无组织多视图图像的自动化三维场景重建
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摘要
从一个静态场景的多幅未标定视图来同时恢复摄像机的运动和场景的三维结构是计算机视觉领域的一个基本问题,拥有着广泛的应用前景。其理论基础多视图几何学在经过了20多年的深入研究后也在近年迈向成熟,相关的教科书也已经相继面世。
本文要挑战的问题是如何在输入大量无组织的多视图图像上实现自动化的度量重建。难点主要体现在两个方面:(1)如果输入的图像组是有序的,如视频序列,则重建可以通过分层迭代的策略来实现;而对于没有任何先验信息的无序图像组,如何采取合适的重建策略是亟待解决的问题,目前的解决方案也只能有效的处理输入视图数较少的情况。(2)现有的系统在重建过程中需要大量专家级的人机交互,实现完全自动化的多视图重建对系统的鲁棒性提出了新的挑战。
本文针对多视图重建的各个子模块提出了改良算法;并提出了一种新颖的基于图论的多视图重建策略,该策略完全不依赖输入图像组的序列信息;最终实现了一个高性能高鲁棒性的自动化多视图重建系统。
基础矩阵鲁棒性估计的主流算法是随机抽样一致性算法RANSAC,我们分析了RANSAC在理论和应用上的缺陷并提出了两种新算法:自适应Tc,d预检验RANSAC以及基于高斯混合模型GMM的随机抽样最大似然算法GMSAC。自适应Tc,d预检验使用了近似优化的预检验参数选择实现了自适应的RANSAC加速。GMSAC详细分析了局外点的成因,并针对不同成因的局外点采用了不同参数集的GMM建模,实现了基础矩阵的最大似然估计。
提出了一种最小化重投影误差的线性射影重建方法,算法实现基于场景结构、摄像机运动以及射影深度之间的加权交替最小二乘法。本射影重建算法可以与作为射影光束法平差的引导算法或者组成混合算法,有效的提高射影重建的效率与精度。
提出了一种基于双向准仿射重建的度量重建方法。使用准仿射重建作为度量重建的中间步骤可以增加算法取得全局最优的机会,提升重建质量。
我们在多个不同类型的图像组上进行了系统实验,包括室内与室外的图像组。实验结果表明,本文的系统能够在不依赖任何人机交互的情况下在复杂的无组织图像组上输出质量良好度量重建结果。
Simultaneous estimation of camera motion and structure of static scene using uncali-brated images from multiple views is a common task in computer vision and of interest formany applications. The theory of multi-view geometry has been intensively studied in thelast two decades and nowadays is subject for textbooks.
In this thesis, the challenging problem of unsupervised metric reconstruction from alarge set of unorganized still images is tackled. The difficulties arise from two main aspects:(1) For ordered image set like video sequences, the reconstruction is straight-forward with ahierarchical process. For unordered image set without any prior information, the desidera-tum is to find a strategy that can achieve successful reconstructions; the state-of-the-art canonly effectively deal with small number of images. (2) For most of the existing systems, alot of professional human-computer interaction is needed during the reconstruction process.To achieve completely unsupervised multi-view reconstruction, our system must faces newchallenges from the lack of robustness.
A series of new algorithms are presented to improve the overall robustness and per-formance. Finally, a novel reconstruction strategy based on graph theory, which has nodependence on the order of the input images, is proposed.
RANSAC(RANdom SAmple and Consensus) is the standard choice for epipolar geom-etry estimation. We addressed some problems of RANSAC posed from both practical andtheoretical standpoints and two new algorithms is presented: RANSAC with adaptive Tc,dtest and the GMSAC(Gaussian Mixture based SAmple and Consensus). Adaptive Tc,d testis an extension of the original RANSAC, which can achieve user independent RANSAC ac-celeration. GMSAC adopts the random sample strategy and maximization likelihood theory,and gaussian mixture is used to model different types of outliers respectively.
For projective reconstruction, a linear algorithm with reprojection error minimizationis derived. Our implementation is based on the weighted alternated least square between thestructure, motion and projective depth. Our method can be used as the booting or compositealgorithm for the standard projective bundle adjustment, which could improve the overallreconstruction quality and performance.
For self-calibration and metric upgrade, a method based on the two-way quasi-affinereconstruction is introduced. Before upgrade to the metric, firstly upgrade to the quasi-affine could increase the chance to reach the global optimal, and so improve the final metric quality.
System test was run on several different image sets, including outdoor and indoorimages. We show experimentally that our system can achieve high quality metric recon-struction on complex unorganized image set without any human-computer interaction.
本文要挑战的问题是如何在输入大量无组织的多视图图像上实现自动化的度量重建。难点主要体现在两个方面:(1)如果输入的图像组是有序的,如视频序列,则重建可以通过分层迭代的策略来实现;而对于没有任何先验信息的无序图像组,如何采取合适的重建策略是亟待解决的问题,目前的解决方案也只能有效的处理输入视图数较少的情况。(2)现有的系统在重建过程中需要大量专家级的人机交互,实现完全自动化的多视图重建对系统的鲁棒性提出了新的挑战。
本文针对多视图重建的各个子模块提出了改良算法;并提出了一种新颖的基于图论的多视图重建策略,该策略完全不依赖输入图像组的序列信息;最终实现了一个高性能高鲁棒性的自动化多视图重建系统。
基础矩阵鲁棒性估计的主流算法是随机抽样一致性算法RANSAC,我们分析了RANSAC在理论和应用上的缺陷并提出了两种新算法:自适应Tc,d预检验RANSAC以及基于高斯混合模型GMM的随机抽样最大似然算法GMSAC。自适应Tc,d预检验使用了近似优化的预检验参数选择实现了自适应的RANSAC加速。GMSAC详细分析了局外点的成因,并针对不同成因的局外点采用了不同参数集的GMM建模,实现了基础矩阵的最大似然估计。
提出了一种最小化重投影误差的线性射影重建方法,算法实现基于场景结构、摄像机运动以及射影深度之间的加权交替最小二乘法。本射影重建算法可以与作为射影光束法平差的引导算法或者组成混合算法,有效的提高射影重建的效率与精度。
提出了一种基于双向准仿射重建的度量重建方法。使用准仿射重建作为度量重建的中间步骤可以增加算法取得全局最优的机会,提升重建质量。
我们在多个不同类型的图像组上进行了系统实验,包括室内与室外的图像组。实验结果表明,本文的系统能够在不依赖任何人机交互的情况下在复杂的无组织图像组上输出质量良好度量重建结果。
Simultaneous estimation of camera motion and structure of static scene using uncali-brated images from multiple views is a common task in computer vision and of interest formany applications. The theory of multi-view geometry has been intensively studied in thelast two decades and nowadays is subject for textbooks.
In this thesis, the challenging problem of unsupervised metric reconstruction from alarge set of unorganized still images is tackled. The difficulties arise from two main aspects:(1) For ordered image set like video sequences, the reconstruction is straight-forward with ahierarchical process. For unordered image set without any prior information, the desidera-tum is to find a strategy that can achieve successful reconstructions; the state-of-the-art canonly effectively deal with small number of images. (2) For most of the existing systems, alot of professional human-computer interaction is needed during the reconstruction process.To achieve completely unsupervised multi-view reconstruction, our system must faces newchallenges from the lack of robustness.
A series of new algorithms are presented to improve the overall robustness and per-formance. Finally, a novel reconstruction strategy based on graph theory, which has nodependence on the order of the input images, is proposed.
