Abstract

In order to improve the accuracy and stability of stereo vision calibration, a novel stereo vision calibration approach based on the group method of data handling (GMDH) neural network is presented. Three GMDH neural networks are utilized to build a spatial mapping relationship adaptively in individual dimension. In the process of modeling, the Levenberg–Marquardt optimization algorithm is introduced as an interior criterion to train each partial model, and the corrected Akaike’s information criterion is introduced as an exterior criterion to evaluate these models. Experiments demonstrate that the proposed approach is stable and able to calibrate three-dimensional (3D) locations more accurately and learn the stereo mapping models adaptively. It is a convenient way to calibrate the stereo vision without specialized knowledge of stereo vision.

© 2012 Optical Society of America

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References

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  1. J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
    [CrossRef]
  2. J. I. González, J. C. Gámez, C. G. Artal, and A. M. N. Cabrera, “Stability study of camera calibration methods,” in Proceedings of CI Workshop en Agentes Fisicos (WAF), Spain, 2005, pp. 1–8.
  3. M. B. Lynch and C. H. Dagli, “Back propagation neural network for stereoscopic vision calibration,” Proc. SPIE 8194, 289–298 (1991).
  4. D. Ge, X. Yao, and W. Chen, “Research of machine vision system based on RBF neural network,” in Proceedings of Computer Science and Information Technology, Singapore, 2008, pp. 218–222.
  5. J. Wen and G. Schweitzer, “Hybrid calibration of CCD cameras using artificial neural nets,” in Proceedings of Neural Networks, Singapore, 1991, pp. 337–342.
  6. A. G. Ivakhnenko, “Polynomial theory of complex systems,” IEEE Trans. Syst. Man Cybernet. 1, 364–378 (1971).
    [CrossRef]
  7. E.-S. M. El-Alfy, “A hierarchical GMDH-based polynomial neural network for handwritten numeral recognition using topological features,” in Proceedings of Neural Networks, Barcelona, 2010, pp. 1–7.
  8. A. G. Ivakhnenko, “The review of problems solvable by algorithms of the group method of data handling (GMDH),” Pattern Recogn. Image Anal. 5, 527–535 (1995).
  9. M. T. Hagan and M. B. Menhaj, “Training feed forward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
    [CrossRef]
  10. M. Lourakis, “Levmar,” http://www.ics.forth.gr/~lourakis/levmar/ .
  11. G. Jekabsons, “Adaptive basis function construction: an approach for adaptive building of sparse polynomial regression models,” in Machine Learning, Y. Zhang, ed. (InTech, 2010), pp. 127–155.
  12. A. Hirotugu, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
    [CrossRef]
  13. M. T. Ahmed, E. E. Hemayed, and A. A. Farag, “Neurocalibration: a neural network that can tell camera calibration parameters,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 1999), pp. 463–468.

1995 (1)

A. G. Ivakhnenko, “The review of problems solvable by algorithms of the group method of data handling (GMDH),” Pattern Recogn. Image Anal. 5, 527–535 (1995).

1994 (1)

M. T. Hagan and M. B. Menhaj, “Training feed forward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef]

1992 (1)

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

1991 (1)

M. B. Lynch and C. H. Dagli, “Back propagation neural network for stereoscopic vision calibration,” Proc. SPIE 8194, 289–298 (1991).

1974 (1)

A. Hirotugu, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

1971 (1)

A. G. Ivakhnenko, “Polynomial theory of complex systems,” IEEE Trans. Syst. Man Cybernet. 1, 364–378 (1971).
[CrossRef]

Ahmed, M. T.

M. T. Ahmed, E. E. Hemayed, and A. A. Farag, “Neurocalibration: a neural network that can tell camera calibration parameters,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 1999), pp. 463–468.

Artal, C. G.

J. I. González, J. C. Gámez, C. G. Artal, and A. M. N. Cabrera, “Stability study of camera calibration methods,” in Proceedings of CI Workshop en Agentes Fisicos (WAF), Spain, 2005, pp. 1–8.

