Abstract

This paper presents a new linear framework to obtain 3D scene reconstruction and camera calibration simultaneously from uncalibrated images using scene geometry. Our strategy uses the constraints of parallelism, coplanarity, colinearity, and orthogonality. These constraints can be obtained in general man-made scenes frequently. This approach can give more stable results with fewer images and allow us to gain the results with only linear operations. In this paper, it is shown that all the geometric constraints used in the previous works performed independently up to now can be implemented easily in the proposed linear method. The study on the situations that cannot be dealt with by the previous approaches is also presented and it is shown that the proposed method being able to handle the cases is more flexible in use. The proposed method uses a stratified approach, in which affine reconstruction is performed first and then metric reconstruction. In this procedure, the additional constraints newly extracted in this paper have an important role for affine reconstruction in practical situations.

© 2013 OSA

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References

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  1. R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses,” IEEE Trans. Robot. Autom.3, 323–344 (1987).
    [CrossRef]
  2. Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell.22, 1330–1334 (2000).
    [CrossRef]
  3. J.-H. Kim and B.-K. Koo, “Convenient calibration method for unsynchronized camera networks using an inaccurate small reference object,” Opt. Express20, 25292–25310 (2012).
    [CrossRef] [PubMed]
  4. M. Pollefeys and L. V. Gool, “Stratified self-calibration with the modulus constraint,” IEEE Trans. Pattern Anal. Mach. Intell.21, 707–724 (1999).
    [CrossRef]
  5. M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
    [CrossRef]
  6. T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
    [CrossRef]
  7. P. Hammarstedt, F. Kahl, and A. Heyden, “Affine reconstruction from translational motion under various auto-calibration constraints,” J. Math. Imaging Vis.24, 245–257 (2006).
    [CrossRef]
  8. L. Agapito, E. Hayman, and I. Reid, “Self-calibration of rotating and zooming cameras,” Int. J. Comput. Vision45, 107–127 (2001).
    [CrossRef]
  9. R. Cipolla, T. Drummond, and D. P. Robertson, “Camera calibration from vanishing points in images of architectural scenes,” in “Proc. British Machine Vision Conferece,” (Nottingham, England, 1999), pp. 382–391.
  10. D. Liebowitz and A. Zisserman, “Combining scene and auto-calibration constraints,” in “Proc. IEEE International Conference on Computer Vision,” (Kerkyra, Greece, 1999), pp. 293–300.
    [CrossRef]
  11. D. Jelinek and C. J. Taylor, “Reconstruction of linearly parameterized models from single images with a camera of unknown focal length,” IEEE Trans. Pattern Anal. Mach. Intell.23, 767–773 (2001).
    [CrossRef]
  12. C. Rother and S. Carlsson, “Linear multi view reconstruction and camera recovery using a reference plane,” Int. J. Comput. Vision49, 117–141 (2002).
    [CrossRef]
  13. M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
    [CrossRef] [PubMed]
  14. E. Grossmann and J. Santos-Victor, “Least-squares 3D reconstruction from one or more views and geometric clues,” Comput. Vis. Image Und.99, 151–174 (2005).
    [CrossRef]
  15. F. C. Wu, F. Q. Duan, and Z. Y. Hu, “An affine invariant of parallelograms and its application to camera calibration and 3D reconstruction,” in “Proc. European Conference on Computer Vision,” (2006), pp. 191–204.
  16. L. G. de la Fraga and O. Schutze, “Direct calibration by fitting of cuboids to a single image using differential evolution,” Int. J. Comput. Vision80, 119–127 (2009).
    [CrossRef]
  17. N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric architecture modeling with a single image,” ACM T. Graphic. (Proc. SIGGRAPH Asia) 28 (2009).
    [CrossRef]
  18. F. Mai, Y. S. Hung, and G. Chesi, “Projective reconstruction of ellipses from multiple images,” Pattern Recogn.43, 545–556 (2010).
    [CrossRef]
  19. K.-Y. K. Wong, G. Zhang, and Z. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process.20, 305–316 (2011).
    [CrossRef]
  20. R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Second Edition (Cambridge University Press, 2003).
  21. Q.-T. Luong and T. Viéville, “Canonical representations for the geometries of multiple perspective views,” Comput. Vis. Image Und.64, 193–229 (1996).
    [CrossRef]
  22. R. Hartley, “In defence of the 8-point algorithm,” in “Proc. International Conference on Computer Vision,” (Sendai, Japan, 1995), pp. 1064–1070.
  23. B. K. P. Horn, H. M. Hilden, and S. Negahdaripour, “Closed form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am5, 1127–1135 (1988).
    [CrossRef]
  24. D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice Hall, 2003).

