J F. Models of light reflection for computer synthesized pictures. In Computer Graphics (Proceedings of SIGGRAPH 77), July 1977, 11: 192~198.
[119] Cook R L, Torrance k E. A reflectance model computer graphics. Computer Graphics, 1981, 15(3): 307~316.
[120] Torrance K E, Sparrow E M. Theory for Off-Specular reflection from roughened surfaces. Optics Society, 1967, 57(3): 1105~1114.
[121] Torrance K E, Sparrow E M. Off-specular peaks in the directional distribution of reflected thermal radiation. In Transactions of the ASME, Chicago, Illinois, November 1965, 1~8
[122] Nayar S K, Ikeuchi K, Kanade T. Surface reflection: Physical and geometrical perspectives. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(7):611~634
[123] Wolff L B. Using polarization to separate reflection components. In: Proc. of the IEEE Computer Vision and Pattern Recognition. 1989. 363~369.
[124] Sato Y, Ikeuchi K. Temporal-Color space analysis of reflection. Journal of the Optical Society of America A, 1994, 11(11).
[125] Nayar S K, Fang X, Boult T E. Removal of specularities using color and polarization. In: Proc. of the IEEE Computer Vision and Pattern Recognition. 1993. 583~590.
[126] Klinker G J, Shafer S A, Kanade T. The measurement of highlights in color images. International Journal of Computer Vision, 1990, 2:7~32.
[127] Shafer S A. Using color to separate reflection components. Color Research and Application, 1985, 10(4):210~218.
[128] Noak C L, Shafer S A. Anatomy of a color histogram. In: Proc. of the IEEE Computer Vision and Pattern Recognition. 1992. 599~605.
[129] Phong B T. Illumination for computing generated images. [Ph.D. Dissertation], University of Utah, July, 1973, 31~35
[130] Williams M M R. The albedo problem with Fresnel reflection. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 98(3): 358~378.
[131] Ikeuchi Katsushi, Sato Kosuke. Determining reflectance properties of an object using range and brightness image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(11):1139~1153
[132] Konrad F Karner, Heinz Mayer, and Michael Gervautz. An image based measurement system for anisotropic reflection. Computer Graphics Forum (Eurographics '96 Proceedings), 1996, 15(3):119~128
[133] Nicodemus F E, Richmond J C, Hsia J J, Ginsberg I W et al. Geometric considerations and nomenclature for reflectance. Monograph 161, National Bureau of Standards (US), October 1977
[134] Sato Yoichi, Wheeler Mark D, Ikeuchi Katsushi. Object shape and reflectance modeling from observation. In Computer Graphics (SIGGRAPH '97 Proceedings), August 1997. 379~387
[135] Gregory J Ward. Measuring and modeling anisotropic reflection. In Computer Graphics (SIGGRAPH '92 Proceedings), July 1992. 265~272
[136] White D Rod, Saunders Peter, Bonsey Stuart J, Ven John van de, Edgar Hamish. Reflectometer for measuring the bidirectional reflectance of rough surfaces. Applied Optics, 1998, 37(16):3450~3454
[137] Westin Stephen H, Li Hongsong, Torrance Kenneth E. A comparison of four BRDF models, Technical report, Cornell University Program of Computer Graphics, PCG-04-2, April, 2004
[2]单东日,柯映林,刘云峰.反求工程中复杂曲面测量规划研究.中国机械工程,2003,14(1): 9~12
[3]孙家广,陈玉健,辜凯宁.计算机辅助几何造型技术.北京:清华大学出版社,1990. 126~165
[4]王宗彦.基于ICT和RP&M技术的产品快速反求系统研究.华北工学院学报,1999,20(4):294~297
[5]邢渊,周雄辉,阮雪榆.集成反向工程系统研究.机械工程学报,1998(3):1~6
[6]徐琳,袁保宗,高文.真实感人脸建模研究的进展与展望.软件学报,2003, 14(4): 804~810
[7]董兰芳,王洵,陈意云.真实感虚拟人脸的实现和应用.小型微型计算机系统,2002, 23(1): 90~92
[8]张青山,陈国良.具有真实感的三维人脸动画.软件学报,2003,14(3): 643~650
[9]王运赣.快速成形技术.武汉:华中理工大学出版社, 1999. 1~10
[10] Horn B K P. Shape From Shading: A method for obtaining the shape of a smooth opaque object from one view: [PhD thesis], MIT, 1970.