RANSAC(RANdom SAmple and Consensus) is the standard choice for epipolar geom-etry estimation. We addressed some problems of RANSAC posed from both practical andtheoretical standpoints and two new algorithms is presented: RANSAC with adaptive Tc,dtest and the GMSAC(Gaussian Mixture based SAmple and Consensus). Adaptive Tc,d testis an extension of the original RANSAC, which can achieve user independent RANSAC ac-celeration. GMSAC adopts the random sample strategy and maximization likelihood theory,and gaussian mixture is used to model different types of outliers respectively.
For projective reconstruction, a linear algorithm with reprojection error minimizationis derived. Our implementation is based on the weighted alternated least square between thestructure, motion and projective depth. Our method can be used as the booting or compositealgorithm for the standard projective bundle adjustment, which could improve the overallreconstruction quality and performance.
For self-calibration and metric upgrade, a method based on the two-way quasi-affinereconstruction is introduced. Before upgrade to the metric, firstly upgrade to the quasi-affine could increase the chance to reach the global optimal, and so improve the final metric quality.
System test was run on several different image sets, including outdoor and indoorimages. We show experimentally that our system can achieve high quality metric recon-struction on complex unorganized image set without any human-computer interaction.
引文
[1] Longuet-Higgins H. A Computer Algorithm for Reconstructing a Scene from Two Projections.Nature, 1981, 293:133–135.
[2] Faugeras O, Luong Q T, Papadopoulo T. The Geometry of Multiple Images: The Laws ThatGovern the Formation of Multiple Images of a Scene and Some of Their Applications. The MITPress, March, 2001.
[3] Hartley R I, Zisserman A. Multiple View Geometry in Computer Vision, Second ed. CambridgeUniversity Press, April, 2004.
[4] Pollefeys M, Gool L V, Vergauwen M, et al. Visual modeling with a hand-held camera. Interna-tional Journal of Computer Vision, 2004, 59(3):207–232.
[5] Bartoli A, Sturm P. Structure From Motion Using Lines: Representation, Triangulation and BundleAdjustment. Computer Vision and Image Understanding, 2005, 100(3):416–441.
[6] Chum O. Two-View Geometry Estimation by Random Sample and Consensus: [PhD Disserta-tion]. Czech Technical University in Prague, 2005.
[7] Scharstein D, Szeliski R. A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspon-dence Algorithms. International Journal of Computer Vision, 2002, 47(1/2/3):7–42.
[8] Seitz S M, Curless B, Diebel J, et al. A Comparison and Evaluation of Multi-View Stereo Recon-struction Algorithms. in: IEEE Conference on Computer Vision and Pattern Recognition, 2006,519-526.
[9] Fitzgibbon A W, Zisserman A. Automatic Camera Recovery for Closed or Open Image Sequences.in: Proceedings of the European Conference on Computer Vision, june, 1998, 311–326.
[10] Niste′r D. Reconstruction from Uncalibrated Sequences with a Hierarchy of Trifocal Tensors. in:ECCV’00: Proceedings of the 6th European Conference on Computer Vision-Part I, London, UK:Springer-Verlag, 2000, 649–663.
[11] Brown M, Lowe D. Unsupervised 3D Object Recognition and Reconstruction in UnorderedDatasets. in: 5th International Conference on 3D Imaging and Modelling (3DIM05), Ottawa,Canada, 2005.
[12] Cornelius H, Sˇa′ra R, Martinec D, et al. Towards Complete Free-Form Reconstruction of Complex3D Scenes from an Unordered Set of Uncalibrated Images. in: Proc ECCV Workshop StatisticalMethods in Video Processing, Prague, Czech Republic, 2004, 1-12.
[13] Schaffalitzky F, Zisserman A. Multi-view Matching for Unordered Image Sets, or”How Do IOrganize My Holiday Snaps?”. in: ECCV’02: Proceedings of the 7th European Conference onComputer Vision-Part I, London, UK: Springer-Verlag, 2002, 414–431.
[14] Niste′r D. An efficient solution to the five-point relative pose problem. IEEE Transactions onPattern Analysis and Machine Intelligence, 2004, 26(6):756–770.
[15] Moving Picture Experts Group. http://www.chiariglione.org/mpeg/.
[16] Smolic A, Kimata H. Applications and Requirements for 3DAV. Technical Report N5877,ISO/IEC JTC1/SC29/WG11, Trondheim, Norway, July, 2003.
[17] Smolic A, Kimata H. Report on 3DAV Exploration. Technical Report N5878, ISO/IECJTC1/SC29/WG11, Trondheim, Norway, July, 2003.
[18] Smolic A, Kauff P. Interactive 3-D video representation and coding technologies. Proceedings ofthe IEEE, 2005, 93(1):98–110.
[19] Smolic A, McCutchen D. 3DAV exploration of video-based rendering technology in MPEG. IEEETransactions on Circuits and Systems for Video Technology, 2004, 14(3):348–356.
[20] Redert A, Op de Beeck M, Fehn C, et al. ATTEST– Advanced Three-Dimensional TelevisionSystem Technologies. in: Proceedings of 1st International Symposium on 3D Data Processing,Visualization and Transmission, Padova, Italy, June, 2002, 313–319.
[21] Fehn C, de la Barre′R, Pastoor S. Interactive 3DTV– Concepts and Key Technologies. Proceedingsof the IEEE, 2006, 94(3):524–538.
[22] PhotoModeler. http://www.photomodeler.com/.
[23] Rodriguez T, Sturm P, Gargallo P, et al. Photorealistic 3D Reconstruction from Handheld Cameras.Machine Vision and Applications, 2005, 16(4):246–257.
[24] Brown M, Lowe D G. Recognising Panoramas. in: International Conference on Computer Vision,Nice, France, October, 2003, 1218-1225.
[25] Sivic J, Zisserman A. Video google: A text retrieval approach to object matching in videos. in:International Conference on Computer Vision, Nice, France, 2003.
[26] Irani M, Anandan P. About Direct Methods. in: Triggs B, Zisserman A, Szeliski R, editors, VisionAlgorithms: Theory and Practice, International Workshop on Vision Algorithms, LNCS, pages267–277. Springer Verlag, 2000.
[27] Sheikh Y, Hakeem A, Shah M. On the Direct Estimation of the Fundamental Matrix. in: IEEEComputer Society Conference on Computer Vision and Pattern Recognition, 2007.
[28] Harris C, Stephens M. A Combined Corner and Edge Detector. in: 4th ALVEY Vision Conference,1988, 147–151.
[29] Schmid C, Mohr R, Bauckhage C. Evaluation of Interest Point Detectors. International Journal ofComputer Vision, 2000, 37(2):151–172.
[30] Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal ofComputer Vision, 2004, 60(2):91–110.
[31] Mikolajczyk K, Schmid C. A Performance Evaluation of Local Descriptors. IEEE Transactionson Pattern Analysis and Machine Intelligence, 2005, 27(10):1615–1630.
[32] Mikolajczyk K, Tuytelaars T, Schmid C, et al. A comparison of affine region detectors. Interna-tional Journal of Computer Vision, 2005, 65(1/2):43–72.
[33] Moreels P, Perona P. Evaluation of Features Detectors and Descriptors based on 3D Objects.International Journal of Computer Vision, 2007, 73(3):263–284.
[34] Mikolajczyk K, Schmid C. Scale and affine invariant interest point detectors. International Journalof Computer Vision, 2004, 60(1):63–86.
[35] Matas J, Chum O, Martin U, et al. Robust Wide baseline Stereo from Maximally Stable ExtremalRegions. in: Rosin P L, Marshall D, editors, Proceedings of the British Machine Vision Confer-ence, London, UK: BMVA, September, 2002, 384-393.