2012

2011

K.-Y. K. Wong, G. Zhang, and Z. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process.20, 305–316 (2011).
[CrossRef]

2010

F. Mai, Y. S. Hung, and G. Chesi, “Projective reconstruction of ellipses from multiple images,” Pattern Recogn.43, 545–556 (2010).
[CrossRef]

2009

L. G. de la Fraga and O. Schutze, “Direct calibration by fitting of cuboids to a single image using differential evolution,” Int. J. Comput. Vision80, 119–127 (2009).
[CrossRef]

N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric architecture modeling with a single image,” ACM T. Graphic. (Proc. SIGGRAPH Asia) 28 (2009).
[CrossRef]

2006

P. Hammarstedt, F. Kahl, and A. Heyden, “Affine reconstruction from translational motion under various auto-calibration constraints,” J. Math. Imaging Vis.24, 245–257 (2006).
[CrossRef]

2005

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

E. Grossmann and J. Santos-Victor, “Least-squares 3D reconstruction from one or more views and geometric clues,” Comput. Vis. Image Und.99, 151–174 (2005).
[CrossRef]

2004

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

2002

C. Rother and S. Carlsson, “Linear multi view reconstruction and camera recovery using a reference plane,” Int. J. Comput. Vision49, 117–141 (2002).
[CrossRef]

2001

L. Agapito, E. Hayman, and I. Reid, “Self-calibration of rotating and zooming cameras,” Int. J. Comput. Vision45, 107–127 (2001).
[CrossRef]

D. Jelinek and C. J. Taylor, “Reconstruction of linearly parameterized models from single images with a camera of unknown focal length,” IEEE Trans. Pattern Anal. Mach. Intell.23, 767–773 (2001).
[CrossRef]

2000

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell.22, 1330–1334 (2000).
[CrossRef]

1999

M. Pollefeys and L. V. Gool, “Stratified self-calibration with the modulus constraint,” IEEE Trans. Pattern Anal. Mach. Intell.21, 707–724 (1999).
[CrossRef]

1996

T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
[CrossRef]

Q.-T. Luong and T. Viéville, “Canonical representations for the geometries of multiple perspective views,” Comput. Vis. Image Und.64, 193–229 (1996).
[CrossRef]

1988

B. K. P. Horn, H. M. Hilden, and S. Negahdaripour, “Closed form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am5, 1127–1135 (1988).
[CrossRef]

1987

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses,” IEEE Trans. Robot. Autom.3, 323–344 (1987).
[CrossRef]

Agapito, L.

L. Agapito, E. Hayman, and I. Reid, “Self-calibration of rotating and zooming cameras,” Int. J. Comput. Vision45, 107–127 (2001).
[CrossRef]

Boyer, E.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

Carlsson, S.

C. Rother and S. Carlsson, “Linear multi view reconstruction and camera recovery using a reference plane,” Int. J. Comput. Vision49, 117–141 (2002).
[CrossRef]

Chen, Z.

K.-Y. K. Wong, G. Zhang, and Z. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process.20, 305–316 (2011).
[CrossRef]

Cheong, L.-F.

