基于视觉图像的三维重构的研究与实现
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摘要
计算机视觉的目标是通过感知的图像理解世界中的各种物体。需要理解的物体的属性信息众多,其中最重要的信息是物体的整体三维结构,所以基于视觉图像的三维重构自从计算机视觉的诞生以来就成为计算机视觉研究的热点和重点。经过将近三十年的研究,此问题已经得到部分解决,并促进了计算机视觉一门分支—计算机多视图几何的诞生。基于视觉图像的三维重构涉及到四种关键技术,包括摄像机标定、特征提取和匹配、运动估计和结构计算。论文从已有的研究成果的基础上,做了以下五个方面的工作:
(1)为了克服传统优化算法的缺点,提高摄像机标定的精度,第3章首次将量子粒子群优化算法应用到摄像机标定中。首先,该方法运用传统的线性方法获得初始值,然后使用QPSO优化初始值,得到一个比较优秀的值。实验数据表明,基于QPSO的摄像机标定的平均反投影误差小于一个像素,是一种可行的方法,且与智能优化算法PSO相比,基于QPSO的摄像机标定具有更小的误差。
(2)论文指出如果两个平面间存在四组点对应,则这两个平面的笛卡尔坐标系之间存在一个非奇异线性变换,即平面单应。这就是射影几何中著名的莫比乌斯定理。2.5节从射影几何的基本定义出发,严格证明了莫比乌斯定理,并给出了计算平面单应的方法。
(3)运动估计是基于视觉图像的三维重构的核心问题,所谓的运动估计就是从拍摄得到的多幅图像中计算出摄像机之间相对位置的过程。Hartley首次给出了从本质矩阵恢复运动的一种估计方法。第5章对该方法进行了深入的研究,首次对Hartley方法提出了一种简单易理解的证明过程。
(4)一般的三维重建系统利用角点等作为特征点进行匹配,这些匹配容易出现较高的错误匹配率。为提高匹配的准确度,第7章构建的实验系统用尺度空间中不变点作为特征点,使用SIFT算法提取和匹配这些点。实验效果显示使用该方法是有效的,具有一定的应用价值。
(5)第4章提出了一种直观且简单的不变特征点提取的统一思想框架,统一了SIFT、SURF以及HARRI等特征点提取算法,指明了不变特征点提取的研究方向。
The goal of Computer Vision is to make decisions about all kinds of objects in the world from the sensed images. These images fulfill numerous information about their properties in which the three dimentional structure is the most noteworthy, so Three-Dimensional Reconstruction from Perspective Views is an important and hot point since the birth of computer vision. The research topic has been partly resolved well and brought a new decipline - multiply views geometry - of Computer Vision. There are just four key technologies in respect to this research topic, including camera calibration, feature extraction and matching, motion estimation, and structure computation. Based on the previous research, this thesis has done some work followed from five aspects:
(1)The Quantum-Behaved Particle Swarm Optimization has been firstly applied to camera calibration, in chapter 3, in order to improve the accuracy and overcome the drawbacks of traditional optimization algorithm. Firstly, this method uses the traditional linear method to achieve the initial value, and then optimizes the initial value with QPSO. Experimental data shows that camera calibration based on QPSO has less average back-projection error than a pixel and is an effective and reliable method. Experiment also shows that this approach has lower error than the one based on PSO.
(2)The thesis points out that if there are four corresponding pairs of points between two planes, there will be existing one non-singular linear transformation, ie homography. This is the famous Mobius theorem in projective geometry. Section 2.5 proves the Mobius theorem from the basic definition of projective geometry and gives the homography calculation method.
(3)Motion Estimation is the core issue in Three-Dimensional Reconstruction from Perspective Views, which is to calculate the relative positions among cameras from multiple images taken of one object from different viewpoints. One outstanging method has firstly appeared in Hartley[27][28] for Estimating Motion from Essential Matrix. Chapter 5 does some deep work on this method and brings out a new and easy proof to it.
(4)The general systems of Three-Dimensional Reconstruction often use corner as feature points for matching, but the rate of matching is prone to be higher. To improve the accuracy of matching, Chapter 7 constructs one experimental system which uses extreme points in scale space as feature points and SIFT to extract and match these points. The experiment demonstrates the feasibility and value of this method.
(5)The fourth chapter addresses one instinctive and simple unified framework which unifies a lot of algorithms, such as SIFT, SURF and HARRI, and directs the reseach for extracting the invariant feature points.