[11] Marr D. Vision. W. H. Freeman and Company, San Francisco.中译本:视觉计算理论.姚国正,刘磊,汪云九译,北京:科学出版社,1988. 6~37
[12] Mishra D K, Chandwani M. CCD camera based automatic dimension measurement and reproduction of 3-D objects. TENCON '93. Proceedings. Computer, Communication, Control and Power Engineering.1993 IEEE Region 10 Conference on Issue 0, Part 40000,19-21 Oct. 1993,4: 530~533
[13] Wang J G, Li Y F. 3D object modeling using a binocular vision system. Instrumentation and Measurement Technology Conference, 1999. IMTC/99. Proceedings of the 16th IEEE Volume 2, 24-26 May 1999, 2: 684~689
[14] Tsai R Y. A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lens. IEEE Journal of Robotics Automation. 1987, RA-3(4): 323~344
[15] Wei Guoqing, Ma Songde. Implicit and explicit camera calibration: theory andexperiments. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, 16(5): 469~480
[16] Ma Songde. A self-calibration technique for active vision systems. Robotics and Automation, IEEE Transactions, 1996, 12(1): 114~120
[17] Hemayed E E. A survey of camera self-calibration. Proceedings. IEEE Conference on Advanced Video and Signal Based Surveillance, 2003. 21-22 2003(7): 351~357
[18]章毓晋.图像理解与计算机视觉.第一版.北京:清华大学出版社,2000
[19] Cryer James Edwin, Tsai Ping-Sing, Shah Mubarak. Integration of shape from X modules: Combining stereo and shading. IEEE computer society conference on: proceeding of computer vision and pattern recognition, 1993(15-17):720~721
[20] Weinshall Daphna. Qualitative depth and shape from stereo - in agreement with psychophysical evidence. ACM Technical report: AIM-1007, 1987
[21] Woodham R J. Photometric stereo: a reflectance map technique for determing surface orientation from a single view. Proc. SPIE, 1978, 155:136~143
[22] Nayar S K, Ikeuchi K, Kanade T. Extracting shape from reflectance of hybrid surfaces by photometric sampling. Image understanding workshop, 1989: 563~583
[23] Nayar S K, Gong Y. Colored interreflection and shape recovery. DARPA Image understanding workshop, 1992
[24] Christensen P H, Shapiro L G. Three dimensional shape from color photometric stereo. International Journal of Computer Vision, 1994, 13(2), p 213~217
[25] Boufama Boubakeur, Weinshall Daphna, Werman Mike. Shape from motion algorithms: a comparative analysis of scaled orthography and perspective. Proceedings of the third European conference on Computer vision, Stocklholm, Sweden, 1994(1): 199~204
[26] Barron J L, Fleet D J, Beauchemin S. Performance of optical flow techniques. International Journal of Computer Vision, 1994, 12(1):43~77
[27] Aloimonos Y, Swain M J. Shape from texture. Biological Cybernetics, 1988, 58(5):345~360
[28] Bajcsy R K, Lieberman L I. Texture gradient as a depth cue. Computer Graphics and Image Processing, 1976, 5(1):52~67
[29] Blostein D, Ahuja N. Shape from texture: Integrating texture-element extraction and surface estimation. IEEE Transaction on Pattern Analysis and MachineIntelligence, 1989, 11(12):1233~1251
[30] Clerc M, Mallat S. The texture gradient equation for recovering shape from texture. IEEE Transaction on Pattern Analysis and Machine Intelligence, 2002, 24(4): 536~549
[31] Weik S A. A passive full body scanner using shape from silhouettes. Proc. International Conference on Pattern Recognition, 2000:1750~1753
[32]唐挺,李鹏程.基于轮廓的运动目标视觉分析的研究.四川理工学院学报, 2006(4):33~36
[33] Laurentini A. How far 3-D shapes can be understood from 2-D silhouettes. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1995, 17 (2): 188~195
[34] Laurentini A. The visual Hull concept for silhouette based image understanding. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1994, 16(2):150~162
[35] Gelli Daniele, Vitulano Domenico. Surface recovery by self shading projection. Signal Processing, 2004, 84(3):467~473
[36] Tankus Ariel, Sochen Nir, Yeshurun Yehezkel. A new perspective on shape from shading. Proceedings of the IEEE International Conference on Computer Vision, 2003(2):862~869
[37] Oliensis J. Uniqueness in shape from shading. International Journal of Computer Vision, 1991, 6(2):75~104
[38] Ragheb Hossein, Hancock Edwin R. Darboux smoothing for shape from shading. Pattern Recognition Letters, 2003, 24(1-3):579~595