[36] Bay H, Tuytelaars T, Gool L V. SURF: Speeded Up Robust Features. in: Proceedings of the NinthEuropean Conference on Computer Vision, 2006.
[37]孟晓桥,胡占义.摄像机自标定方法的研究与进展.自动化学报, 2003, 29(1):110–124.
[38] Hartley R I. Theory and Practice of Projective Rectification. International Journal of ComputerVision, 1999, 35(2):115–127.
[39] Zhang Z. Determining the Epipolar Geometry and its Uncertainty: A Review. International Journalof Computer Vision, 1998, 27(2):161–195.
[40] Hartley R I. In Defense of the Eight-Point Algorithm. IEEE Transactions on Pattern Analysis andMachine Intelligence, 1997, 19(6):580–593.
[41] Hartley R I, Sturm P F. Triangulation. Computer Vision and Image Understanding, 1997,68(2):146–157.
[42] Zhang Z. On the Optimization Criteria Used in Two-View Motion Analysis. IEEE Transactionson Pattern Analysis and Machine Intelligence, 1998, 20(7):717–729.
[43] Fischler M A, Bolles R C. Random sample consensus: a paradigm for model fitting with applica-tions to image analysis and automated cartography. Communications ACM, 1981, 24(6):381–395.
[44] Torr P, Zisserman A. MLESAC: A new robust estimator with application to estimating imagegeometry. Computer Vision and Image Understanding, 2000, 78:138–156.
[45] Tang C K, Medioni G, Lee M S. N-Dimensional Tensor Voting and Application to EpipolarGeometry Estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001,23(8):829–844.
[46] Torr P H S, Murray D W. The Development and Comparison of Robust Methodsfor Estimatingthe Fundamental Matrix. International Journal of Computer Vision, 1997, 24(3):271–300.
[47] Torr P H S, Zisserman A. Robust Parameterization and Computation of the Trifocal Tensor. Imageand Vision Computing, 1997, 15:591–607.
[48] Torr P H S. Outlier Detection and Motion Segmentation: [PhD Dissertation]. University of Oxford,1995.
[49] McLauchlan P F, Jaenicke A. Image Mosaicing using Sequential Bundle Adjustment. Image andVision Computing, 2002, 20(9-10):751–759.
[50] Leonardis A, Bischof H. Robust recognition using eigenimages. Computer Vision and ImageUnderstanding, 2000, 78(1):99–118.
[51] 25 Years of RANSAC Workshop in conjunction with CVPR 2006. http://cmp.felk.cvut.cz/ransac-cvpr2006/.
[52] Beardsley P A, Zisserman A, Murray D W. Sequential Updating of Projective and Affine Structurefrom Motion. International Journal of Computer Vision, 1997, 23(3):235–259.
[53] Buchanan A M, Fitzgibbon A W. Damped Newton Algorithms for Matrix Factorization withMissing Data. in: CVPR’05: Proceedings of the 2005 IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR’05) - Volume 2, Washington, DC, USA: IEEEComputer Society, 2005, 316–322.
[54] Guilbert N, Bartoli A, Heyden A. Affine Approximation for Direct Batch Recovery of Euclid-ian Structure and Motion from Sparse Data. International Journal of Computer Vision, 2006,69(3):317–333.
[55] Hartley R, Schaffalizky F. PowerFactorization: 3D Reconstruction with Missing or UncertainData. in: Australia-Japan Advanced Workshop on Computer Vision, 2003.
[56] Jacobs D W. Linear Fitting with Missing Data for Structure-from-Motion. Computer Vision andImage Understanding, 2001, 82(2):57–81.
[57] Martinec D, Pajdla T. 3D Reconstruction by Fitting Low-Rank Matrices with Missing Data. in:CVPR’05: Proceedings of the 2005 IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR’05) - Volume 1, Washington, DC, USA: IEEE Computer Society,2005, 198–205.
[58] Martinec D, Pajdla T. Structure from Many Perspective Images with Occlusions. in: ECCV’02:Proceedings of the 7th European Conference on Computer Vision-Part II, London, UK: Springer-Verlag, 2002, 355–369.
[59] Oliensis J, Hartley R. Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Non-convergence. in: H. Bischof A L, Pinz A, editors, Proceedings of the European Conference onComputer Vision, 2006, 214-227.
[60] Sturm P, Triggs B. A Factorization Based Algorithm for Multi-Image Projective Structure andMotion. in: Proceedings of the European Conference on Computer Vision, 1996, 709-720.
[61] Tomasi C, Kanade T. Shape and motion from image streams under orthography: a factorizationmethod. International Journal of Computer Vision, 1992, 9(2):137–154.
[62] Okatani T, Deguchi K. On the Wiberg Algorithm for Matrix Factorization in the Presence ofMissing Components. International Journal of Computer Vision, 2007, 72(3):329–337.
[63] Golub G H, Loan C F V. Matrix Computations, 3rd ed. Baltimore, MD, USA: Johns HopkinsUniversity Press, 1996.
[64] Cornelis K, Verbiest F, Gool L V. Drift Detection and Removal for Sequential Structure fromMotion Algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004,26(10):1249–1259.
[65] Vidal R, Hartley R. Motion Segmentation with Missing Data using PowerFactorization and GPCA.in: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR’04), 2004, 310-316.
[66]邱茂林,马颂德,李毅.计算机视觉中摄像机定标综述.自动化学报, 2000, 26(1):43–55.
[67] Maybank S J, Faugeras O D. A theory of self-calibration of a moving camera. International Journalof Computer Vision, 1992, 8(2):123–151.
[68] Faugeras O D, Luong Q T, Maybank S J. Camera Self-Calibration: Theory and Experiments. in:European Conference on Computer Vision, 1992, 321-334.
[69] Kruppa E. Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung. Sitz-Ber. Akad. Wiss., Wien, Math. Narurw. Abt. IIa., 1913, 122:1939–1948.
[70] Triggs B. Autocalibration and the Absolute Quadric. in: Proceedings of the IEEE Conferenceon Computer Vision and Pattern Recognition, Puerto Rico, USA. IEEE Computer Society Press,June, 1997, 609–614.
[71] Pollefeys M, Koch R, Gool L V. Self-Calibration and Metric Reconstruction Inspite of Varying andUnknown Intrinsic Camera Parameters. International Journal of Computer Vision, 1999, 32(1):7–25.
[72] Heyden A, A?stro¨m K. Flexible Calibration: Minimal Cases for Auto-calibration. in: ICCV’99:The Proceedings of the Seventh IEEE International Conference on on Computer Vision, Kerkyra,Greece, 1999, 350-355.
[73] Hu Z, Wu Y, Wu F, et al. The Number of Independent Kruppa Constraints from N Images. Journalof Computer Science and Technology, 2006, 21(2):209–217.
[74] Hartley R I, Agapito L, Reid I D, et al. Camera Calibration and the Search for Infinity. in:ICCV’99: The Proceedings of the Seventh IEEE International Conference on Computer Vision,1999, 510-517.
[75] Niste′r D. Untwisting a Projective Reconstruction. International Journal of Computer Vision, 2004,60(2):165–183.
[76] Thorma¨hlen T, Broszio H, Mikulastik P. Robust Linear Auto-calibration of a Moving Camerafrom Image Sequences. in: Narayanan P J, Nayar S K, Shum H Y, editors, 7th Asian Conferenceon Computer Vision, Hyderabad, India, 2006, 71-80.