(1)为了克服传统优化算法的缺点,提高摄像机标定的精度,第3章首次将量子粒子群优化算法应用到摄像机标定中。首先,该方法运用传统的线性方法获得初始值,然后使用QPSO优化初始值,得到一个比较优秀的值。实验数据表明,基于QPSO的摄像机标定的平均反投影误差小于一个像素,是一种可行的方法,且与智能优化算法PSO相比,基于QPSO的摄像机标定具有更小的误差。
(2)论文指出如果两个平面间存在四组点对应,则这两个平面的笛卡尔坐标系之间存在一个非奇异线性变换,即平面单应。这就是射影几何中著名的莫比乌斯定理。2.5节从射影几何的基本定义出发,严格证明了莫比乌斯定理,并给出了计算平面单应的方法。
(3)运动估计是基于视觉图像的三维重构的核心问题,所谓的运动估计就是从拍摄得到的多幅图像中计算出摄像机之间相对位置的过程。Hartley首次给出了从本质矩阵恢复运动的一种估计方法。第5章对该方法进行了深入的研究,首次对Hartley方法提出了一种简单易理解的证明过程。
(4)一般的三维重建系统利用角点等作为特征点进行匹配,这些匹配容易出现较高的错误匹配率。为提高匹配的准确度,第7章构建的实验系统用尺度空间中不变点作为特征点,使用SIFT算法提取和匹配这些点。实验效果显示使用该方法是有效的,具有一定的应用价值。
(5)第4章提出了一种直观且简单的不变特征点提取的统一思想框架,统一了SIFT、SURF以及HARRI等特征点提取算法,指明了不变特征点提取的研究方向。
The goal of Computer Vision is to make decisions about all kinds of objects in the world from the sensed images. These images fulfill numerous information about their properties in which the three dimentional structure is the most noteworthy, so Three-Dimensional Reconstruction from Perspective Views is an important and hot point since the birth of computer vision. The research topic has been partly resolved well and brought a new decipline - multiply views geometry - of Computer Vision. There are just four key technologies in respect to this research topic, including camera calibration, feature extraction and matching, motion estimation, and structure computation. Based on the previous research, this thesis has done some work followed from five aspects:
(1)The Quantum-Behaved Particle Swarm Optimization has been firstly applied to camera calibration, in chapter 3, in order to improve the accuracy and overcome the drawbacks of traditional optimization algorithm. Firstly, this method uses the traditional linear method to achieve the initial value, and then optimizes the initial value with QPSO. Experimental data shows that camera calibration based on QPSO has less average back-projection error than a pixel and is an effective and reliable method. Experiment also shows that this approach has lower error than the one based on PSO.
(2)The thesis points out that if there are four corresponding pairs of points between two planes, there will be existing one non-singular linear transformation, ie homography. This is the famous Mobius theorem in projective geometry. Section 2.5 proves the Mobius theorem from the basic definition of projective geometry and gives the homography calculation method.
(3)Motion Estimation is the core issue in Three-Dimensional Reconstruction from Perspective Views, which is to calculate the relative positions among cameras from multiple images taken of one object from different viewpoints. One outstanging method has firstly appeared in Hartley[27][28] for Estimating Motion from Essential Matrix. Chapter 5 does some deep work on this method and brings out a new and easy proof to it.
(4)The general systems of Three-Dimensional Reconstruction often use corner as feature points for matching, but the rate of matching is prone to be higher. To improve the accuracy of matching, Chapter 7 constructs one experimental system which uses extreme points in scale space as feature points and SIFT to extract and match these points. The experiment demonstrates the feasibility and value of this method.
(5)The fourth chapter addresses one instinctive and simple unified framework which unifies a lot of algorithms, such as SIFT, SURF and HARRI, and directs the reseach for extracting the invariant feature points.