[39] Ascher Uri M, Carter Paul M. Multigrid method for shape from shading. SIAM Journal on Numerical Analysis, 1993, 30(1):102~115
[40] Ikeda Osamu. A robust shape from shading algorithm using two images and control of boundary conditions. IEEE International conference on image processing, 2003(1): 405~408
[41] Oliensis J. Shape from shading as a partially well constrained problem. CVGIP: Image understanding, 1991, 54(2):163~183
[42] Saxberg Bror V H. Existence and uniqueness for shape from shading around critical points: Theory and an algorithm. International Journal of Robotics Research, 1992, 11(3):202~224
[43] Barnes Nick, Liu Zhiqing. Knowledge-based shape from shading. International Journal of Pattern Recognition and Artificial Intelligence, 1999, 13(1):1~23
[44] Zhong Sheng, Shi Qingyun, Cheng Minte. Fast shape from shading based on wavelet transform. Proceedings of SPIE: The International Society for Optical Engineering, 1994(2242):169~178
[45] Ramachandran V S. Perceiving shape from shading. Scientific America, 1988(159): 76~83
[46] Hayakawa Hideki , Nishida Shin'ya, Wada Yasuhiro, Kawato Mitsuo. Computational model for shape estimation by integration of shading and edge information. Neural Networks, 1994, 7(8):1193~1209
[47] Oren M, Nayar S K. Diffuse reflectance from rough surfaces. IEEE Proc. Computer Vision and Pattern Recognition, 1993: 763~764
[48] Forsyth D, Zisserman A. Mutual illumination. IEEE Proc. Computer Vision and Pattern Recognition, 1989: 466~473
[49] Prados Emmanuel, Faugeras Olivier, Camilli Fabio. Shape from shading: a well-posed problem? INRIA Research Report, No.RR-5297, August 2004.
[50] Zhang R, Tsai P S, Cryer J E, Shah M. Shape from shading: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(8):690~706
[51]郭东明,乌秀春,王晓明等.反求工程中基于图像灰度信息的三维曲面重构.机械工程学报, 2003, 39(1):47~50
[52] Horn B K P. Height and gradient from shading. International Journal of Computer Vision, 1989:37~75
[53] Ikeuchi K, Horn B K P. Numerical shape from shading and occluding boundaries. Artificial Intelligence, 1981, 17(1-3): 141~184
[54] Camilli F, Grune L. Numerical approximation of the maximal solutions for a class of degenerate Hamilton-Jacobi equations. SIAM Journal on Numerical Analysis, 2000, 38(5):1540~1560
[55] Frankot R T, Chellappa R. A method for enforcing integrability in shape from shading algorithms. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1988(10): 439~451
[56] Christophe S. A survey of shading and reflectance models. Computer Graphics Forum 1994, 13(2): 121~131
[57] Pentland A P. Local shading analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1984, 6(2):170~187
[58] Lee C H, Rosenfeld A. Improved methods of estimating shape from shading using the light source coordinate system. Artificial Intelligence, 1985, 26: 125~143
[59] Lee K M , Kuo C C J. Shape from shading with a linear triangular element surface model. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1993, 15(8): 815~822
[60] Collings Simon. Single image shape from shading. [PhD Thesis], Computer science department, University of Western Australia, Sep.,2001
[61] Collings Simon, Kozera Ryszard, Noakes Lyle. A Piecewise quadratic approach to single image shape from shading. In Proc. 16th Int. Conf. Pattern Recognition ICPR'02, Quebec, Canada, 2002, (4): 126~129
[62] Prados E, Faugeras O, Rouy E. Shape from shading and viscosity solutions. In Proceedings of the 7th European Conference on Computer Vision, Copenhagen, Denmark, 2002(2): 790~804
[63] Prados E, Faugeras O. "Perspective shape from shading" and viscosity solutions. In Proceedings of the Ninth IEEE International Conference on Computer Vision, 2003. 826~831
[64] Rouy E, Tourin A. A viscosity solutions approach to shape from shading. SIAM Journal of Numerical Analysis, 1992, 29(3):867~884
[65] Lions P L, Rouy E, Tourin A. Shape-from-shading, viscosity solutions and edges. Numerical Math., 1993, 64:323~353
[66] Kimia B B, Kimmel R, Siddiqqi K, Bruckstein A M. Shape from shading: Level set propagation and viscosity solutions. International Journal of Computer Vision, 1995, (16):107~133.