N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric architecture modeling with a single image,” ACM T. Graphic. (Proc. SIGGRAPH Asia) 28 (2009).
[CrossRef]

Chesi, G.

F. Mai, Y. S. Hung, and G. Chesi, “Projective reconstruction of ellipses from multiple images,” Pattern Recogn.43, 545–556 (2010).
[CrossRef]

Cipolla, R.

R. Cipolla, T. Drummond, and D. P. Robertson, “Camera calibration from vanishing points in images of architectural scenes,” in “Proc. British Machine Vision Conferece,” (Nottingham, England, 1999), pp. 382–391.

Cornelis, K.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

de la Fraga, L. G.

L. G. de la Fraga and O. Schutze, “Direct calibration by fitting of cuboids to a single image using differential evolution,” Int. J. Comput. Vision80, 119–127 (2009).
[CrossRef]

Drummond, T.

R. Cipolla, T. Drummond, and D. P. Robertson, “Camera calibration from vanishing points in images of architectural scenes,” in “Proc. British Machine Vision Conferece,” (Nottingham, England, 1999), pp. 382–391.

Duan, F. Q.

F. C. Wu, F. Q. Duan, and Z. Y. Hu, “An affine invariant of parallelograms and its application to camera calibration and 3D reconstruction,” in “Proc. European Conference on Computer Vision,” (2006), pp. 191–204.

Forsyth, D. A.

D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice Hall, 2003).

Gool, L. V.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

M. Pollefeys and L. V. Gool, “Stratified self-calibration with the modulus constraint,” IEEE Trans. Pattern Anal. Mach. Intell.21, 707–724 (1999).
[CrossRef]

T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
[CrossRef]

Grossmann, E.

E. Grossmann and J. Santos-Victor, “Least-squares 3D reconstruction from one or more views and geometric clues,” Comput. Vis. Image Und.99, 151–174 (2005).
[CrossRef]

Hammarstedt, P.

P. Hammarstedt, F. Kahl, and A. Heyden, “Affine reconstruction from translational motion under various auto-calibration constraints,” J. Math. Imaging Vis.24, 245–257 (2006).
[CrossRef]

Hartley, R.

R. Hartley, “In defence of the 8-point algorithm,” in “Proc. International Conference on Computer Vision,” (Sendai, Japan, 1995), pp. 1064–1070.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Second Edition (Cambridge University Press, 2003).

Hayman, E.

L. Agapito, E. Hayman, and I. Reid, “Self-calibration of rotating and zooming cameras,” Int. J. Comput. Vision45, 107–127 (2001).
[CrossRef]

Heyden, A.

P. Hammarstedt, F. Kahl, and A. Heyden, “Affine reconstruction from translational motion under various auto-calibration constraints,” J. Math. Imaging Vis.24, 245–257 (2006).
[CrossRef]

Hilden, H. M.

B. K. P. Horn, H. M. Hilden, and S. Negahdaripour, “Closed form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am5, 1127–1135 (1988).
[CrossRef]

Horn, B. K. P.

B. K. P. Horn, H. M. Hilden, and S. Negahdaripour, “Closed form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am5, 1127–1135 (1988).
[CrossRef]

Hu, Z. Y.

F. C. Wu, F. Q. Duan, and Z. Y. Hu, “An affine invariant of parallelograms and its application to camera calibration and 3D reconstruction,” in “Proc. European Conference on Computer Vision,” (2006), pp. 191–204.

Hung, Y. S.

F. Mai, Y. S. Hung, and G. Chesi, “Projective reconstruction of ellipses from multiple images,” Pattern Recogn.43, 545–556 (2010).
[CrossRef]

Jelinek, D.

D. Jelinek and C. J. Taylor, “Reconstruction of linearly parameterized models from single images with a camera of unknown focal length,” IEEE Trans. Pattern Anal. Mach. Intell.23, 767–773 (2001).
[CrossRef]

Jiang, N.

