投影相机系统的自标定技术及其应用研究
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摘要
计算机视觉和计算机图形学研究的一项重要内容,就是如何创建一个逼真的虚拟世界,而投影仪相机自标定正是利用物体的二维图像获取三维空间信息、建立三维世界的关键技术。其在机器视觉、虚拟现实、增强现实、三维重构、图像测量及医学图像等领域都有着非常广泛的应用。同时,在实际应用中,通过人工标定方法获取参数信息,其标定过程十分繁琐,标定方法不灵活;而直接使用生产厂商提供的光学参数,其精度又往往不能满足应用的要求。因此,需要对各参数进行简单、灵活以及精确地标定。由此可知,投影相机自标定技术在计算机视觉中占有非常重要的地位,是计算机视觉工作中进行其它方面研究的基础。
本课题的目的是,研究分析与自标定算法相关的技术,包括不同图像对应点的匹配、不同视角间基本矩阵的估计、系统内外参数的估计,以及系统参数的优化。这些技术都是自标定算法流程中的重要环节。在此基础上,本文提出一种将空间几何约束转换为内参矩阵约束的自标定方法,并将这种新的自标定方法应用于已有的投影相机系统,以改善原有系统繁琐的人工标定过程。本文的主要工作包括以下部分:
首先,本文介绍了自标定技术所涉及到的基本理论知识,包括相机投影系统的数学模型,多视与对极几何等。对相关的概念及理论做了较为全面的介绍,为后续的自标定算法研究奠定了理论基础。
其次,本文研究了对应点匹配和基本矩阵估计的方法。对应点匹配是自标定技术中的关键步骤。为了获得不同图像之间可靠的对应关系,本文采用了基于结构光的主动视觉方法。从实验结果可知,该方法可以得到高精度的对应点关系。同时,本文分析了估计基本矩阵的算法,讨论了如何使用RANSAC算法提高其可靠性,并给出了相应的实验结果。
然后,本文介绍了外参估计和三维重建的算法。通过外参估计,可以计算出相机在世界坐标系下的空间位置和方位信息。利用得到的参数信息能够完成场景的三维重建。此外,还介绍了BA优化算法。本文实现了基于本质矩阵分解的外参估计算法,通过实验验证了算法的正确性。同时,将估计结果用于三维重建,并通过优化,得到精细、直观的三维模型。
最后,本文论述了基于本质矩阵的自标定算法的基本理论,并提出了一种将空间几何约束转化为内参矩阵约束的自标定算法。与传统的标定方法相比,除了改变投影仪的空间位置,本文方法不需要其他的人为操作,就可以估算出系统的内外参数。通过替换原有的人工标定算法,我们将本文方法应用于已有的投影相机建模系统,使系统原来繁琐的标定过程变得更加方便、灵活。本文对提出的自标定方法进行了多组实验,并对标定的结果进行了优化。通过对比分析,验证和说明了本文方法的有效性和可行性。
One of the important tasks in computer vision and computer graphics is how to create a vivid virtual world. And camera-projector self-calibration method is the key technique, which is using 2D images of the objects to get 3D information and to build 3D models. Recently, self-calibration method is becoming more and more popular, and has various applications in the field of machine vision, virtual reality, augment reality, 3D reconstruction, image measurement and medical image processing. In practice, to acquire the parameters using traditional method by hand, is time consuming and is not flexible. And the precision always fails to meet the requirements of applications when using the parameters provided by the manufacturers. Therefore, we need a simple and flexible method to calibrate the parameters with precise results. Thus it is clear that camera-projector self-calibration method is a very important part of computer vision, and is the basis for doing other researches in computer vision.
The main object of this work is to study the techniques related to self-calibration method, including correspondence between different images, estimation of fundamental matrix, estimation of intrinsic and extrinsic parameters, and optimization of parameters. All these techniques are important parts in self-calibration method. On the basis of these studies, we propose a self-calibration method by converting a space constraint into intrinsic parameter space. And this method is applied to our camera-projector system, to improving the calibration process. The main contribution of this work includes the following parts:
First, all related concepts and theories are considered and explained in detail in this work, including mathematical model of camera, multi-view and epipolar geometry. These are the basis for subsequent researches on self-calibration techniques.