[67] Kimmel R, Bruckstein A M. Tracking level sets by level sets: A method for solving the shape from shading problem. Computer Vision and Image Understanding, 1995, 62(2):47~48.
[68] Dupuis P, Oliensis J. Direct method for reconstructing shape from shading. IEEE Proc. Computer Vision and Pattern Recognition, 1992. 453~458
[69] Ishii H, Ramaswamy M. Uniqueness results for a class of Hamilton-Jacobi equations with singular coefficients. Communications in Partial DifferentialEquations, 1995(20):2187~2213
[70] Saito H, Usami K. Shape from shading using genetic algorithm. JECON’93, 1993:1620~1625
[71] Crouzil A, Descombes X, Durou J D. A multiresolution approach for shape from shading coupling deterministic and stochastic optimization. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(11):1416~1421
[72]杨敬安.基于照明参数与反射系数的分层SFS算法.自动化学报, 1999, 25(6): 735~742
[73] Hsieh J W, Liao M H Y, Ko M T, FanK C. Wavelet-based shape from shading. CVGIP: Graphical Models and Image Processing, 1995, (57):343~362
[74] Hsieh J W, Liao M H Y, FanK C, Ko M T. Wavelet-based shape from shading. Images & Recognition, 1994, 2(6):125~129
[75] Jiang Guang-Shan, Peng Danping. Weighted ENO Schemes for Hamilton-Jacobi Equations. SIAM Journal on Scientific Computing, 2000, 21(6):2126~2143
[76] Bichsel M, Pentland A P. A simple algorithm for shape from shading. IEEE Proc. Computer Vision and Pattern Recognition, 1992: 459~465
[77] Durou J D, Piau D. Ambiguous Shape from shading with critical points. Journal of Mathematical Imaging and Vision, 2000, 12(2):99~108
[78] Cheung W P, Lee C K, Li K C. Direct shape from shading with improved rate of convergence. Pattern Recognition, 1997, 30(3):353~365
[79] Pentland A P. Shape Information from Shading: A theory about human perception. Proc. Int'l Conf. Computer Vision, 1988: 404~413
[80] Tsai P S, Shah M. Shape from shading using linear approximation. Image and Vision Computing Journal, 1994, 12(8):487~488
[81]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,2001, 17(6):521~527
[82]赵歆波,张定华,Petrou M等.基于分形的从明暗恢复形状算法研究.中国图像图形学报. 2002, 7(5): 440~444
[83]乌秀春,郭东明,王晓明等.由灰度图像重构曲面三维形状算法研究与实现.大连理工大学学报,2002, 42(6):701~705
[84] Durou J D, Falcone M, Sagona M. A survey of numerical methods for shape from shading. Technical report, IRIT, 2004
[85] Zhang R, Tsai P S, Cryer J E, Shah M. A survey analysis of shape from shading technique. Technical report, Computer Science Department, University of Central Florida, 2000.