N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric architecture modeling with a single image,” ACM T. Graphic. (Proc. SIGGRAPH Asia) 28 (2009).
[CrossRef]

Kahl, F.

P. Hammarstedt, F. Kahl, and A. Heyden, “Affine reconstruction from translational motion under various auto-calibration constraints,” J. Math. Imaging Vis.24, 245–257 (2006).
[CrossRef]

Kim, J.-H.

Koch, R.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

Koo, B.-K.

Liebowitz, D.

D. Liebowitz and A. Zisserman, “Combining scene and auto-calibration constraints,” in “Proc. IEEE International Conference on Computer Vision,” (Kerkyra, Greece, 1999), pp. 293–300.
[CrossRef]

Luong, Q.-T.

Q.-T. Luong and T. Viéville, “Canonical representations for the geometries of multiple perspective views,” Comput. Vis. Image Und.64, 193–229 (1996).
[CrossRef]

Mai, F.

F. Mai, Y. S. Hung, and G. Chesi, “Projective reconstruction of ellipses from multiple images,” Pattern Recogn.43, 545–556 (2010).
[CrossRef]

Moons, T.

T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
[CrossRef]

Negahdaripour, S.

B. K. P. Horn, H. M. Hilden, and S. Negahdaripour, “Closed form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am5, 1127–1135 (1988).
[CrossRef]

Pauwels, E.

T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
[CrossRef]

Pollefeys, M.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

M. Pollefeys and L. V. Gool, “Stratified self-calibration with the modulus constraint,” IEEE Trans. Pattern Anal. Mach. Intell.21, 707–724 (1999).
[CrossRef]

Ponce, J.

D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice Hall, 2003).

Proesmans, M.

T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
[CrossRef]

Reid, I.

L. Agapito, E. Hayman, and I. Reid, “Self-calibration of rotating and zooming cameras,” Int. J. Comput. Vision45, 107–127 (2001).
[CrossRef]

Robertson, D. P.

R. Cipolla, T. Drummond, and D. P. Robertson, “Camera calibration from vanishing points in images of architectural scenes,” in “Proc. British Machine Vision Conferece,” (Nottingham, England, 1999), pp. 382–391.

Rother, C.

C. Rother and S. Carlsson, “Linear multi view reconstruction and camera recovery using a reference plane,” Int. J. Comput. Vision49, 117–141 (2002).
[CrossRef]

Santos-Victor, J.

E. Grossmann and J. Santos-Victor, “Least-squares 3D reconstruction from one or more views and geometric clues,” Comput. Vis. Image Und.99, 151–174 (2005).
[CrossRef]

Schutze, O.

L. G. de la Fraga and O. Schutze, “Direct calibration by fitting of cuboids to a single image using differential evolution,” Int. J. Comput. Vision80, 119–127 (2009).
[CrossRef]

Sturm, P.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

Tan, P.

N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric architecture modeling with a single image,” ACM T. Graphic. (Proc. SIGGRAPH Asia) 28 (2009).
[CrossRef]

Taylor, C. J.

D. Jelinek and C. J. Taylor, “Reconstruction of linearly parameterized models from single images with a camera of unknown focal length,” IEEE Trans. Pattern Anal. Mach. Intell.23, 767–773 (2001).
[CrossRef]

Tops, J.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

Tsai, R.

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses,” IEEE Trans. Robot. Autom.3, 323–344 (1987).
[CrossRef]

Verbiest, F.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

Vergauwen, M.

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

Viéville, T.

Q.-T. Luong and T. Viéville, “Canonical representations for the geometries of multiple perspective views,” Comput. Vis. Image Und.64, 193–229 (1996).
[CrossRef]

Wilczkowiak, M.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

Wong, K.-Y. K.

K.-Y. K. Wong, G. Zhang, and Z. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process.20, 305–316 (2011).
[CrossRef]

Wu, F. C.

