臺灣博碩士論文加值系統

在本篇論文中，我們提出一個利用投影機-相機系統以量測物體三維形貌的演算法。為了達到此目的，相機與投影機的特性需要透過校正而得，以及利用結構光的技術來獲取投影機像素與相機像素之間的對應關係。最後，物體的三維形貌則是利用極線幾何來建構。

In this thesis, we propose a 3D point cloud construction algorithm via using projector-camera system. In order to achieve this purpose, the camera and projector property should be accurately estimated by using calibration algorithm. The relationship between camera pixel and projector pixel can be linked by structure light technique. Finally, the object shape can be reconstructed in the form of a point cloud by considering the epipolar geometry.

Abstract-Chinese i
Abstract-English ii
Acknowledgement iii
Contents iv
1 Introduction 1
2 Related Work 3
2.1 Camera Model . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 The coordinate transformation from world to camera . 4
2.1.2 The coordinate transformation from camera to image 4
2.2 Camera Calibration . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.1 Calibration with 3D reference object . . . . . . . . . . 8
2.2.2 Calibration with 2D object . . . . . . . . . . . . . . . 12
2.3 Camera Distortion Model . . . . . . . . . . . . . . . . . . . . 17
3 Projector Calibration 21
3.1 Pre-process . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Determine the image plane of projector and its coordinate . . 26
3.3 Initial guess of intrinsic parameter . . . . . . . . . . . . . . . 29
3.4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 Point Cloud Generation 33
4.1 Structured Light . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.1.1 Binary code . . . . . . . . . . . . . . . . . . . . . . . . 34
4.1.2 Gray code . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.3 n-ary code . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.1.4 De Bruijn sequence . . . . . . . . . . . . . . . . . . . . 36
4.2 Multiple View Geometry . . . . . . . . . . . . . . . . . . . . . 37
4.2.1 Fundamental matrix . . . . . . . . . . . . . . . . . . . 37
4.2.2 Essential matrix . . . . . . . . . . . . . . . . . . . . . 41
4.2.3 Depth information . . . . . . . . . . . . . . . . . . . . 42
5 Experimental Results 45
5.1 Equipment Setup . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.2 Calibration Result . . . . . . . . . . . . . . . . . . . . . . . . 45
5.3 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4 Reconstruction Results . . . . . . . . . . . . . . . . . . . . . . 55
6 Conclusion 61
A The soluion of projector centre derived in CH 3.1 67