引文
1. Abdel-Aziz Y I, Karara HM. Direct linear transformation into object space coordinates in Close-Range Photogrammetry[C]. in Proceedings Symposium on Close-Range Photogrammetry,1971:1-8
2. R Y Tsai. An efficient and accurate camera calibration technique for 3D machine vision[C] . Proceedings of Computer Vision and PaRem Recognition,1986:164-374
3. Zhang Z.A. Flexible New Technique for Camera Calibration[J].IEEE Trans on Pattern Analysis and MachineIntelligence,2000,22(11):1330-1334
4. Q. Faugeras, T . Luong , S . Maybank. Camera Self-Calibration : Theory and Experiments[C] .In Proceedings of the 7th Eurpean Conference on Computer Vision,Lecture Notes in Computer Science,1992,01(588):32l-334
5. R. Hartley. Euclidean reconstruction and invariants from multiple images[C]. In Proceedings of the International Conference on Pattem Recognition,1996:339-343
6. B Triggs.Auto-calibration and the absolute quadric[C]. In Proceedings of the Conference on Computer Vision and Pattem Recognition, 1997:609-614
7. M. Pollefeys,LV.Gool, A.Oosterlinck. The modulus constraint:a new constraint for self-calibration[C]. In Proceedings of International Conference of Pauern Recognition,1996:349-353
8. R. I. Hartley. Projective reconstruction from line correspondence[C]. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, 1994.
9. A. Zisserman, J. Mundy, D. Forsyth, J. Liu, N. Pillow, C. Rothwell, and S. Utcke. Class-based grouping in perspective images[C]. In Proc. International Conference on Computer Vision, 1995.
10. M. Armstrong, A. Zisserman, R. Hartley. Self-calibration from image triplets[C]. In Proc. European Conference on Computer Vision, 1996:3-16
11. H. P. Moravec. Towards Automatic Visual Obstacle Avoidance[C]. Proc. 5th International Joint Conference on Artificial Intelligence, 1997:584
12. H. P. Moravec. Visual Mapping by a Robot Rover[C]. International Joint Conference on Artificial Intelligence, 1979:598-600
13. C. Harris , M. Stephens. A Combined Corner and Edge Detector[C]. Proc. Alvey Vision Conf., 1988:147-151, 1988
14. M Smith,J.M.Brady. SUSAN-a new approach to low level image processing[J]. International Journal ofComputer Vision,1997,23(1):45-78
15. J. Canny. A Computational Appruach To Edge Detection[J]. IEEE Trans. Pattern Analysis and machine Intelligence, 1986,8:679-714
16. Z. Zhang, R. Deriche, O. Faugeras, Q.T. Luong. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry[J]. Artificial Intelligence, 1995,78:87-119.
17. C. Schmid, R. Mohr. Local grayvalue invariants for image retrieval[J]. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1997,19(5):530-534
18. D.G. Lowe,.Object recognition from loc-al scale invariant features[C].In International Conference on Computer Vision, 1999:1150-1157
19. D.G. Lowe. Distinctive image features from scale invariant key-points[J].International Journal of Computer Vision,2004,60(2):91-110
20. Y. Ke , R. Sukthankar. PCA-SIFT: A More Distinctive Representation for Local Image Descriptors[C]. Proc. Conf. Computer Vision and Pattern Recognition, 2004 :511-517
21. H, Bay, T. Tuytelaars, L. Van Gool. SURF: Speeded Up Robust Features[C]. 9th European Conference on Computer Vision,2006
22. H. Nagel. Image sequences - ten (octal) years- from phenomenology towards a theoretical foundation[J]. International Journal of Pattern Recognition and Artificial Intelligence,1988,2(3):459-483
23. J. K. Aggarwal, N. Nandhakumar. On the computation of motion from sequences of images—a review[C]. Proc. IEEE, 1988,76(8):917–935
24. T.S. Huang, A.N. Netravali. Motion and structure from feature correspondences: A review[C]. Proc. IEEE, 1994,82(2):252–268
25. Ullman,S.(1979),The Interpretation of Visual Motion[M],MIT Press
26. H. C. Longuet-Higgins. A computer algorithm for reconstructing a scene from two projections[J]. Nature, 1981:293
27. Richard I. Hartley. Estimation of relative camera positions for uncalibrated cameras[C]. Proceedings of European Conference on Computer Vision,1992
28. R. Harley, R. Gupta, T. Chang. Stereo from Uncalibrated cameras[C]. Proc. IEEE Conf. Comp.Vision and Patt. Recog.,1992:761-764
29. Olivier D. Faugeras . What can be seen in three dimensions with an uncalibrated stereo rig?[C]. Proceedings of European Conference on Computer Vision,1992
30. J. W. Roach , J. K. Aggarwal. Determining the movement of objects from a sequence of images[J]. IEEE Trans. Patt. And Machine Intell., 1980,2(6) :554-562
31. Juyang Weng.Optimal Motion and Structure Estimation[J]. I IEEE Trans. Patt. And Machine Intell. 1993,15(9)
32. Zhang. Motion and Structure From Two Perspective Views: From Essential Parameters to Euclidean Motion Via Fundamental Matrix[R] INRIA Research Report No.2910, 1996
33. Martin A. Fischler ,Robert C. Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography[J]. Communications of the ACM ,1981,24(6): 726– 740
34. Carlo Tomasi, Takeo Kanade. Detection and Tracking of Point Features. Carnegie Mellon University[R]. Technical Report CMU-CS-91-132, 1991