F. C. Wu, F. Q. Duan, and Z. Y. Hu, “An affine invariant of parallelograms and its application to camera calibration and 3D reconstruction,” in “Proc. European Conference on Computer Vision,” (2006), pp. 191–204.

Zhang, G.

K.-Y. K. Wong, G. Zhang, and Z. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process.20, 305–316 (2011).
[CrossRef]

Zhang, Z.

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell.22, 1330–1334 (2000).
[CrossRef]

Zisserman, A.

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Second Edition (Cambridge University Press, 2003).

D. Liebowitz and A. Zisserman, “Combining scene and auto-calibration constraints,” in “Proc. IEEE International Conference on Computer Vision,” (Kerkyra, Greece, 1999), pp. 293–300.
[CrossRef]

ACM T. Graphic.

N. Jiang, P. Tan, and L.-F. Cheong, “Symmetric architecture modeling with a single image,” ACM T. Graphic. (Proc. SIGGRAPH Asia) 28 (2009).
[CrossRef]

Comput. Vis. Image Und.

E. Grossmann and J. Santos-Victor, “Least-squares 3D reconstruction from one or more views and geometric clues,” Comput. Vis. Image Und.99, 151–174 (2005).
[CrossRef]

Q.-T. Luong and T. Viéville, “Canonical representations for the geometries of multiple perspective views,” Comput. Vis. Image Und.64, 193–229 (1996).
[CrossRef]

IEEE Trans. Image Process.

K.-Y. K. Wong, G. Zhang, and Z. Chen, “A stratified approach for camera calibration using spheres,” IEEE Trans. Image Process.20, 305–316 (2011).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell.

M. Wilczkowiak, P. Sturm, and E. Boyer, “Using geometric constraints through parallelepipeds for calibration and 3D modelling,” IEEE Trans. Pattern Anal. Mach. Intell.27, 194–207 (2005).
[CrossRef] [PubMed]

M. Pollefeys and L. V. Gool, “Stratified self-calibration with the modulus constraint,” IEEE Trans. Pattern Anal. Mach. Intell.21, 707–724 (1999).
[CrossRef]

T. Moons, L. V. Gool, M. Proesmans, and E. Pauwels, “Affine reconstruction from perspective image pairs with a relative object-camera translation in between,” IEEE Trans. Pattern Anal. Mach. Intell.18, 77–83 (1996).
[CrossRef]

D. Jelinek and C. J. Taylor, “Reconstruction of linearly parameterized models from single images with a camera of unknown focal length,” IEEE Trans. Pattern Anal. Mach. Intell.23, 767–773 (2001).
[CrossRef]

Z. Zhang, “A flexible new technique for camera calibration,” IEEE Trans. Pattern Anal. Mach. Intell.22, 1330–1334 (2000).
[CrossRef]

IEEE Trans. Robot. Autom.

R. Tsai, “A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf tv cameras and lenses,” IEEE Trans. Robot. Autom.3, 323–344 (1987).
[CrossRef]

Int. J. Comput. Vision

C. Rother and S. Carlsson, “Linear multi view reconstruction and camera recovery using a reference plane,” Int. J. Comput. Vision49, 117–141 (2002).
[CrossRef]

L. Agapito, E. Hayman, and I. Reid, “Self-calibration of rotating and zooming cameras,” Int. J. Comput. Vision45, 107–127 (2001).
[CrossRef]

M. Pollefeys, L. V. Gool, M. Vergauwen, F. Verbiest, K. Cornelis, J. Tops, and R. Koch, “Visual modeling with a hand-held camera,” Int. J. Comput. Vision59, 207–232 (2004).
[CrossRef]

L. G. de la Fraga and O. Schutze, “Direct calibration by fitting of cuboids to a single image using differential evolution,” Int. J. Comput. Vision80, 119–127 (2009).
[CrossRef]

J. Math. Imaging Vis.

P. Hammarstedt, F. Kahl, and A. Heyden, “Affine reconstruction from translational motion under various auto-calibration constraints,” J. Math. Imaging Vis.24, 245–257 (2006).
[CrossRef]

J. Opt. Soc. Am

B. K. P. Horn, H. M. Hilden, and S. Negahdaripour, “Closed form solution of absolute orientation using orthonormal matrices,” J. Opt. Soc. Am5, 1127–1135 (1988).
[CrossRef]

Opt. Express

Pattern Recogn.