[77] Urban M, Pajdla T, Hlavac V. Projective Reconstruction from N Views Having One View inCommon. in: Triggs B, Zisserman A, Szeliski R, editors, Vision Algorithms: Theory and Practice,International Workshop on Vision Algorithms, Corfu, Greece, 2000, 116-131.
[78] Semple J G, Kneebone G T. Algebraic Projective Geometry. Oxford University Press, 1952.
[79] Sturm P, Ramalingam S, Lodha S. On Calibration, Structure from Motion and Multi-View Geom-etry for Generic Camera Models. in: Daniilidis K, Klette R, editors, Imaging Beyond the PinholeCamera, volume 33 of Computational Imaging and Vision. Springer, aug, 2006.
[80]黄克智,薛明德,陆明万.张量分析.清华大学出版社, 2003.
[81] Triggs B. The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image.Circulated in 1995. Accepted subject to revision to IJCV in 1995, but never completed, 1995.
[82] Heyden A, A?stro¨m K. Algebraic Properties of Multilinear Constraints. Mathematical Methods inthe Applied Scinces, 1997, 20(13):1135–1162.
[83] Heyden A. A Common Framework for Multiple View Tensors. in: ECCV’98: Proceedings ofthe 5th European Conference on Computer Vision-Volume I, London, UK: Springer-Verlag, 1998,3–19.
[84] Hartley R I. Computation of the Quadrifocal Tensor. in: ECCV’98: Proceedings of the 5thEuropean Conference on Computer Vision-Volume I, London, UK: Springer-Verlag, 1998, 20–35.
[85] Hartley R I. Chirality. International Journal of Computer Vision, 1998, 26(1):41–61.
[86] Werner T, Pajdla T, Hlava′cˇV. Oriented Projective Reconstruction. in: Gengler M, Prinz M, Schus-ter E, editors, Pattern Recognition and Medical Computer Vision: 22-nd Workshop of the AustrianAssociation for Pattern Recognition (O¨AGM/IAPR), Wien, Austria: O¨sterreichische ComputerGesselschaft, May 14–15, 1998, 245–254.
[87] Laveau S, Faugeras O D. Oriented Projective Geometry for Computer Vision. in: ECCV’96: Pro-ceedings of the 4th European Conference on Computer Vision-Volume I, London, UK: Springer-Verlag, 1996, 147–156.
[88] Chum O, Werner T, Pajdla T. Joint Orientation of Epipoles. in: Harvey R, editor, BMVC 2003:Proceedings of the 14th British Machine Vision Conference, London, UK: BMVA, September,2003, BMVA, 73–82.
[89] Chum O, Werner T, Matas J. Epipolar Geometry Estimation via RANSAC Benefits from theOriented Epipolar Constraint. in: Josef Kittler M N, editor, Proceedings of ICPR 2004 17thInternational Conference on Pattern Recognition, 10662 Los Vaqueros Circle, P.O.Box 3014, CA90720-1314, Los Alamitos, USA: IEEE Computer Society, August, 2004, IEEE, 112–115.
[90] Chojnacki W, Brooks M J, Hengel A, et al. Revisiting Hartley’s Normalized Eight-Point Algo-rithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(9):1172–1177.
[91] Wu F C, Hu Z Y, Duan F Q. 8-Point Algorithm Revisited: Factorized 8-Point Algorithm. in: ICCV’05: Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV’05)Volume 1, Washington, DC, USA: IEEE Computer Society, 2005, 488–494.
[92] Torr P, Fitzgibbon A. Invariant Fitting of Two View Geometry. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2004, 26(5):648–650.
[93] Chum O, Matas J, Kittler J. Locally optimized RANSAC. in: G. Goos J v L, editor, DAGM2003: Proceedings of the 25th DAGM Symposium, Heidelberger Platz 3, 14197, Berlin, Germany:Springer-Verlag, September, 2003, 236–243.
[94] Chum O, Matas J, Obdrzˇa′lek Sˇ. Enhancing RANSAC by Generalized Model Optimization. in:Hong K S, Zhang Z, editors, Proc. of the Asian Conference on Computer Vision (ACCV), Seoul,Korea South: Asian Federation of Computer Vision Societies, January, 2004, 812–817.
[95] Matas J, Chum O. Randomized RANSAC with Td,d test. Image and Vision Computing, 2004,22:837–842.
[96]陈付幸,王润生.基于预检验的快速随机抽样一致性算法.软件学报, 2005, 16(08):1431–1437.
[97] Niste′r D. Preemptive RANSAC for live structure and motion estimation. Machine Vision andApplications, 2005, 16(5):321–329.
[98] Capel D P. An Effective Bail-out Test for RANSAC Consensus Scoring. in: Proc. British MachineVision Conf., 2005.
[99] Torr P H S. Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Mani-fold Fitting. International Journal of Computer Vision, 2002, 50(1):35–61.
[100] Torr P H, Davidson C. IMPSAC: Synthesis of Importance Sampling and Random Sample Con-sensus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(3):354–364.
[101]陈付幸,王润生.基础矩阵估计的聚类分析算法.计算机辅助设计与图形学学报, 2005,17(10):2251–2256.
[102] Brandt S S. Maximum Likelihood Robust Regression by Mixture Models. Journal of MathematicalImaging and Vision, 2006, 25:25–48.
[103] Rousseeuw P J, Leroy A M. Robust regression and outlier detection. New York, NY, USA: JohnWiley & Sons, Inc., 1987.
[104] Triggs B. Matching constraints and the joint image. in: Grimson E, editor, ICCV’95: Proceedingsof the Fifth International Conference on Computer Vision, Washington, DC, USA: IEEE ComputerSociety, 1995, 338–343.
[105] Dempster A P, Laird N M, Rubin D B. Maximum Likelihood from Incomplete Data via the EMAlgorithm. Journal of the Royal Statistical Society. Series B (Methodological), 1977, 39(1):1–38.
[106] Vapnik V N. The Nature of Statistical Learning Theory. New York, NY, USA: Springer-VerlagNew York, Inc., 1995.
[107] Biernacki C, Celeux G, Govaert G. Choosing starting values for the EM algorithm for gettingthe highest likelihood in multivariate Gaussian mixture models. Computational Statistics & DataAnalysis, 2003, 41(3-4):561–575.
[108] Tordoff B J, Murray D W. Guided-MLESAC: Faster Image Transform Estimation by Using Match-ing Priors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(10):1523–1535.
[109] Triggs B, McLauchlan P, Hartley R, et al. Bundle Adjustment– A Modern Synthesis. in: Triggs B,Zisserman A, Szeliski R, editors, Vision Algorithms: Theory and Practice, International Workshopon Vision Algorithms, LNCS, pages 298–375. Springer Verlag, 2000.
[110] Wiberg T. Computation of Principal Components when Data are Missing. in: Second Symposiumof Computational Statistics, 1976, 229-326.
[111] Hung Y S, Tang W K. Projective Reconstruction from Multiple Views with Minimization of 2DReprojection Error. International Journal of Computer Vision, 2006, 66(3):305–317.
[112] Svoboda T, Martinec D, Pajdla T. A Convenient Multi-Camera Self-Calibration for Virtual Envi-ronments. PRESENCE: Teleoperators and Virtual Environments, 2005, 14(4):407–422.
[113] Lourakis M, Argyros A. The Design and Implementation of a Generic Sparse Bundle AdjustmentSoftware Package Based on the Levenberg-Marquardt Algorithm. Technical Report 340, Instituteof Computer Science - FORTH, Heraklion, Crete, Greece, Aug., 2004. http://www.ics.forth.gr/～lourakis/sba.