35. Paul Beardsley ,Paul Beardsley,et al. 3D Model Acquisition from Extended Image Sequences [C]. ECCV 1996(2):683-695.
36. Paul E. Debevec, Camillo J. Taylor, and Jitendra Malik. Modeling and Rendering Architecture from Photographs[C]. In SIGGRAPH '96, 1996(30):11-20.
37. Heung-yeung Shum , Mei Han , Richard Szeliski. Interactive Construction of 3D Models from Panoramic Mosaics[C]. CVPR,1998:234-240.
38. Olivier Faugeras ,et al. 3-D Reconstruction of Urban Scenes from Sequences of Images[C]. Computer vision and Image Understanding. 1998,69(3):292-309.
39. Juyang Weng. Camera Calibration with Distortion Models and Accuracy Evaluation[J]. ieee transactions on patern analysis and machine intelligence, 1992,14(10)
40. D. C. Brown. Decentering distortion of lenses[J]. Photogrammetric Eng. Remote Sensing, 1966:444-462.
41. W. Faig. Calibration of close-range photogrammetric systems: Mathematical formulation[J]. Photogrammetric Eng. Remote Sensing, 1975, 41(12): 1479-1486
42. Manual of Photogrammetry[M]. Amer. Soc. Photogrammetry, 1980, 4th ed
43. J.J. More, The Levenberg-Marquardt Algorithm: Implementation and Theory[R].Lecture Notes in Mathematics, 1978
44. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision[J]. Cambridge University Press, 2000
45. Kennedy J, Eberhart R C. Particle Swarm Optimization [C]. Proceedings of the IEEE International Conference on Neural Networks.1995:1945-1948
46. Jun Sun, Bin Feng, Wenbo Xu. Particle Swarm Optimization [C].IEEE Proceedings of Congress on Evolutionary Computation.2004:325-331
47. Jun Sun, Wenbo Xu, Bin Feng. A global search strategy of quantum-behaved particle swarm optimization [C].Proceedings of IEEE Conference on Cybernetics and Intelligent Systems.2004:111-116
48. Jun Sun, Wenbo Xu, Jing Liu. Parameter selection of quantum-behaved particle swarm optimization[R].Springer Berlin/Heidelberg.2005,3162:543-552
49. http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node21.html
50. T.S. Huang , O.D. Faugeras. Some properties of the E matrix in two-view motion estimation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989,11(12):1310–1312
51. R.Hartley. In defense ofthe 8-point algorithm[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(6):580-593
52. F. C. Wu, Z. Y. Hu, F. Q. Duan. 8-Point Algorithm Revisited: Factorized 8-Point Algorithm[C]. Proceedings of the Tenth IEEE International Conference on Computer Vision,2005
53. Olivier Faugeras. Three-Dimensional Computer Vision: a Geometric Viewpoint[M]. MIT Press, 1993
54. Z. Zhang. A new multistage approach to motion and structure estimation: From essential parameters to euclidean motion via fundamental matrix[R].Research Report 2910, INRIA Sophia-Antipolis, 1996
55. P. J. Green and R. Sibson. Computing Dirichlet tessellations in the plane[J]. Computer Journal, 1978,21(2):168-173
56. Dani Lischinski. Incremental Delaunay triangulation[M]. Academic Press, Boston, MA , 1994,Graphics Gems IV: 47–59
57. http://www.cs.cmu.edu/afs/andrew/scs/cs/15-463/2001/pub/src/a2/quadedge.html
58.许晓伟,王知衍,张艳青,梁英宏,曹晓叶.视觉图像三维重构计算一般性框架研究.计算机科学, 2008, 35(18):208-212
59.章权兵,王海贤,韦穗.线性多视图重构的新算法.中国图象图形学报, 2004, 8(10):1210-1215
2. R Y Tsai. An efficient and accurate camera calibration technique for 3D machine vision[C] . Proceedings of Computer Vision and PaRem Recognition,1986:164-374
3. Zhang Z.A. Flexible New Technique for Camera Calibration[J].IEEE Trans on Pattern Analysis and MachineIntelligence,2000,22(11):1330-1334
4. Q. Faugeras, T . Luong , S . Maybank. Camera Self-Calibration : Theory and Experiments[C] .In Proceedings of the 7th Eurpean Conference on Computer Vision,Lecture Notes in Computer Science,1992,01(588):32l-334
5. R. Hartley. Euclidean reconstruction and invariants from multiple images[C]. In Proceedings of the International Conference on Pattem Recognition,1996:339-343
6. B Triggs.Auto-calibration and the absolute quadric[C]. In Proceedings of the Conference on Computer Vision and Pattem Recognition, 1997:609-614
7. M. Pollefeys,LV.Gool, A.Oosterlinck. The modulus constraint:a new constraint for self-calibration[C]. In Proceedings of International Conference of Pauern Recognition,1996:349-353
8. R. I. Hartley. Projective reconstruction from line correspondence[C]. In Proc. IEEE Conference on Computer Vision and Pattern Recognition, 1994.