Cabrera, A. M. N.

J. I. González, J. C. Gámez, C. G. Artal, and A. M. N. Cabrera, “Stability study of camera calibration methods,” in Proceedings of CI Workshop en Agentes Fisicos (WAF), Spain, 2005, pp. 1–8.

Chen, W.

D. Ge, X. Yao, and W. Chen, “Research of machine vision system based on RBF neural network,” in Proceedings of Computer Science and Information Technology, Singapore, 2008, pp. 218–222.

Cohen, P.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Dagli, C. H.

M. B. Lynch and C. H. Dagli, “Back propagation neural network for stereoscopic vision calibration,” Proc. SPIE 8194, 289–298 (1991).

El-Alfy, E.-S. M.

E.-S. M. El-Alfy, “A hierarchical GMDH-based polynomial neural network for handwritten numeral recognition using topological features,” in Proceedings of Neural Networks, Barcelona, 2010, pp. 1–7.

Farag, A. A.

M. T. Ahmed, E. E. Hemayed, and A. A. Farag, “Neurocalibration: a neural network that can tell camera calibration parameters,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 1999), pp. 463–468.

Gámez, J. C.

J. I. González, J. C. Gámez, C. G. Artal, and A. M. N. Cabrera, “Stability study of camera calibration methods,” in Proceedings of CI Workshop en Agentes Fisicos (WAF), Spain, 2005, pp. 1–8.

Ge, D.

D. Ge, X. Yao, and W. Chen, “Research of machine vision system based on RBF neural network,” in Proceedings of Computer Science and Information Technology, Singapore, 2008, pp. 218–222.

González, J. I.

J. I. González, J. C. Gámez, C. G. Artal, and A. M. N. Cabrera, “Stability study of camera calibration methods,” in Proceedings of CI Workshop en Agentes Fisicos (WAF), Spain, 2005, pp. 1–8.

Hagan, M. T.

M. T. Hagan and M. B. Menhaj, “Training feed forward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef]

Hemayed, E. E.

M. T. Ahmed, E. E. Hemayed, and A. A. Farag, “Neurocalibration: a neural network that can tell camera calibration parameters,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 1999), pp. 463–468.

Herniou, M.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Hirotugu, A.

A. Hirotugu, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

Ivakhnenko, A. G.

A. G. Ivakhnenko, “The review of problems solvable by algorithms of the group method of data handling (GMDH),” Pattern Recogn. Image Anal. 5, 527–535 (1995).

A. G. Ivakhnenko, “Polynomial theory of complex systems,” IEEE Trans. Syst. Man Cybernet. 1, 364–378 (1971).
[CrossRef]

Jekabsons, G.

G. Jekabsons, “Adaptive basis function construction: an approach for adaptive building of sparse polynomial regression models,” in Machine Learning, Y. Zhang, ed. (InTech, 2010), pp. 127–155.

Lynch, M. B.

M. B. Lynch and C. H. Dagli, “Back propagation neural network for stereoscopic vision calibration,” Proc. SPIE 8194, 289–298 (1991).

Menhaj, M. B.

M. T. Hagan and M. B. Menhaj, “Training feed forward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef]

Schweitzer, G.

J. Wen and G. Schweitzer, “Hybrid calibration of CCD cameras using artificial neural nets,” in Proceedings of Neural Networks, Singapore, 1991, pp. 337–342.

Wen, J.

J. Wen and G. Schweitzer, “Hybrid calibration of CCD cameras using artificial neural nets,” in Proceedings of Neural Networks, Singapore, 1991, pp. 337–342.

Weng, J.

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

Yao, X.

D. Ge, X. Yao, and W. Chen, “Research of machine vision system based on RBF neural network,” in Proceedings of Computer Science and Information Technology, Singapore, 2008, pp. 218–222.