Second, we study the method for finding correspondence and estimating fundamental matrix. Finding correspondence is the key step in self-calibration method. To getting reliable correspondences between different images, we use the active geometric method based on structured light. Experimental result shows that, high precise correspondences can be found using this method. Meanwhile, we discuss the method for estimating fundamental matrix, and how to increase the robustness with RANSAC algorithm. Related experiments are given at the end of the chapter.
Third, techniques of extrinsic parameters estimation and 3D reconstruction are brought to evaluate the position and orientation of camera in space and to build the 3D model. Besides these, Optimization method of bundle adjustment is mentioned here. Estimation method based on essential matrix decomposition is studied and realized. Visualized experimental results are given by building the optimized 3D model with estimated value.
Finally, basic theories of self-calibration method based on essential matrix is discussed. And a new method by converting space constraint into intrinsic parameter space is proposed. Compare to the traditional method, we can evaluate the intrinsic and extrinsic parameters with only a few moves of the projector. We substitute this method for the traditional one in our camera-projector system to simplify the calibration process. After the evaluation and optimization, experimental verification and result analysis are given. The results show the effectiveness of our approach.
本课题的目的是,研究分析与自标定算法相关的技术,包括不同图像对应点的匹配、不同视角间基本矩阵的估计、系统内外参数的估计,以及系统参数的优化。这些技术都是自标定算法流程中的重要环节。在此基础上,本文提出一种将空间几何约束转换为内参矩阵约束的自标定方法,并将这种新的自标定方法应用于已有的投影相机系统,以改善原有系统繁琐的人工标定过程。本文的主要工作包括以下部分:
首先,本文介绍了自标定技术所涉及到的基本理论知识,包括相机投影系统的数学模型,多视与对极几何等。对相关的概念及理论做了较为全面的介绍,为后续的自标定算法研究奠定了理论基础。
其次,本文研究了对应点匹配和基本矩阵估计的方法。对应点匹配是自标定技术中的关键步骤。为了获得不同图像之间可靠的对应关系,本文采用了基于结构光的主动视觉方法。从实验结果可知,该方法可以得到高精度的对应点关系。同时,本文分析了估计基本矩阵的算法,讨论了如何使用RANSAC算法提高其可靠性,并给出了相应的实验结果。
然后,本文介绍了外参估计和三维重建的算法。通过外参估计,可以计算出相机在世界坐标系下的空间位置和方位信息。利用得到的参数信息能够完成场景的三维重建。此外,还介绍了BA优化算法。本文实现了基于本质矩阵分解的外参估计算法,通过实验验证了算法的正确性。同时,将估计结果用于三维重建,并通过优化,得到精细、直观的三维模型。
最后,本文论述了基于本质矩阵的自标定算法的基本理论,并提出了一种将空间几何约束转化为内参矩阵约束的自标定算法。与传统的标定方法相比,除了改变投影仪的空间位置,本文方法不需要其他的人为操作,就可以估算出系统的内外参数。通过替换原有的人工标定算法,我们将本文方法应用于已有的投影相机建模系统,使系统原来繁琐的标定过程变得更加方便、灵活。本文对提出的自标定方法进行了多组实验,并对标定的结果进行了优化。通过对比分析,验证和说明了本文方法的有效性和可行性。
One of the important tasks in computer vision and computer graphics is how to create a vivid virtual world. And camera-projector self-calibration method is the key technique, which is using 2D images of the objects to get 3D information and to build 3D models. Recently, self-calibration method is becoming more and more popular, and has various applications in the field of machine vision, virtual reality, augment reality, 3D reconstruction, image measurement and medical image processing. In practice, to acquire the parameters using traditional method by hand, is time consuming and is not flexible. And the precision always fails to meet the requirements of applications when using the parameters provided by the manufacturers. Therefore, we need a simple and flexible method to calibrate the parameters with precise results. Thus it is clear that camera-projector self-calibration method is a very important part of computer vision, and is the basis for doing other researches in computer vision.