[86]俞鸿波,赵荣椿,王兵.基于阴影的三维表面重构技术的概述.计算机工程与技术,2004(10): 30~33
[87] Nicolis G, Prigogine I. Self-organization in non-equilibrium systems. John Wiley & Sons, 1977.中译本:非平衡系统的自组织,徐锡申等译.北京:科学出版社,1986:475~524.
[88] Haken H. Information and self-organization. Springer, 1987.中译本:信息与自组织,宁存政等译.成都:四川教育出版社,1988,6:1~70.
[89]师汉民.从“他组织”走向自组织——关于制造这里的沉思.中国机械工程,2000,11(1-2):80~85
[90] Prigogine, Stengers I. Order out of chaos, Bantam Books, Inc. 1984.中译本:从混沌到有序.曾庆宏,沈小峰译.上海:上海译文出版社,1987,8:174~258.
[91] J.von Neumann. Theory of self-reproducing automata. Edited an completed by Burks A W, University Of Illinois Press, Champaign,Ⅱ, 1996
[92]谢惠民.复杂性与动力系统.上海:上海科技教育出版社,1994
[93]吴彤.生长的旋律——自组织演化的科学.济南:山东教育出版社,1996
[94] Stephen Wolfram. Cellular automata and complexity. Addison-Wesley Company, 1994:1~69.
[95] Gotts Nicholas Mark, Callahan Paul B. Emergent structure in spare field of conway’s“game of life”. Artificial Live VI, Proceedings of Sixth International Conference on Artificial Life, A Bradford Book, The MIT Press, 1998, 104~113.
[96] Packard N, Wolfram S. Two-dimensional cellular automata. J. Stat. Phys., 1985, (38): 901
[97] Flocchini P, Geurts F, Mingarelli A, Santoro N. Convergence and aperiodicity in fuzzy cellular automata: revisiting rule 90. Physica D: Nonlinear Phenomena, 2000, 142(1-2): 20~28
[98] Bruss A R. The Eikonal Equation: Some results applicable to computer vision. Journal of Math. Physics, 1982, 23(5): 890~896.
[99] Horn Berthold K P, Brooks Michael J. The variational approach to shape from shading. Computer vision, graphics, and image processing, 1986, 33:174~208
[100] Ulich Gabriele. A new variational technique for shape from shading. Lecture Notes in Control and Information Sciences,ICAOS, 1996, 219: 253~259
[101] Marquardt D W. An algorithm for least-squares estimation of nonlinear parameters. JSIAM , 1963, 11(2):431~441
[102] Oren M, Nayar S K. Generalization of Lambert’s reflectance model. In Proceedings of SIGGRAPH 94, Computer Graphics Proceedings, Annual Conference Series, 1994, 239~246.
[103] Smith W A P, Hancock E R. Recovering facial shape using a statistical model of surface normal direction. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(12):1914~1930
[104] Smith W A P, Hancock E R. Recovering facial shape using a statistical surface normal model. In Proc. ICIP, 2005, 2:113~116
[105] Worthington P L, Hancock E R. Modeling needle-map consistency with novel constraints. Computer Analysis of Images and Patterns, 1999, 1689:498~507
[106] Worthington P L, Hancock E R. Needle map recovery using robust regularizers. Image and Vision Computing, 1999, 17(8):545~557
[107] Worthington P L, Hancock E R. New constraints on data-closeness and needle map consistency for shape-from-shading. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1999, 21(12):1250~1267
[108] Zheng Q, Chellappa R. Estimation of illuminant direction, albedo, and shape from shading. IEEE Transaction on Pattern Analysis and Machine Intelligence, 1991, 13(7): 680~702
[109] Smith G D J, Bors A G. Height estimation from vector fields of surface normals. Proc. 14th Intel. Conference on Digital Signal Processing, Santorini, Greece, vol. II, 2002: 1031~1034.