IEEE Trans. Autom. Control (1)

A. Hirotugu, “A new look at the statistical model identification,” IEEE Trans. Autom. Control 19, 716–723 (1974).
[CrossRef]

IEEE Trans. Neural Netw. (1)

M. T. Hagan and M. B. Menhaj, “Training feed forward networks with the Marquardt algorithm,” IEEE Trans. Neural Netw. 5, 989–993 (1994).
[CrossRef]

IEEE Trans. Pattern Anal. Machine Intell. (1)

J. Weng, P. Cohen, and M. Herniou, “Camera calibration with distortion models and accuracy evaluation,” IEEE Trans. Pattern Anal. Machine Intell. 14, 965–980 (1992).
[CrossRef]

IEEE Trans. Syst. Man Cybernet. (1)

A. G. Ivakhnenko, “Polynomial theory of complex systems,” IEEE Trans. Syst. Man Cybernet. 1, 364–378 (1971).
[CrossRef]

Pattern Recogn. Image Anal. (1)

A. G. Ivakhnenko, “The review of problems solvable by algorithms of the group method of data handling (GMDH),” Pattern Recogn. Image Anal. 5, 527–535 (1995).

Proc. SPIE (1)

M. B. Lynch and C. H. Dagli, “Back propagation neural network for stereoscopic vision calibration,” Proc. SPIE 8194, 289–298 (1991).

Other (7)

D. Ge, X. Yao, and W. Chen, “Research of machine vision system based on RBF neural network,” in Proceedings of Computer Science and Information Technology, Singapore, 2008, pp. 218–222.

J. Wen and G. Schweitzer, “Hybrid calibration of CCD cameras using artificial neural nets,” in Proceedings of Neural Networks, Singapore, 1991, pp. 337–342.

J. I. González, J. C. Gámez, C. G. Artal, and A. M. N. Cabrera, “Stability study of camera calibration methods,” in Proceedings of CI Workshop en Agentes Fisicos (WAF), Spain, 2005, pp. 1–8.

E.-S. M. El-Alfy, “A hierarchical GMDH-based polynomial neural network for handwritten numeral recognition using topological features,” in Proceedings of Neural Networks, Barcelona, 2010, pp. 1–7.

M. Lourakis, “Levmar,” http://www.ics.forth.gr/~lourakis/levmar/ .

G. Jekabsons, “Adaptive basis function construction: an approach for adaptive building of sparse polynomial regression models,” in Machine Learning, Y. Zhang, ed. (InTech, 2010), pp. 127–155.

M. T. Ahmed, E. E. Hemayed, and A. A. Farag, “Neurocalibration: a neural network that can tell camera calibration parameters,” in Proceedings of IEEE Conference on Computer Vision (IEEE, 1999), pp. 463–468.

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Figures (2)

Fig. 1.
Fig. 1.

Structure of GMDH neural network.

Fig. 2.
Fig. 2.

The planar checkerboard.

Tables (3)

Tables Icon

Table 1. Comparison of Calibration Results Between Three Approaches for Train Dataset

Tables Icon

Table 2. Comparison of Calibration Results Between Three Approaches for Test Dataset

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Table 3. Comparison of Calibration Results Between Three Approaches for Noise Dataset

Equations (12)

Equations on this page are rendered with MathJax. Learn more.

f(v1,v2)=w1+w2v1+w3v2+w4v1v2+w5v12+w6v22,
w=[w1,w2,w3,w4,w5,w6].
E=12q=1Q(p^qpq)2=12q=1Qeq2,
eq=p^qpq,
e(w)=[e1,e2,,eQ],
w(t+1)=w(t)+Δw(t),
Δw(t)=[JT(w)J(w)+μI]1JT(w)e(w),
J(w)=[e1(w)w1e1(w)wNeQ(w)w1eQ(w)wN],
AICC=Qln(MSE)+2k+2k(k+1)Qk1,
MSE=1Qq=1Q(p^qpq)2.
RMSE=i=1n[(xix^i)2+(yiy^i)2+(ziz^i)2]n,
RRMSE(c)=RMSE(c)var(c),c=xoryorz.

Metrics