The main object of this work is to study the techniques related to self-calibration method, including correspondence between different images, estimation of fundamental matrix, estimation of intrinsic and extrinsic parameters, and optimization of parameters. All these techniques are important parts in self-calibration method. On the basis of these studies, we propose a self-calibration method by converting a space constraint into intrinsic parameter space. And this method is applied to our camera-projector system, to improving the calibration process. The main contribution of this work includes the following parts:
First, all related concepts and theories are considered and explained in detail in this work, including mathematical model of camera, multi-view and epipolar geometry. These are the basis for subsequent researches on self-calibration techniques.
Second, we study the method for finding correspondence and estimating fundamental matrix. Finding correspondence is the key step in self-calibration method. To getting reliable correspondences between different images, we use the active geometric method based on structured light. Experimental result shows that, high precise correspondences can be found using this method. Meanwhile, we discuss the method for estimating fundamental matrix, and how to increase the robustness with RANSAC algorithm. Related experiments are given at the end of the chapter.
Third, techniques of extrinsic parameters estimation and 3D reconstruction are brought to evaluate the position and orientation of camera in space and to build the 3D model. Besides these, Optimization method of bundle adjustment is mentioned here. Estimation method based on essential matrix decomposition is studied and realized. Visualized experimental results are given by building the optimized 3D model with estimated value.
Finally, basic theories of self-calibration method based on essential matrix is discussed. And a new method by converting space constraint into intrinsic parameter space is proposed. Compare to the traditional method, we can evaluate the intrinsic and extrinsic parameters with only a few moves of the projector. We substitute this method for the traditional one in our camera-projector system to simplify the calibration process. After the evaluation and optimization, experimental verification and result analysis are given. The results show the effectiveness of our approach.
引文
[1] Bradski G, Kaehler A. Learning OpenCV: Computer Vision with the OpenCV Library[M]. O’Reilly Media, Inc., 2008.
[2] Hartley R. Estimation of Relative Camera Positions for Uncalibrated Cameras[C]// Proceedings of the Second European Conference on Computer Vision, 1992, pp. 579-587.
[3] Faugeras O. What Can be Seen in Three Dimensions With an Uncalibrated Stereo Rig[C]// Proceedings of the Second European Conference on Computer Vision, 1992, pp. 563-578.
[4] Hemayed E. A Survey of Camera Self-Calibration[C]// Proceedings. IEEE Conference on Advanced Video and Signal Based Surveillance, 2003, pp. 351-357.
[5] Faugeras O, Luong Q, Maybank S. Camera Self-calibration: Theory and Experiments[C]// Proceedings of the 2nd European Conference on Computer Vision, 1992, pp. 321-334.
[6] Hartley R. Projective Reconstruction and Invariants from Multiple Images[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, 16(10): 1036-1041.
[7] Triggs B. Auto-calibration and the Absolute Quadric[C]// Proceedings. of Computer Vision and Pattern Recognition, 1997, pp. 609-614.
[8] Pollefeys M, Van Gool L, Oosterlinck A. The Modulus Constraint: A New Constraint for Self-calibration[C]// Proceedings of 13th International Conference on Pattern Recognition, 1996, pp. 349-353.
[9] Sen P, Chen B, Garg G, etc. Dual Photography[J]. ACM Transactions on Graphics(Proc. of ACM SIGGRAPH), 2005, 24(3): 745-755.
[10] Aliaga D. Digital Inspection: An Interactive Stage for Viewing Surface Details[C]// Proc. of Symposium on Interactive 3D Graphics and Games(I3D’08), 2008, pp. 53-60.
[11] Aliaga D, Xu Y. Photogeometric Structured Light: A Self-calibrating and Multi-viewpoint Framework for Accurate 3D Modeling[C]// IEEE Conference on Computer Vision and Pattern Recognition, 2008, pp. 1-8.
[12] Aliaga D, Xu Y. A Self-calibrating Method for Photogeometric Acquisition of 3D Objects[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 2010, 32(4): 747-754.
[13] Kawasaki H, Safawa R, Yagi Y, etc. One-shot Scanning Method Using an Uncalibrated Projector and Camera System[C]// IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2010, pp. 104-111.