[1] R. Hartley and A. Zisserman, "Multiple view geometry in computer vision," Robotica 23, 271-271 (2005).
[2] O. Faugeras, Three-dimensional computer vision: a geometric viewpoint(MIT press, 1993).
[3] Z. Zhang, "Camera calibration,".
[4] Z. Zhang, "A flexible new technique for camera calibration," IEEE Transactions on pattern analysis and machine intelligence 22, 1330-1334 (2000).
[5] Z. Zhang, "Flexible camera calibration by viewing a plane from un-
known orientations," in "Computer Vision, 1999. The Proceedings of the Seventh IEEE International Conference on", vol. 1 (Ieee, 1999), vol. 1, pp. 666-673.
[6] P. F. Sturm and S. J. Maybank, "On plane-based camera calibration: A general algorithm, singularities, applications," in "Computer Vision and Pattern Recognition, 1999. IEEE Computer Society Conference
on.", , vol. 1 (IEEE, 1999), vol. 1, pp. 432-437
[7] G. Falcao, N. Hurtos, J. Massich, and D. Fo, "Projector-camera calibration toolbox," Erasumus Mundus Masters in Vision and Robotics (2009).
[8] G. Falcao, N. Hurtos, and J. Massich, "Plane-based calibration of a projector-camera system," VIBOT master 9, 1-12 (2008).
[9] T. Okatani and K. Deguchi, "Autocalibration of a projector-camera system," IEEE transactions on pattern analysis and machine intelligence 27, 1845-1855 (2005).
[10] Q. Hu, P. S. Huang, Q. Fu, and F.-P. Chiang, "Calibration of a three-dimensional shape measurement system," Optical Engineering 42, 487-493 (2003).
[11] S. Zhang and P. S. Huang, "Novel method for structured light system calibration," Optical Engineering 45, 083601-083601 (2006).
[12] R. J. Valkenburg and A. M. McIvor, "Accurate 3d measurement using a structured light system," Image and Vision Computing 16, 99-110 (1998).
[13] J. L. Posdamer and M. Altschuler, "Surface measurement by space-encoded projected beam systems," Computer graphics and image processing 18, 1-17 (1982).
[14] M. D. Altschuler, K. Bae, B. R. Altschuler, J. T. Dijak, L. A. Tamburino, and B. Woolford, "Robot vision by encoded light beams," in "Three-dimensional machine vision," (Springer, 1987), pp. 97-149.
[15] H. Fredricksen, "A survey of full length nonlinear shift register cycle algorithms," SIAM review 24, 195-221 (1982).
[16] Y.-C. Hsieh, "A note on the structured light of three-dimensional imaging systems," Pattern recognition letters 19, 315-318 (1998).
[17] Y.-C. Hsieh, "Decoding structured light patterns for three-dimensional imaging systems," Pattern Recognition 34, 343-349 (2001).
[18] R. Tsai, "A versatile camera calibration technique for high-accuracy 3d machine vision metrology using off-the-shelf tv cameras and lenses," IEEE Journal on Robotics and Automation 3, 323-344 (1987).
[19] C. Harris and M. Stephens, "A combined corner and edge detector." in "Alvey vision conference", vol. 15 (Manchester, UK, 1988), vol. 15, pp. 10-5244.
[20] Y. Abdel-Aziz, "Karara. hm (1971) direct linear transformation from comparator coordinates into object-space coordinates in close-range photogrammetry," in "Proceedings ASP/VI Symp. On Close-Range Photogrammetry," (1971), pp. 1-17.
[21] O. D. Faugeras and G. Toscani, "The calibration problem for stereo," in "Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition", vol. 86 (1986), vol. 86, pp. 15-20.
[22] J. J. More, "The levenberg-marquardt algorithm: implementation and theory," in "Numerical analysis," (Springer, 1978), pp. 105-116.
[23] C. McGlone, E. Mikhail, and J. Bethel, "Manual of photogrammetry," (1980).
[24] J. Heikkila and O. Silven, "A four-step camera calibration procedure with implicit image correction," in "Computer Vision and Pattern Recognition, 1997. Proceedings., 1997 IEEE Computer Society Conference on," (IEEE, 1997), pp. 1106-1112.
[25] J.-Y. Bouguet, "Camera calibration toolbox for matlab," (2004).
[26] J. Salvi, J. Pages, and J. Batlle, "Pattern codication strategies in structured light systems," Pattern recognition 37, 827-849 (2004).
[27] J. Geng, "Structured-light 3d surface imaging: a tutorial," Advances in Optics and Photonics 3, 128-160 (2011).
[28] S. Inokuchi, "Range-imaging system for 3d object recognition," in "Proc. of 7th International Conference on Pattern Recognition, 1984," (1984).
[29] C. Rocchini, P. Cignoni, C. Montani, P. Pingi, and R. Scopigno, "A low cost 3d scanner based on structured light," in "Computer Graphics Forum," , vol. 20 (Wiley Online Library, 2001), vol. 20, pp. 299-308.
[30] T. Helleseth, De Bruijn Sequence (Springer US, Boston, MA, 2011), pp. 315-316.
[31] H. C. Longuet-Higgins, "A computer algorithm for reconstructing a scene from two projections," Nature 293, 133{135 (1981).
[32] R. I. Hartley, "In defense of the eight-point algorithm," IEEE Transactions on pattern analysis and machine intelligence 19, 580-593 (1997).