[114] Agapito L, Hayman E, Reid I. Self-Calibration of Rotating and Zooming Cameras. InternationalJournal of Computer Vision, 2002, 47(1-3):287–287.
[115] Chum O, Pajdla T, Sturm P. The geometric error for homographies. Computer Vision and ImageUnderstanding, 2005, 97(1):86–102.
[116] Pollefeys M, Gool L V. Stratified Self-Calibration with the Modulus Constraint. IEEE Transactionson Pattern Analysis and Machine Intelligence, 1999, 21(8):707–724.
[117] Pollefeys M, Verbiest F, Gool L J V. Surviving Dominant Planes in Uncalibrated Structure andMotion Recovery. in: ECCV’02: Proceedings of the 7th European Conference on ComputerVision, London, UK: Springer-Verlag, 2002, 837–851.
[118] Ferrari V, Tuytelaars T, Gool L V. Wide-baseline muliple-view Correspondences. in: IEEE Com-puter Society Conference on Computer Vision and Pattern Recognition, Madison, USA, June,2003.
[119] Shafique K, Shah M. A Non-Iterative Greedy Algorithm for Multi-frame Point Correspondence.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(1):1–15.
[120] Levi N, Werman M. The Viewing Graph. in: IEEE Computer Society Conference on ComputerVision and Pattern Recognition, 2003, 518-522.
[121] Hartley R, Kahl F. Critical Configurations for Projective Reconstruction from Multiple Views.International Journal of Computer Vision, 2007, 71(1):5–47.
[122] Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms, Second ed. Cambridge,MA, USA: MIT Press, 2001.
[123] Martinec D, Pajdla T. 3D Reconstruction by Gluing Pair-Wise Euclidean Reconstructions, or”How to Achieve a Good Reconstruction from Bad Images”. in: Third International Symposiumon 3D Data Processing, Visualization, and Transmission, Chapel Hill, NC, USA, 2006, 25-32.
[124] Kahl F. Multiple View Geometry and the L∞-Norm. in: International Conference on ComputerVision, Beijing, China, 2005, 1002–1009.
[125] Vidal R, Ma Y, Soatto S, et al. Two-View Multibody Structure from Motion. Int. J. Comput.Vision, 2006, 68(1):7–25.
[126] Sheikh Y, Gritai A, Shah M. On the Spacetime Geometry of Galilean Cameras. in: IEEE ComputerSociety Conference on Computer Vision and Pattern Recognition, 2007.
[127] Sinha S, Frahm J M, Pollefeys M, et al. Feature Tracking and Matching in Video Using Pro-grammable Graphics Hardware. Machine Vision and Application, 2007.
[128] Mordohai P, Frahm J M, Akbarzadeh A, et al. Real-Time Video-Based Reconstruction of UrbanEnvironments. in: 3D Virtual Reconstruction and Visualization of Complex Architectures, July,2007.
[129] Martinec D, Pajdla T. Robust Rotation and Translation Estimation in Multiview Reconstruction.in: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Minneapo-lis, MN, USA, 2007.
[130] Bocquillon B, Bartoli A, Gurdjos P, et al. On Constant Focal Length Self-Calibration From Mul-tiple Views. in: IEEE Conference on Computer Vision and Pattern Recognition, 2007.
[131] Chandraker M, Agarwal S, Kahl F, et al. Autocalibration via Rank-Constrained Estimation of theAbsolute Quadric. in: IEEE Conference on Computer Vision and Pattern Recognition, 2007.
[132] Bilmes J. A Gentle Tutorial on the EM Algorithm and its Application to Parameter Estimation forGaussian Mixture and Hidden Markov Models, 1997. citeseer.ist.psu.edu/bilmes98gentle.html.
[133] Redner R, Walker H. Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAMReview, 1984, 26(2):195–239.
[134] Minka T. Expectation-Maximization as lower bound maximization, 1998. citeseer.ist.psu.edu/minka98expectationmaximization.html.
[135] Gelman A, Carlin J B, Stern H S, et al. Bayesian Data Analysis, Second ed. Chapman & Hall/CRC,July, 2003.
[2] Faugeras O, Luong Q T, Papadopoulo T. The Geometry of Multiple Images: The Laws ThatGovern the Formation of Multiple Images of a Scene and Some of Their Applications. The MITPress, March, 2001.
[3] Hartley R I, Zisserman A. Multiple View Geometry in Computer Vision, Second ed. CambridgeUniversity Press, April, 2004.
[4] Pollefeys M, Gool L V, Vergauwen M, et al. Visual modeling with a hand-held camera. Interna-tional Journal of Computer Vision, 2004, 59(3):207–232.
[5] Bartoli A, Sturm P. Structure From Motion Using Lines: Representation, Triangulation and BundleAdjustment. Computer Vision and Image Understanding, 2005, 100(3):416–441.
[6] Chum O. Two-View Geometry Estimation by Random Sample and Consensus: [PhD Disserta-tion]. Czech Technical University in Prague, 2005.
[7] Scharstein D, Szeliski R. A Taxonomy and Evaluation of Dense Two-Frame Stereo Correspon-dence Algorithms. International Journal of Computer Vision, 2002, 47(1/2/3):7–42.
[8] Seitz S M, Curless B, Diebel J, et al. A Comparison and Evaluation of Multi-View Stereo Recon-struction Algorithms. in: IEEE Conference on Computer Vision and Pattern Recognition, 2006,519-526.
[9] Fitzgibbon A W, Zisserman A. Automatic Camera Recovery for Closed or Open Image Sequences.in: Proceedings of the European Conference on Computer Vision, june, 1998, 311–326.
[10] Niste′r D. Reconstruction from Uncalibrated Sequences with a Hierarchy of Trifocal Tensors. in:ECCV’00: Proceedings of the 6th European Conference on Computer Vision-Part I, London, UK:Springer-Verlag, 2000, 649–663.
[11] Brown M, Lowe D. Unsupervised 3D Object Recognition and Reconstruction in UnorderedDatasets. in: 5th International Conference on 3D Imaging and Modelling (3DIM05), Ottawa,Canada, 2005.
[12] Cornelius H, Sˇa′ra R, Martinec D, et al. Towards Complete Free-Form Reconstruction of Complex3D Scenes from an Unordered Set of Uncalibrated Images. in: Proc ECCV Workshop StatisticalMethods in Video Processing, Prague, Czech Republic, 2004, 1-12.
[13] Schaffalitzky F, Zisserman A. Multi-view Matching for Unordered Image Sets, or”How Do IOrganize My Holiday Snaps?”. in: ECCV’02: Proceedings of the 7th European Conference onComputer Vision-Part I, London, UK: Springer-Verlag, 2002, 414–431.
[14] Niste′r D. An efficient solution to the five-point relative pose problem. IEEE Transactions onPattern Analysis and Machine Intelligence, 2004, 26(6):756–770.
[15] Moving Picture Experts Group. http://www.chiariglione.org/mpeg/.
[16] Smolic A, Kimata H. Applications and Requirements for 3DAV. Technical Report N5877,ISO/IEC JTC1/SC29/WG11, Trondheim, Norway, July, 2003.
[17] Smolic A, Kimata H. Report on 3DAV Exploration. Technical Report N5878, ISO/IECJTC1/SC29/WG11, Trondheim, Norway, July, 2003.
[18] Smolic A, Kauff P. Interactive 3-D video representation and coding technologies. Proceedings ofthe IEEE, 2005, 93(1):98–110.
[19] Smolic A, McCutchen D. 3DAV exploration of video-based rendering technology in MPEG. IEEETransactions on Circuits and Systems for Video Technology, 2004, 14(3):348–356.