[14] Longuet-Higgins H. A Computer Algorithm for Reconstructing a Scene From Two Projections[S]// Fischler M, Firschein O. Readings in Computer Vision: Issues, Problem, Principles, and Paradigms. San Francisco, Morgan Kaufmann Publishers Inc. 1987, pp. 61-62.
[15] Tian J, Ding Y, Peng X. Self-Calibration of a Fringe Projection System using Epipolar Constraint[J]. Optics and Laser Technology, 2008, 40(3): 538-544.
[16] Ma S. A Self-calibration Technique for Active Vision System[J]. IEEE Trans. on Robotics and Automation, 1996, 12(1): 114-120.
[17] Basu A. Active Calibration: Alternative Strategy and Analysis[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1993, pp. 495-500.
[18] Du F, Brady M. Self-calibration of the Intrinsic Parameters of Cameras for Active Vision Systems[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1993, pp. 477-482.
[19] Triggs B. Autocalibration from Planar Scenes[C]// Proceedings of the 5th European Conference on Computer Vision, 1998, pp. 89-105.
[20] Gurdjos P, Sturm P. Methods and Geometry for Plane-Based Self-Calibration[C]// IEEE Conference on Computer Vision and Pattern Recognition, 2003, pp. 491-496.
[21] Pollefeys M, Van Gool L. Self-calibration from the Absolute Conic on the Plane at Infinity[C]// Proceedings of the 7th International Conference on Computer Analysis of Images and Patterns, 1997, pp. 175-182.
[22] Sturm P. Self-calibration of a Moving Camera by Pre-calibration[C]// Proceedings of the 7th British Machine Vision Conference, 1996, pp. 675-684.
[23] Heyden A, Astrom K. Euclidean Reconstruction from Image Sequences with Varying and Unknown Focal Length and Principal Point[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1977, pp. 438-443.
[24]马颂德,张正友.计算机视觉—计算理论与算法基础[M].北京,科学出版社,1998.
[25] Hartley R, Zisserman A. Multiple View geometry in Computer Vision[M]. 2nd Edition, Cambridge University Press, 2003.
[26] Fischler M, Bolles R. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography[J]. Communications of the ACM, 1981, 24(6): 381-395.
[27] Faugeras O, Maybank S. Motion from Point Matches: Multiplicity of Solutions[J]. International Journal Of Computer Vision, 1990, 4(3): 225-246.
[28] Luong Q, Deriche R, Faugeras O, etc. On Determining the Fundamental Matrix: Analysis of Different Methods and Experimental Results[R]. INRIA, 1993.
[29] Zhang Z. Determining the Epipolar Geometry and Its Uncertainty: A Review[R]. INRIA, 1996.
[30] Hartley R. Euclidean Reconstruction from Uncalibrated Views[C]// Proceedings of the 2nd Joint Europe-US Workshop on Applications of Invariance in Computer Vision, pp. 237-256.
[31] Beardsley P, Zisserman A, Murray D. Navigation Using Affine Structure from Motion[C]// Proceedings of the 3rd European Conference on Computer Vision, 1994, pp. 85-96.
[32] Hartley R, In Defense of the Eight-point Algorithm[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 1997, 19(6): 580-593.
[33] Fusiello A. The Mendonca and Cipolla Self-calibration Algorithm Experimental Evaluation[R]. 1999.
[34] Triggs B, McLauchlan F, Hartley R, etc. Bundle Adjustment– A Modern Synthesis[J]. Lecture Notes in Computer Science, 2000, 1883: 153-177.
[35] Zhang Z. A Flexible New Technique for Camera Calibration[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 2000, 22(11): 1330-1334.
[36] Lourakis M, Argyros A. SBA: A Software Package for Generic Sparse Bundle Adjustment[J]. ACM Trans. Math. Softw., 2009, 36(1): 1-30.
[37] Huang T, Faugeras O. Some Properties of The E Matrix in Two-view Motion Estimation[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 1989, 11(12): 215-244.