9. A. Zisserman, J. Mundy, D. Forsyth, J. Liu, N. Pillow, C. Rothwell, and S. Utcke. Class-based grouping in perspective images[C]. In Proc. International Conference on Computer Vision, 1995.
10. M. Armstrong, A. Zisserman, R. Hartley. Self-calibration from image triplets[C]. In Proc. European Conference on Computer Vision, 1996:3-16
11. H. P. Moravec. Towards Automatic Visual Obstacle Avoidance[C]. Proc. 5th International Joint Conference on Artificial Intelligence, 1997:584
12. H. P. Moravec. Visual Mapping by a Robot Rover[C]. International Joint Conference on Artificial Intelligence, 1979:598-600
13. C. Harris , M. Stephens. A Combined Corner and Edge Detector[C]. Proc. Alvey Vision Conf., 1988:147-151, 1988
14. M Smith,J.M.Brady. SUSAN-a new approach to low level image processing[J]. International Journal ofComputer Vision,1997,23(1):45-78
15. J. Canny. A Computational Appruach To Edge Detection[J]. IEEE Trans. Pattern Analysis and machine Intelligence, 1986,8:679-714
16. Z. Zhang, R. Deriche, O. Faugeras, Q.T. Luong. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry[J]. Artificial Intelligence, 1995,78:87-119.
17. C. Schmid, R. Mohr. Local grayvalue invariants for image retrieval[J]. IEEE Trans. on Pattern Analysis and Machine Intelligence, 1997,19(5):530-534
18. D.G. Lowe,.Object recognition from loc-al scale invariant features[C].In International Conference on Computer Vision, 1999:1150-1157
19. D.G. Lowe. Distinctive image features from scale invariant key-points[J].International Journal of Computer Vision,2004,60(2):91-110
20. Y. Ke , R. Sukthankar. PCA-SIFT: A More Distinctive Representation for Local Image Descriptors[C]. Proc. Conf. Computer Vision and Pattern Recognition, 2004 :511-517
21. H, Bay, T. Tuytelaars, L. Van Gool. SURF: Speeded Up Robust Features[C]. 9th European Conference on Computer Vision,2006
22. H. Nagel. Image sequences - ten (octal) years- from phenomenology towards a theoretical foundation[J]. International Journal of Pattern Recognition and Artificial Intelligence,1988,2(3):459-483
23. J. K. Aggarwal, N. Nandhakumar. On the computation of motion from sequences of images—a review[C]. Proc. IEEE, 1988,76(8):917–935
24. T.S. Huang, A.N. Netravali. Motion and structure from feature correspondences: A review[C]. Proc. IEEE, 1994,82(2):252–268
25. Ullman,S.(1979),The Interpretation of Visual Motion[M],MIT Press
26. H. C. Longuet-Higgins. A computer algorithm for reconstructing a scene from two projections[J]. Nature, 1981:293
27. Richard I. Hartley. Estimation of relative camera positions for uncalibrated cameras[C]. Proceedings of European Conference on Computer Vision,1992
28. R. Harley, R. Gupta, T. Chang. Stereo from Uncalibrated cameras[C]. Proc. IEEE Conf. Comp.Vision and Patt. Recog.,1992:761-764
29. Olivier D. Faugeras . What can be seen in three dimensions with an uncalibrated stereo rig?[C]. Proceedings of European Conference on Computer Vision,1992
30. J. W. Roach , J. K. Aggarwal. Determining the movement of objects from a sequence of images[J]. IEEE Trans. Patt. And Machine Intell., 1980,2(6) :554-562
31. Juyang Weng.Optimal Motion and Structure Estimation[J]. I IEEE Trans. Patt. And Machine Intell. 1993,15(9)
32. Zhang. Motion and Structure From Two Perspective Views: From Essential Parameters to Euclidean Motion Via Fundamental Matrix[R] INRIA Research Report No.2910, 1996
33. Martin A. Fischler ,Robert C. Bolles. Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography[J]. Communications of the ACM ,1981,24(6): 726– 740
34. Carlo Tomasi, Takeo Kanade. Detection and Tracking of Point Features. Carnegie Mellon University[R]. Technical Report CMU-CS-91-132, 1991