[20] Redert A, Op de Beeck M, Fehn C, et al. ATTEST– Advanced Three-Dimensional TelevisionSystem Technologies. in: Proceedings of 1st International Symposium on 3D Data Processing,Visualization and Transmission, Padova, Italy, June, 2002, 313–319.
[21] Fehn C, de la Barre′R, Pastoor S. Interactive 3DTV– Concepts and Key Technologies. Proceedingsof the IEEE, 2006, 94(3):524–538.
[22] PhotoModeler. http://www.photomodeler.com/.
[23] Rodriguez T, Sturm P, Gargallo P, et al. Photorealistic 3D Reconstruction from Handheld Cameras.Machine Vision and Applications, 2005, 16(4):246–257.
[24] Brown M, Lowe D G. Recognising Panoramas. in: International Conference on Computer Vision,Nice, France, October, 2003, 1218-1225.
[25] Sivic J, Zisserman A. Video google: A text retrieval approach to object matching in videos. in:International Conference on Computer Vision, Nice, France, 2003.
[26] Irani M, Anandan P. About Direct Methods. in: Triggs B, Zisserman A, Szeliski R, editors, VisionAlgorithms: Theory and Practice, International Workshop on Vision Algorithms, LNCS, pages267–277. Springer Verlag, 2000.
[27] Sheikh Y, Hakeem A, Shah M. On the Direct Estimation of the Fundamental Matrix. in: IEEEComputer Society Conference on Computer Vision and Pattern Recognition, 2007.
[28] Harris C, Stephens M. A Combined Corner and Edge Detector. in: 4th ALVEY Vision Conference,1988, 147–151.
[29] Schmid C, Mohr R, Bauckhage C. Evaluation of Interest Point Detectors. International Journal ofComputer Vision, 2000, 37(2):151–172.
[30] Lowe D G. Distinctive image features from scale-invariant keypoints. International Journal ofComputer Vision, 2004, 60(2):91–110.
[31] Mikolajczyk K, Schmid C. A Performance Evaluation of Local Descriptors. IEEE Transactionson Pattern Analysis and Machine Intelligence, 2005, 27(10):1615–1630.
[32] Mikolajczyk K, Tuytelaars T, Schmid C, et al. A comparison of affine region detectors. Interna-tional Journal of Computer Vision, 2005, 65(1/2):43–72.
[33] Moreels P, Perona P. Evaluation of Features Detectors and Descriptors based on 3D Objects.International Journal of Computer Vision, 2007, 73(3):263–284.
[34] Mikolajczyk K, Schmid C. Scale and affine invariant interest point detectors. International Journalof Computer Vision, 2004, 60(1):63–86.
[35] Matas J, Chum O, Martin U, et al. Robust Wide baseline Stereo from Maximally Stable ExtremalRegions. in: Rosin P L, Marshall D, editors, Proceedings of the British Machine Vision Confer-ence, London, UK: BMVA, September, 2002, 384-393.
[36] Bay H, Tuytelaars T, Gool L V. SURF: Speeded Up Robust Features. in: Proceedings of the NinthEuropean Conference on Computer Vision, 2006.
[37]孟晓桥,胡占义.摄像机自标定方法的研究与进展.自动化学报, 2003, 29(1):110–124.
[38] Hartley R I. Theory and Practice of Projective Rectification. International Journal of ComputerVision, 1999, 35(2):115–127.
[39] Zhang Z. Determining the Epipolar Geometry and its Uncertainty: A Review. International Journalof Computer Vision, 1998, 27(2):161–195.
[40] Hartley R I. In Defense of the Eight-Point Algorithm. IEEE Transactions on Pattern Analysis andMachine Intelligence, 1997, 19(6):580–593.
[41] Hartley R I, Sturm P F. Triangulation. Computer Vision and Image Understanding, 1997,68(2):146–157.
[42] Zhang Z. On the Optimization Criteria Used in Two-View Motion Analysis. IEEE Transactionson Pattern Analysis and Machine Intelligence, 1998, 20(7):717–729.
[43] Fischler M A, Bolles R C. Random sample consensus: a paradigm for model fitting with applica-tions to image analysis and automated cartography. Communications ACM, 1981, 24(6):381–395.
[44] Torr P, Zisserman A. MLESAC: A new robust estimator with application to estimating imagegeometry. Computer Vision and Image Understanding, 2000, 78:138–156.
[45] Tang C K, Medioni G, Lee M S. N-Dimensional Tensor Voting and Application to EpipolarGeometry Estimation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001,23(8):829–844.
[46] Torr P H S, Murray D W. The Development and Comparison of Robust Methodsfor Estimatingthe Fundamental Matrix. International Journal of Computer Vision, 1997, 24(3):271–300.
[47] Torr P H S, Zisserman A. Robust Parameterization and Computation of the Trifocal Tensor. Imageand Vision Computing, 1997, 15:591–607.
[48] Torr P H S. Outlier Detection and Motion Segmentation: [PhD Dissertation]. University of Oxford,1995.
[49] McLauchlan P F, Jaenicke A. Image Mosaicing using Sequential Bundle Adjustment. Image andVision Computing, 2002, 20(9-10):751–759.
[50] Leonardis A, Bischof H. Robust recognition using eigenimages. Computer Vision and ImageUnderstanding, 2000, 78(1):99–118.
[51] 25 Years of RANSAC Workshop in conjunction with CVPR 2006. http://cmp.felk.cvut.cz/ransac-cvpr2006/.
[52] Beardsley P A, Zisserman A, Murray D W. Sequential Updating of Projective and Affine Structurefrom Motion. International Journal of Computer Vision, 1997, 23(3):235–259.
[53] Buchanan A M, Fitzgibbon A W. Damped Newton Algorithms for Matrix Factorization withMissing Data. in: CVPR’05: Proceedings of the 2005 IEEE Computer Society Conference onComputer Vision and Pattern Recognition (CVPR’05) - Volume 2, Washington, DC, USA: IEEEComputer Society, 2005, 316–322.
[54] Guilbert N, Bartoli A, Heyden A. Affine Approximation for Direct Batch Recovery of Euclid-ian Structure and Motion from Sparse Data. International Journal of Computer Vision, 2006,69(3):317–333.
[55] Hartley R, Schaffalizky F. PowerFactorization: 3D Reconstruction with Missing or UncertainData. in: Australia-Japan Advanced Workshop on Computer Vision, 2003.
[56] Jacobs D W. Linear Fitting with Missing Data for Structure-from-Motion. Computer Vision andImage Understanding, 2001, 82(2):57–81.
[57] Martinec D, Pajdla T. 3D Reconstruction by Fitting Low-Rank Matrices with Missing Data. in:CVPR’05: Proceedings of the 2005 IEEE Computer Society Conference on Computer Visionand Pattern Recognition (CVPR’05) - Volume 1, Washington, DC, USA: IEEE Computer Society,2005, 198–205.
[58] Martinec D, Pajdla T. Structure from Many Perspective Images with Occlusions. in: ECCV’02:Proceedings of the 7th European Conference on Computer Vision-Part II, London, UK: Springer-Verlag, 2002, 355–369.
[59] Oliensis J, Hartley R. Iterative Extensions of the Sturm/Triggs Algorithm: Convergence and Non-convergence. in: H. Bischof A L, Pinz A, editors, Proceedings of the European Conference onComputer Vision, 2006, 214-227.
[60] Sturm P, Triggs B. A Factorization Based Algorithm for Multi-Image Projective Structure andMotion. in: Proceedings of the European Conference on Computer Vision, 1996, 709-720.