[110] Daniel P, Durou J D. From deterministic to stochastic methods for shape from shading. In Proceedings of the 4th Asian Conference on Computer Vision, Taipei, Taiwan, January 2000, 187~192
[111] Falcone M, Sagona M. An algorithm for the global solution of the shape from shading model. In Proceedings of the 9th International Conference on Image Analysis and Processing, volume I, Florence, Italy, September 1997, 596~603
[112]彭群生.计算机真实感图形的算法基础.北京:科学出版社, 1999
[113] Westin Stephen H, Li Hongsong, Torrance Kenneth E. A field guide to BRDF models. Technical report, PCG-04-1,Cornell University, Jan., 2004
[114]程路.高等光学.北京:科学出版社,2000
[115] Ditteon Richard.詹涵菁译,现代几何光学,长沙:湖南大学出版社,2004
[116] Oren M, Nayar S K. Generalization of Lambert’s reflectance model. In Proceedings of SIGGRAPH 94, Computer Graphics Proceedings, Annual Conference Series, 1994, 239~246.
[117] Phong B T. Illumination for computer generated pictures. Communications of the ACM, 1975, 18(6): 311~317.
[118] Blinn J F. Models of light reflection for computer synthesized pictures. In Computer Graphics (Proceedings of SIGGRAPH 77), July 1977, 11: 192~198.
[119] Cook R L, Torrance k E. A reflectance model computer graphics. Computer Graphics, 1981, 15(3): 307~316.
[120] Torrance K E, Sparrow E M. Theory for Off-Specular reflection from roughened surfaces. Optics Society, 1967, 57(3): 1105~1114.
[121] Torrance K E, Sparrow E M. Off-specular peaks in the directional distribution of reflected thermal radiation. In Transactions of the ASME, Chicago, Illinois, November 1965, 1~8
[122] Nayar S K, Ikeuchi K, Kanade T. Surface reflection: Physical and geometrical perspectives. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(7):611~634
[123] Wolff L B. Using polarization to separate reflection components. In: Proc. of the IEEE Computer Vision and Pattern Recognition. 1989. 363~369.
[124] Sato Y, Ikeuchi K. Temporal-Color space analysis of reflection. Journal of the Optical Society of America A, 1994, 11(11).
[125] Nayar S K, Fang X, Boult T E. Removal of specularities using color and polarization. In: Proc. of the IEEE Computer Vision and Pattern Recognition. 1993. 583~590.
[126] Klinker G J, Shafer S A, Kanade T. The measurement of highlights in color images. International Journal of Computer Vision, 1990, 2:7~32.
[127] Shafer S A. Using color to separate reflection components. Color Research and Application, 1985, 10(4):210~218.
[128] Noak C L, Shafer S A. Anatomy of a color histogram. In: Proc. of the IEEE Computer Vision and Pattern Recognition. 1992. 599~605.
[129] Phong B T. Illumination for computing generated images. [Ph.D. Dissertation], University of Utah, July, 1973, 31~35
[130] Williams M M R. The albedo problem with Fresnel reflection. Journal of Quantitative Spectroscopy & Radiative Transfer, 2006, 98(3): 358~378.
[131] Ikeuchi Katsushi, Sato Kosuke. Determining reflectance properties of an object using range and brightness image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1991, 13(11):1139~1153
[132] Konrad F Karner, Heinz Mayer, and Michael Gervautz. An image based measurement system for anisotropic reflection. Computer Graphics Forum (Eurographics '96 Proceedings), 1996, 15(3):119~128
[133] Nicodemus F E, Richmond J C, Hsia J J, Ginsberg I W et al. Geometric considerations and nomenclature for reflectance. Monograph 161, National Bureau of Standards (US), October 1977
[134] Sato Yoichi, Wheeler Mark D, Ikeuchi Katsushi. Object shape and reflectance modeling from observation. In Computer Graphics (SIGGRAPH '97 Proceedings), August 1997. 379~387
[135] Gregory J Ward. Measuring and modeling anisotropic reflection. In Computer Graphics (SIGGRAPH '92 Proceedings), July 1992. 265~272
[136] White D Rod, Saunders Peter, Bonsey Stuart J, Ven John van de, Edgar Hamish. Reflectometer for measuring the bidirectional reflectance of rough surfaces. Applied Optics, 1998, 37(16):3450~3454
[137] Westin Stephen H, Li Hongsong, Torrance Kenneth E. A comparison of four BRDF models, Technical report, Cornell University Program of Computer Graphics, PCG-04-2, April, 2004