F. Mai, Y. S. Hung, and G. Chesi, “Projective reconstruction of ellipses from multiple images,” Pattern Recogn.43, 545–556 (2010).
[CrossRef]

Other

R. Hartley and A. Zisserman, Multiple View Geometry in Computer Vision, Second Edition (Cambridge University Press, 2003).

F. C. Wu, F. Q. Duan, and Z. Y. Hu, “An affine invariant of parallelograms and its application to camera calibration and 3D reconstruction,” in “Proc. European Conference on Computer Vision,” (2006), pp. 191–204.

R. Cipolla, T. Drummond, and D. P. Robertson, “Camera calibration from vanishing points in images of architectural scenes,” in “Proc. British Machine Vision Conferece,” (Nottingham, England, 1999), pp. 382–391.

D. Liebowitz and A. Zisserman, “Combining scene and auto-calibration constraints,” in “Proc. IEEE International Conference on Computer Vision,” (Kerkyra, Greece, 1999), pp. 293–300.
[CrossRef]

D. A. Forsyth and J. Ponce, Computer Vision: A Modern Approach (Prentice Hall, 2003).

R. Hartley, “In defence of the 8-point algorithm,” in “Proc. International Conference on Computer Vision,” (Sendai, Japan, 1995), pp. 1064–1070.

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Figures (14)

Fig. 1
Fig. 1

Examples of imaged parallelograms in camera images due to the two sets of parallel lines with different directions: Only (a) depicts the imaged parallelogram corresponding to an actual parallelogram existing on a plane in 3D.

Fig. 2
Fig. 2

Relationship between the original H and the newly defined H r, which is the infinite homography between the rectified images.

Fig. 3
Fig. 3

Examples of the position of vanishing points in general man-made scenes. Since all parallel lines are orthogonal or parallel to the ground plane, there are only three independent vanishing points. The vanishing points v2, v3, v4, v5, and v6 are collinear and on the vanishing line of the ground plane.

Fig. 4
Fig. 4

The environment of the simulated experiment for performance evaluation. The arrows illustrate the systematical variation of the relevant parameters.

Fig. 5
Fig. 5

The results from the simulated experiments to analyze the relation between the performance and noise magnitude ((a) and (d)), size of parallelograms ((b) and (e)), and angle between the two planes ((c) and (f)). [tx, ty, tz] and [X, Y, Z] indicate the position error of the estimated cameras and parallelograms, respectively.

Fig. 6
Fig. 6

The results of the camera parameter estimates with simulated data: The mean of the absolute error of the calibration parameters are shown as a function of the noise levels for various methods. The cases in which three and four vanishing points exist are indicated by 3vps and 4vps, respectively. (a) and (d) refer to fu. (b) and (e) refer to the skew angle. (c) and (f) refer to u0.

Fig. 7
Fig. 7

Line extraction examples for the Plant Scene experiment presented in Section 7.2.2.

Fig. 8
Fig. 8

Three images used in the Tower Scene experiment and reconstructed model and camera poses.

Fig. 9
Fig. 9

Four captured images for Plant Scene experiment. (a) Image 0. (b) Image 1. (c) Image 2. (d) Image 3.

Fig. 10
Fig. 10

Reconstructed model and camera poses for Plant Scene experiment.

Fig. 11
Fig. 11

Five images for the experiment of the scene of Bank of China. (a) Image 0. (b) Image 1. (c) Image 2. (d) Image 3. (e) Image 4.