[61] Tomasi C, Kanade T. Shape and motion from image streams under orthography: a factorizationmethod. International Journal of Computer Vision, 1992, 9(2):137–154.
[62] Okatani T, Deguchi K. On the Wiberg Algorithm for Matrix Factorization in the Presence ofMissing Components. International Journal of Computer Vision, 2007, 72(3):329–337.
[63] Golub G H, Loan C F V. Matrix Computations, 3rd ed. Baltimore, MD, USA: Johns HopkinsUniversity Press, 1996.
[64] Cornelis K, Verbiest F, Gool L V. Drift Detection and Removal for Sequential Structure fromMotion Algorithms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2004,26(10):1249–1259.
[65] Vidal R, Hartley R. Motion Segmentation with Missing Data using PowerFactorization and GPCA.in: Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and PatternRecognition (CVPR’04), 2004, 310-316.
[66]邱茂林,马颂德,李毅.计算机视觉中摄像机定标综述.自动化学报, 2000, 26(1):43–55.
[67] Maybank S J, Faugeras O D. A theory of self-calibration of a moving camera. International Journalof Computer Vision, 1992, 8(2):123–151.
[68] Faugeras O D, Luong Q T, Maybank S J. Camera Self-Calibration: Theory and Experiments. in:European Conference on Computer Vision, 1992, 321-334.
[69] Kruppa E. Zur Ermittlung eines Objektes aus zwei Perspektiven mit innerer Orientierung. Sitz-Ber. Akad. Wiss., Wien, Math. Narurw. Abt. IIa., 1913, 122:1939–1948.
[70] Triggs B. Autocalibration and the Absolute Quadric. in: Proceedings of the IEEE Conferenceon Computer Vision and Pattern Recognition, Puerto Rico, USA. IEEE Computer Society Press,June, 1997, 609–614.
[71] Pollefeys M, Koch R, Gool L V. Self-Calibration and Metric Reconstruction Inspite of Varying andUnknown Intrinsic Camera Parameters. International Journal of Computer Vision, 1999, 32(1):7–25.
[72] Heyden A, A?stro¨m K. Flexible Calibration: Minimal Cases for Auto-calibration. in: ICCV’99:The Proceedings of the Seventh IEEE International Conference on on Computer Vision, Kerkyra,Greece, 1999, 350-355.
[73] Hu Z, Wu Y, Wu F, et al. The Number of Independent Kruppa Constraints from N Images. Journalof Computer Science and Technology, 2006, 21(2):209–217.
[74] Hartley R I, Agapito L, Reid I D, et al. Camera Calibration and the Search for Infinity. in:ICCV’99: The Proceedings of the Seventh IEEE International Conference on Computer Vision,1999, 510-517.
[75] Niste′r D. Untwisting a Projective Reconstruction. International Journal of Computer Vision, 2004,60(2):165–183.
[76] Thorma¨hlen T, Broszio H, Mikulastik P. Robust Linear Auto-calibration of a Moving Camerafrom Image Sequences. in: Narayanan P J, Nayar S K, Shum H Y, editors, 7th Asian Conferenceon Computer Vision, Hyderabad, India, 2006, 71-80.
[77] Urban M, Pajdla T, Hlavac V. Projective Reconstruction from N Views Having One View inCommon. in: Triggs B, Zisserman A, Szeliski R, editors, Vision Algorithms: Theory and Practice,International Workshop on Vision Algorithms, Corfu, Greece, 2000, 116-131.
[78] Semple J G, Kneebone G T. Algebraic Projective Geometry. Oxford University Press, 1952.
[79] Sturm P, Ramalingam S, Lodha S. On Calibration, Structure from Motion and Multi-View Geom-etry for Generic Camera Models. in: Daniilidis K, Klette R, editors, Imaging Beyond the PinholeCamera, volume 33 of Computational Imaging and Vision. Springer, aug, 2006.
[80]黄克智,薛明德,陆明万.张量分析.清华大学出版社, 2003.
[81] Triggs B. The Geometry of Projective Reconstruction I: Matching Constraints and the Joint Image.Circulated in 1995. Accepted subject to revision to IJCV in 1995, but never completed, 1995.
[82] Heyden A, A?stro¨m K. Algebraic Properties of Multilinear Constraints. Mathematical Methods inthe Applied Scinces, 1997, 20(13):1135–1162.
[83] Heyden A. A Common Framework for Multiple View Tensors. in: ECCV’98: Proceedings ofthe 5th European Conference on Computer Vision-Volume I, London, UK: Springer-Verlag, 1998,3–19.
[84] Hartley R I. Computation of the Quadrifocal Tensor. in: ECCV’98: Proceedings of the 5thEuropean Conference on Computer Vision-Volume I, London, UK: Springer-Verlag, 1998, 20–35.
[85] Hartley R I. Chirality. International Journal of Computer Vision, 1998, 26(1):41–61.
[86] Werner T, Pajdla T, Hlava′cˇV. Oriented Projective Reconstruction. in: Gengler M, Prinz M, Schus-ter E, editors, Pattern Recognition and Medical Computer Vision: 22-nd Workshop of the AustrianAssociation for Pattern Recognition (O¨AGM/IAPR), Wien, Austria: O¨sterreichische ComputerGesselschaft, May 14–15, 1998, 245–254.
[87] Laveau S, Faugeras O D. Oriented Projective Geometry for Computer Vision. in: ECCV’96: Pro-ceedings of the 4th European Conference on Computer Vision-Volume I, London, UK: Springer-Verlag, 1996, 147–156.
[88] Chum O, Werner T, Pajdla T. Joint Orientation of Epipoles. in: Harvey R, editor, BMVC 2003:Proceedings of the 14th British Machine Vision Conference, London, UK: BMVA, September,2003, BMVA, 73–82.
[89] Chum O, Werner T, Matas J. Epipolar Geometry Estimation via RANSAC Benefits from theOriented Epipolar Constraint. in: Josef Kittler M N, editor, Proceedings of ICPR 2004 17thInternational Conference on Pattern Recognition, 10662 Los Vaqueros Circle, P.O.Box 3014, CA90720-1314, Los Alamitos, USA: IEEE Computer Society, August, 2004, IEEE, 112–115.
[90] Chojnacki W, Brooks M J, Hengel A, et al. Revisiting Hartley’s Normalized Eight-Point Algo-rithm. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(9):1172–1177.
[91] Wu F C, Hu Z Y, Duan F Q. 8-Point Algorithm Revisited: Factorized 8-Point Algorithm. in: ICCV’05: Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV’05)Volume 1, Washington, DC, USA: IEEE Computer Society, 2005, 488–494.
[92] Torr P, Fitzgibbon A. Invariant Fitting of Two View Geometry. IEEE Transactions on PatternAnalysis and Machine Intelligence, 2004, 26(5):648–650.
[93] Chum O, Matas J, Kittler J. Locally optimized RANSAC. in: G. Goos J v L, editor, DAGM2003: Proceedings of the 25th DAGM Symposium, Heidelberger Platz 3, 14197, Berlin, Germany:Springer-Verlag, September, 2003, 236–243.
[94] Chum O, Matas J, Obdrzˇa′lek Sˇ. Enhancing RANSAC by Generalized Model Optimization. in:Hong K S, Zhang Z, editors, Proc. of the Asian Conference on Computer Vision (ACCV), Seoul,Korea South: Asian Federation of Computer Vision Societies, January, 2004, 812–817.
[95] Matas J, Chum O. Randomized RANSAC with Td,d test. Image and Vision Computing, 2004,22:837–842.