35. Paul Beardsley ,Paul Beardsley,et al. 3D Model Acquisition from Extended Image Sequences [C]. ECCV 1996(2):683-695.
36. Paul E. Debevec, Camillo J. Taylor, and Jitendra Malik. Modeling and Rendering Architecture from Photographs[C]. In SIGGRAPH '96, 1996(30):11-20.
37. Heung-yeung Shum , Mei Han , Richard Szeliski. Interactive Construction of 3D Models from Panoramic Mosaics[C]. CVPR,1998:234-240.
38. Olivier Faugeras ,et al. 3-D Reconstruction of Urban Scenes from Sequences of Images[C]. Computer vision and Image Understanding. 1998,69(3):292-309.
39. Juyang Weng. Camera Calibration with Distortion Models and Accuracy Evaluation[J]. ieee transactions on patern analysis and machine intelligence, 1992,14(10)
40. D. C. Brown. Decentering distortion of lenses[J]. Photogrammetric Eng. Remote Sensing, 1966:444-462.
41. W. Faig. Calibration of close-range photogrammetric systems: Mathematical formulation[J]. Photogrammetric Eng. Remote Sensing, 1975, 41(12): 1479-1486
42. Manual of Photogrammetry[M]. Amer. Soc. Photogrammetry, 1980, 4th ed
43. J.J. More, The Levenberg-Marquardt Algorithm: Implementation and Theory[R].Lecture Notes in Mathematics, 1978
44. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision[J]. Cambridge University Press, 2000
45. Kennedy J, Eberhart R C. Particle Swarm Optimization [C]. Proceedings of the IEEE International Conference on Neural Networks.1995:1945-1948
46. Jun Sun, Bin Feng, Wenbo Xu. Particle Swarm Optimization [C].IEEE Proceedings of Congress on Evolutionary Computation.2004:325-331
47. Jun Sun, Wenbo Xu, Bin Feng. A global search strategy of quantum-behaved particle swarm optimization [C].Proceedings of IEEE Conference on Cybernetics and Intelligent Systems.2004:111-116
48. Jun Sun, Wenbo Xu, Jing Liu. Parameter selection of quantum-behaved particle swarm optimization[R].Springer Berlin/Heidelberg.2005,3162:543-552
49. http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/EPSRC_SSAZ/node21.html
50. T.S. Huang , O.D. Faugeras. Some properties of the E matrix in two-view motion estimation[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1989,11(12):1310–1312
51. R.Hartley. In defense ofthe 8-point algorithm[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 1997, 19(6):580-593
52. F. C. Wu, Z. Y. Hu, F. Q. Duan. 8-Point Algorithm Revisited: Factorized 8-Point Algorithm[C]. Proceedings of the Tenth IEEE International Conference on Computer Vision,2005
53. Olivier Faugeras. Three-Dimensional Computer Vision: a Geometric Viewpoint[M]. MIT Press, 1993
54. Z. Zhang. A new multistage approach to motion and structure estimation: From essential parameters to euclidean motion via fundamental matrix[R].Research Report 2910, INRIA Sophia-Antipolis, 1996
55. P. J. Green and R. Sibson. Computing Dirichlet tessellations in the plane[J]. Computer Journal, 1978,21(2):168-173
56. Dani Lischinski. Incremental Delaunay triangulation[M]. Academic Press, Boston, MA , 1994,Graphics Gems IV: 47–59
57. http://www.cs.cmu.edu/afs/andrew/scs/cs/15-463/2001/pub/src/a2/quadedge.html
58.许晓伟,王知衍,张艳青,梁英宏,曹晓叶.视觉图像三维重构计算一般性框架研究.计算机科学, 2008, 35(18):208-212
59.章权兵,王海贤,韦穗.线性多视图重构的新算法.中国图象图形学报, 2004, 8(10):1210-1215