[38] Lourakis M, Deriche R. Camera Self-calibration Using the Singular Value Decomposition of the Fundamental Matrix: From Point Correspondences to 3D Measurements[R]. 1999.
[39] Trivedi H. Can Multiple Views Make Up for Lack of Camera Registration?[J]. Image and Vision Computing, 1988, 6(1): 29-32.
[40] Luong Q, Faugeras O. Self-calibration of a Moving Camera from Point Correspondences and Fundamental Matrix[J]. International Journal of Computer Vision, 1997, 22(3): 261-289.
[41] Fusiello A. A New Autocalibration Algorithm: Experimental Evaluation[C]// Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns, 2001, pp. 707-714.
[42] Mendonca P, Cipolla R. A Simple Technique for Self-calibration[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1999, pp. 500-505.
[2] Hartley R. Estimation of Relative Camera Positions for Uncalibrated Cameras[C]// Proceedings of the Second European Conference on Computer Vision, 1992, pp. 579-587.
[3] Faugeras O. What Can be Seen in Three Dimensions With an Uncalibrated Stereo Rig[C]// Proceedings of the Second European Conference on Computer Vision, 1992, pp. 563-578.
[4] Hemayed E. A Survey of Camera Self-Calibration[C]// Proceedings. IEEE Conference on Advanced Video and Signal Based Surveillance, 2003, pp. 351-357.
[5] Faugeras O, Luong Q, Maybank S. Camera Self-calibration: Theory and Experiments[C]// Proceedings of the 2nd European Conference on Computer Vision, 1992, pp. 321-334.
[6] Hartley R. Projective Reconstruction and Invariants from Multiple Images[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1994, 16(10): 1036-1041.
[7] Triggs B. Auto-calibration and the Absolute Quadric[C]// Proceedings. of Computer Vision and Pattern Recognition, 1997, pp. 609-614.
[8] Pollefeys M, Van Gool L, Oosterlinck A. The Modulus Constraint: A New Constraint for Self-calibration[C]// Proceedings of 13th International Conference on Pattern Recognition, 1996, pp. 349-353.
[9] Sen P, Chen B, Garg G, etc. Dual Photography[J]. ACM Transactions on Graphics(Proc. of ACM SIGGRAPH), 2005, 24(3): 745-755.
[10] Aliaga D. Digital Inspection: An Interactive Stage for Viewing Surface Details[C]// Proc. of Symposium on Interactive 3D Graphics and Games(I3D’08), 2008, pp. 53-60.
[11] Aliaga D, Xu Y. Photogeometric Structured Light: A Self-calibrating and Multi-viewpoint Framework for Accurate 3D Modeling[C]// IEEE Conference on Computer Vision and Pattern Recognition, 2008, pp. 1-8.
[12] Aliaga D, Xu Y. A Self-calibrating Method for Photogeometric Acquisition of 3D Objects[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 2010, 32(4): 747-754.
[13] Kawasaki H, Safawa R, Yagi Y, etc. One-shot Scanning Method Using an Uncalibrated Projector and Camera System[C]// IEEE Conference on Computer Vision and Pattern Recognition Workshops, 2010, pp. 104-111.
[14] Longuet-Higgins H. A Computer Algorithm for Reconstructing a Scene From Two Projections[S]// Fischler M, Firschein O. Readings in Computer Vision: Issues, Problem, Principles, and Paradigms. San Francisco, Morgan Kaufmann Publishers Inc. 1987, pp. 61-62.
[15] Tian J, Ding Y, Peng X. Self-Calibration of a Fringe Projection System using Epipolar Constraint[J]. Optics and Laser Technology, 2008, 40(3): 538-544.
[16] Ma S. A Self-calibration Technique for Active Vision System[J]. IEEE Trans. on Robotics and Automation, 1996, 12(1): 114-120.
[17] Basu A. Active Calibration: Alternative Strategy and Analysis[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1993, pp. 495-500.
[18] Du F, Brady M. Self-calibration of the Intrinsic Parameters of Cameras for Active Vision Systems[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1993, pp. 477-482.