Fig. 12
Fig. 12

Reconstructed model and camera poses for the experiment of Bank of China.

Fig. 13
Fig. 13

Ten images for the experiment of the scene of Casa da Música. (a) Image 0. (b) Image 1. (c) Image 2. (d) Image 3. (e) Image 4. (f) Image 5. (g) Image 6. (h) Image 7. (i) Image 8. (j) Image 9.

Fig. 14
Fig. 14

Reconstructed model and camera poses for the experiment of Casa da Música.

Equations (32)

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v i H v i , for i 1 , , 4 ,
λ x [ 1 0 0 ] T = H r [ 1 0 0 ] T
λ y [ 0 1 0 ] T = H r [ 0 1 0 ] T ,
H r = [ λ x 0 u 0 λ y v 0 0 w ] ,
H H r 2 1 H r H r 1 .
K = [ f u s u 0 0 f v v 0 0 0 1 ] ,
H i = [ h i 1 h i 2 h i 3 ] [ 1 cot θ 0 0 a i / r 0 0 0 1 ] .
( h i 1 ± j h i 2 ) T ω r i ( h i 1 ± j h i 2 ) = 0
h i 1 T ω r i h i 2 = 0 and h i 1 T ω r i h i 1 = h i 2 T ω r i h i 2 .
ω r i [ sin 2 θ ( r / a i ) sin θ cos θ α ( r / a i ) sin θ cos θ r 2 / a i 2 β α β γ ] ,
K r i [ sin θ cos θ α 0 ( a i / r ) sin θ β 0 0 γ ] ,
R I = [ 1 0 0 0 1 0 0 0 1 ] or R I ¯ = [ 1 0 0 0 1 0 0 0 1 ] .
H i K r i [ r 1 r 2 t ]
μ K r i 1 H i = [ r 1 r 2 t ] ,
μ [ sin θ 0 α 0 sin θ β 0 0 γ ] = [ r 1 r 2 t ] ,
H r K r 2 R r K r 1 1 [ 1 0 u 0 a 2 a 1 v 0 0 w ] ,
H H r 2 k 1 H r k H r 1 k , for k = 1 , , m
A [ H 11 , H 12 , , H 33 , λ x 1 , ( λ y 1 ) , u 1 , v 1 , w 1 , , λ x m , ( λ y m ) , u m , v m , w m ] T = 0 ,
H 0 i = H j i H 0 j .
[ u v 1 ] P [ X ˜ 1 ] [ h 1 T t 1 h 2 T t 2 h 3 T t 3 ] [ X ˜ 1 ] .
[ u h 3 T h 1 T 1 0 u v h 3 T h 2 T 0 1 v ] [ X ˜ t ] = 0
X ˜ = Σ D ,
[ ( x h 3 T h 1 ) Σ 1 0 x ( y h 3 T h 2 ) Σ 0 1 y ] [ D t ] = 0 .
H E A = [ A 0 0 1 ] .
d A 1 T Ω A d A 2 = 0 .
d E 1 T d E 1 / d E 2 T d E 2 = r 2
d A 1 T Ω A d A 1 = r 2 d A 2 T Ω A d A 2 .
cos θ = d E 1 T d E 2 ( d E 1 T d E 1 ) 1 / 2 ( d E 2 T d E 2 ) 1 / 2
d A 1 T Ω A d A 2 = r cos θ d A 2 T Ω A d A 2 .
Q * A = [ ( Ω A ) 1 0 0 0 ] .
ω i ( P i Q * A P i T ) 1 = H 0 i T Ω A H 0 i 1 .
{ ( H 0 i T Ω A H 0 i 1 ) 12 = 0 ( H 0 i T Ω A H 0 i 1 ) 13 = ( H 0 i T Ω A H 0 i 1 ) 23 = 0 r 2 ( H 0 i T Ω A H 0 i 1 ) 11 = ( H 0 i T Ω A H 0 i 1 ) 22 .

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