[96]陈付幸,王润生.基于预检验的快速随机抽样一致性算法.软件学报, 2005, 16(08):1431–1437.
[97] Niste′r D. Preemptive RANSAC for live structure and motion estimation. Machine Vision andApplications, 2005, 16(5):321–329.
[98] Capel D P. An Effective Bail-out Test for RANSAC Consensus Scoring. in: Proc. British MachineVision Conf., 2005.
[99] Torr P H S. Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Mani-fold Fitting. International Journal of Computer Vision, 2002, 50(1):35–61.
[100] Torr P H, Davidson C. IMPSAC: Synthesis of Importance Sampling and Random Sample Con-sensus. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(3):354–364.
[101]陈付幸,王润生.基础矩阵估计的聚类分析算法.计算机辅助设计与图形学学报, 2005,17(10):2251–2256.
[102] Brandt S S. Maximum Likelihood Robust Regression by Mixture Models. Journal of MathematicalImaging and Vision, 2006, 25:25–48.
[103] Rousseeuw P J, Leroy A M. Robust regression and outlier detection. New York, NY, USA: JohnWiley & Sons, Inc., 1987.
[104] Triggs B. Matching constraints and the joint image. in: Grimson E, editor, ICCV’95: Proceedingsof the Fifth International Conference on Computer Vision, Washington, DC, USA: IEEE ComputerSociety, 1995, 338–343.
[105] Dempster A P, Laird N M, Rubin D B. Maximum Likelihood from Incomplete Data via the EMAlgorithm. Journal of the Royal Statistical Society. Series B (Methodological), 1977, 39(1):1–38.
[106] Vapnik V N. The Nature of Statistical Learning Theory. New York, NY, USA: Springer-VerlagNew York, Inc., 1995.
[107] Biernacki C, Celeux G, Govaert G. Choosing starting values for the EM algorithm for gettingthe highest likelihood in multivariate Gaussian mixture models. Computational Statistics & DataAnalysis, 2003, 41(3-4):561–575.
[108] Tordoff B J, Murray D W. Guided-MLESAC: Faster Image Transform Estimation by Using Match-ing Priors. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(10):1523–1535.
[109] Triggs B, McLauchlan P, Hartley R, et al. Bundle Adjustment– A Modern Synthesis. in: Triggs B,Zisserman A, Szeliski R, editors, Vision Algorithms: Theory and Practice, International Workshopon Vision Algorithms, LNCS, pages 298–375. Springer Verlag, 2000.
[110] Wiberg T. Computation of Principal Components when Data are Missing. in: Second Symposiumof Computational Statistics, 1976, 229-326.
[111] Hung Y S, Tang W K. Projective Reconstruction from Multiple Views with Minimization of 2DReprojection Error. International Journal of Computer Vision, 2006, 66(3):305–317.
[112] Svoboda T, Martinec D, Pajdla T. A Convenient Multi-Camera Self-Calibration for Virtual Envi-ronments. PRESENCE: Teleoperators and Virtual Environments, 2005, 14(4):407–422.
[113] Lourakis M, Argyros A. The Design and Implementation of a Generic Sparse Bundle AdjustmentSoftware Package Based on the Levenberg-Marquardt Algorithm. Technical Report 340, Instituteof Computer Science - FORTH, Heraklion, Crete, Greece, Aug., 2004. http://www.ics.forth.gr/～lourakis/sba.
[114] Agapito L, Hayman E, Reid I. Self-Calibration of Rotating and Zooming Cameras. InternationalJournal of Computer Vision, 2002, 47(1-3):287–287.
[115] Chum O, Pajdla T, Sturm P. The geometric error for homographies. Computer Vision and ImageUnderstanding, 2005, 97(1):86–102.
[116] Pollefeys M, Gool L V. Stratified Self-Calibration with the Modulus Constraint. IEEE Transactionson Pattern Analysis and Machine Intelligence, 1999, 21(8):707–724.
[117] Pollefeys M, Verbiest F, Gool L J V. Surviving Dominant Planes in Uncalibrated Structure andMotion Recovery. in: ECCV’02: Proceedings of the 7th European Conference on ComputerVision, London, UK: Springer-Verlag, 2002, 837–851.
[118] Ferrari V, Tuytelaars T, Gool L V. Wide-baseline muliple-view Correspondences. in: IEEE Com-puter Society Conference on Computer Vision and Pattern Recognition, Madison, USA, June,2003.
[119] Shafique K, Shah M. A Non-Iterative Greedy Algorithm for Multi-frame Point Correspondence.IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(1):1–15.
[120] Levi N, Werman M. The Viewing Graph. in: IEEE Computer Society Conference on ComputerVision and Pattern Recognition, 2003, 518-522.
[121] Hartley R, Kahl F. Critical Configurations for Projective Reconstruction from Multiple Views.International Journal of Computer Vision, 2007, 71(1):5–47.
[122] Cormen T H, Leiserson C E, Rivest R L, et al. Introduction to Algorithms, Second ed. Cambridge,MA, USA: MIT Press, 2001.
[123] Martinec D, Pajdla T. 3D Reconstruction by Gluing Pair-Wise Euclidean Reconstructions, or”How to Achieve a Good Reconstruction from Bad Images”. in: Third International Symposiumon 3D Data Processing, Visualization, and Transmission, Chapel Hill, NC, USA, 2006, 25-32.
[124] Kahl F. Multiple View Geometry and the L∞-Norm. in: International Conference on ComputerVision, Beijing, China, 2005, 1002–1009.
[125] Vidal R, Ma Y, Soatto S, et al. Two-View Multibody Structure from Motion. Int. J. Comput.Vision, 2006, 68(1):7–25.
[126] Sheikh Y, Gritai A, Shah M. On the Spacetime Geometry of Galilean Cameras. in: IEEE ComputerSociety Conference on Computer Vision and Pattern Recognition, 2007.
[127] Sinha S, Frahm J M, Pollefeys M, et al. Feature Tracking and Matching in Video Using Pro-grammable Graphics Hardware. Machine Vision and Application, 2007.
[128] Mordohai P, Frahm J M, Akbarzadeh A, et al. Real-Time Video-Based Reconstruction of UrbanEnvironments. in: 3D Virtual Reconstruction and Visualization of Complex Architectures, July,2007.
[129] Martinec D, Pajdla T. Robust Rotation and Translation Estimation in Multiview Reconstruction.in: IEEE Computer Society Conference on Computer Vision and Pattern Recognition, Minneapo-lis, MN, USA, 2007.
[130] Bocquillon B, Bartoli A, Gurdjos P, et al. On Constant Focal Length Self-Calibration From Mul-tiple Views. in: IEEE Conference on Computer Vision and Pattern Recognition, 2007.
[131] Chandraker M, Agarwal S, Kahl F, et al. Autocalibration via Rank-Constrained Estimation of theAbsolute Quadric. in: IEEE Conference on Computer Vision and Pattern Recognition, 2007.
[132] Bilmes J. A Gentle Tutorial on the EM Algorithm and its Application to Parameter Estimation forGaussian Mixture and Hidden Markov Models, 1997. citeseer.ist.psu.edu/bilmes98gentle.html.
[133] Redner R, Walker H. Mixture Densities, Maximum Likelihood and the EM Algorithm. SIAMReview, 1984, 26(2):195–239.
[134] Minka T. Expectation-Maximization as lower bound maximization, 1998. citeseer.ist.psu.edu/minka98expectationmaximization.html.
[135] Gelman A, Carlin J B, Stern H S, et al. Bayesian Data Analysis, Second ed. Chapman & Hall/CRC,July, 2003.