[19] Triggs B. Autocalibration from Planar Scenes[C]// Proceedings of the 5th European Conference on Computer Vision, 1998, pp. 89-105.
[20] Gurdjos P, Sturm P. Methods and Geometry for Plane-Based Self-Calibration[C]// IEEE Conference on Computer Vision and Pattern Recognition, 2003, pp. 491-496.
[21] Pollefeys M, Van Gool L. Self-calibration from the Absolute Conic on the Plane at Infinity[C]// Proceedings of the 7th International Conference on Computer Analysis of Images and Patterns, 1997, pp. 175-182.
[22] Sturm P. Self-calibration of a Moving Camera by Pre-calibration[C]// Proceedings of the 7th British Machine Vision Conference, 1996, pp. 675-684.
[23] Heyden A, Astrom K. Euclidean Reconstruction from Image Sequences with Varying and Unknown Focal Length and Principal Point[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1977, pp. 438-443.
[24]马颂德,张正友.计算机视觉—计算理论与算法基础[M].北京,科学出版社,1998.
[25] Hartley R, Zisserman A. Multiple View geometry in Computer Vision[M]. 2nd Edition, Cambridge University Press, 2003.
[26] Fischler M, Bolles R. Random Sample Consensus: A Paradigm for Model Fitting with Applications to Image Analysis and Automated Cartography[J]. Communications of the ACM, 1981, 24(6): 381-395.
[27] Faugeras O, Maybank S. Motion from Point Matches: Multiplicity of Solutions[J]. International Journal Of Computer Vision, 1990, 4(3): 225-246.
[28] Luong Q, Deriche R, Faugeras O, etc. On Determining the Fundamental Matrix: Analysis of Different Methods and Experimental Results[R]. INRIA, 1993.
[29] Zhang Z. Determining the Epipolar Geometry and Its Uncertainty: A Review[R]. INRIA, 1996.
[30] Hartley R. Euclidean Reconstruction from Uncalibrated Views[C]// Proceedings of the 2nd Joint Europe-US Workshop on Applications of Invariance in Computer Vision, pp. 237-256.
[31] Beardsley P, Zisserman A, Murray D. Navigation Using Affine Structure from Motion[C]// Proceedings of the 3rd European Conference on Computer Vision, 1994, pp. 85-96.
[32] Hartley R, In Defense of the Eight-point Algorithm[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 1997, 19(6): 580-593.
[33] Fusiello A. The Mendonca and Cipolla Self-calibration Algorithm Experimental Evaluation[R]. 1999.
[34] Triggs B, McLauchlan F, Hartley R, etc. Bundle Adjustment– A Modern Synthesis[J]. Lecture Notes in Computer Science, 2000, 1883: 153-177.
[35] Zhang Z. A Flexible New Technique for Camera Calibration[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 2000, 22(11): 1330-1334.
[36] Lourakis M, Argyros A. SBA: A Software Package for Generic Sparse Bundle Adjustment[J]. ACM Trans. Math. Softw., 2009, 36(1): 1-30.
[37] Huang T, Faugeras O. Some Properties of The E Matrix in Two-view Motion Estimation[J]. IEEE Trans. on Pattern Analysis and Machine Intel., 1989, 11(12): 215-244.
[38] Lourakis M, Deriche R. Camera Self-calibration Using the Singular Value Decomposition of the Fundamental Matrix: From Point Correspondences to 3D Measurements[R]. 1999.
[39] Trivedi H. Can Multiple Views Make Up for Lack of Camera Registration?[J]. Image and Vision Computing, 1988, 6(1): 29-32.
[40] Luong Q, Faugeras O. Self-calibration of a Moving Camera from Point Correspondences and Fundamental Matrix[J]. International Journal of Computer Vision, 1997, 22(3): 261-289.
[41] Fusiello A. A New Autocalibration Algorithm: Experimental Evaluation[C]// Proceedings of the 9th International Conference on Computer Analysis of Images and Patterns, 2001, pp. 707-714.
[42] Mendonca P, Cipolla R. A Simple Technique for Self-calibration[C]// IEEE Conference on Computer Vision and Pattern Recognition, 1999, pp. 500-505.