Abstract

The use of non-metric digital cameras in close-range photogrammetric applications and machine vision has become a popular research agenda. Being an essential component of photogrammetric evaluation, camera calibration is a crucial stage for non-metric cameras. Therefore, accurate camera calibration and orientation procedures have become prerequisites for the extraction of precise and reliable 3D metric information from images. The lack of accurate inner orientation parameters can lead to unreliable results in the photogrammetric process. A camera can be well defined with its principal distance, principal point offset and lens distortion parameters. Different camera models have been formulated and used in close-range photogrammetry, but generally sensor orientation and calibration is performed with a perspective geometrical model by means of the bundle adjustment. In this study, support vector machines (SVMs) using radial basis function kernel is employed to model the distortions measured for Olympus Aspherical Zoom lens Olympus E10 camera system that are later used in the geometric calibration process. It is intended to introduce an alternative approach for the on-the-job photogrammetric calibration stage. Experimental results for DSLR camera with three focal length settings (9, 18 and 36mm) were estimated using bundle adjustment with additional parameters, and analyses were conducted based on object point discrepancies and standard errors. Results show the robustness of the SVMs approach on the correction of image coordinates by modelling total distortions on-the-job calibration process using limited number of images.

© 2010 OSA

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  1. J. Cardenal, E. Mata, P. Castro, J. Delgado, M. A. Hernandez, J. L. Perez, M. Ramos, and M. Torres, “Evaluation of a digital non metric camera (Canon D30) for the photogrammetric recording of historical buildings,” International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Istanbul, Turkey, 34, Part XXX (2004).
  2. F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogramm. Remote Sens. XXXVI(5), 309–314 (2006).
  3. C. S. Fraser and M. R. Shortis, “Variation of distortion within the photographic field,” Photogramm. Eng. Remote Sensing 58, 851–855 (1992).
  4. K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles Publishing, 1996).
  5. A. Mathur and G. M. Foody, “Crop classification by support vector machines with intelligently selected training data for an operational application,” Int. J. Remote Sens. 29(8), 2227–2240 (2008).
    [CrossRef]
  6. V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-Verlag, 1995).
  7. M. R. Shortis, S. Robson, and H. A. Beyer, “Principal point behaviour and calibration parameter models for Kodak DCS cameras,” Photogramm. Rec. 16(92), 165–186 (1998).
    [CrossRef]
  8. C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. 52(4), 149–159 (1997).
    [CrossRef]
  9. D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. Remote Sensing 37, 855–866 (1971).
  10. T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
    [CrossRef]
  11. A. Gruen, and H. A. Beyer, “System calibration through self-calibration,”. Chapter 7 in Calibration and Orientation of Cameras in Computer Vision (Eds. A. Gruen and T.S. Huang), Springer Series in Information Sciences 34, Springer, Berlin. 235 pages: 163–194 (2001).
  12. C. S. Fraser, “On the use of non-metric cameras in analytical non-metric photogrammetry,” Int. Arch. Photogramm. Remote Sens. 24, 156–166 (1982).
  13. C. S. Fraser, M. R. Shortis, and G. Ganci, “Multi-sensor system self-calibration,” in Proceedings of Videometrics IV Conference (SPIE, 1995) 2598, pp 2–18.
  14. S. Abraham, and T. Hau, “Towards autonomous high precision calibration of digital cameras,” in Proceedings of SPIE Annual Meeting, San Diego, 82–93 (1997).
  15. C. S. Fraser and S. Al-Ajlouni, “Zoom-dependent camera calibration in digital close-range photogrammetry,” Photogramm. Eng. Remote Sensing 72, 1017–1026 (2006).
  16. C. Bellman, and M. R. Shortis, “A machine learning approach to building recognition in aerial photographs,” in Proceedings ISPRS Commission III Symposium on Photogrammetric Computer Vision 2002, Graz, Austria, 9–13 September, Part A, pp 50–54 (2002).
  17. C. Bellman, and M. R. Shortis, “Using support vector machines for building recognition in aerial photographs,” presented at 11th Remote Sensing and Photogrammetry Conference on Images to Information, Brisbane, Australia, 2–6 Sept. 2002.
  18. R. Mohamed, A. Ahmed, A. Eid, and A. Farag, “Support vector machines for camera calibration problem,” in Proceedings of IEEE International Conference on Image Processing (ICIP'06), Atlanta, USA. pp. 1029–1032 (2006).
  19. K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
    [CrossRef] [PubMed]
  20. B. Möller, and S. Posch, “Identifying lens distortions in image registration by learning from examples,” in Proceedings of British Machine Vision Conference (BMVC '07), University of Warwick, Coventry, UK. pp. 152–161 (2007).
  21. A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14(3), 199–222 (2004).
    [CrossRef]
  22. J. Meng, Y. Gao, and Y. Shi, “Support vector regression model for measuring the permittivity of asphalt concrete,” IEEE Microw. Wirel. Co. 17(12), 819–821 (2007).
    [CrossRef]
  23. Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
    [CrossRef]
  24. T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
    [CrossRef] [PubMed]
  25. D. Sebald and J. Bucklew, “Support vector machines and the multiple hypothesis test problem,” IEEE T, Signal Process. 49, 2865–2872 (2001).
    [CrossRef]
  26. B. E. Boser, I. M. Guyon, and V. Vapnik, “A training algorithm for optimum margin classifiers,” in Proceedings of the Fifth Annual Workshop on Computational Learning Theory 5, (ACM, 1992), pp. 144–152.
  27. C. Huang, L. S. Davis, and J. R. G. Townshend, “An assessment of support vector machines for land cover classification,” Int. J. Remote Sens. 23(4), 725–749 (2002).
    [CrossRef]
  28. C. W. Hsu, C. C. Chang, and C. J. Lin, “A practical guide to support vector classification,” http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf .

2008 (2)

A. Mathur and G. M. Foody, “Crop classification by support vector machines with intelligently selected training data for an operational application,” Int. J. Remote Sens. 29(8), 2227–2240 (2008).
[CrossRef]

Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
[CrossRef]

2007 (1)

J. Meng, Y. Gao, and Y. Shi, “Support vector regression model for measuring the permittivity of asphalt concrete,” IEEE Microw. Wirel. Co. 17(12), 819–821 (2007).
[CrossRef]

2006 (4)

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

C. S. Fraser and S. Al-Ajlouni, “Zoom-dependent camera calibration in digital close-range photogrammetry,” Photogramm. Eng. Remote Sensing 72, 1017–1026 (2006).

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
[CrossRef] [PubMed]

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogramm. Remote Sens. XXXVI(5), 309–314 (2006).

2004 (1)

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14(3), 199–222 (2004).
[CrossRef]

2002 (1)

C. Huang, L. S. Davis, and J. R. G. Townshend, “An assessment of support vector machines for land cover classification,” Int. J. Remote Sens. 23(4), 725–749 (2002).
[CrossRef]

2001 (1)

D. Sebald and J. Bucklew, “Support vector machines and the multiple hypothesis test problem,” IEEE T, Signal Process. 49, 2865–2872 (2001).
[CrossRef]

1998 (2)

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[CrossRef]

M. R. Shortis, S. Robson, and H. A. Beyer, “Principal point behaviour and calibration parameter models for Kodak DCS cameras,” Photogramm. Rec. 16(92), 165–186 (1998).
[CrossRef]

1997 (1)

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. 52(4), 149–159 (1997).
[CrossRef]

1992 (1)

C. S. Fraser and M. R. Shortis, “Variation of distortion within the photographic field,” Photogramm. Eng. Remote Sensing 58, 851–855 (1992).

1982 (1)

C. S. Fraser, “On the use of non-metric cameras in analytical non-metric photogrammetry,” Int. Arch. Photogramm. Remote Sens. 24, 156–166 (1982).

1971 (1)

D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. Remote Sensing 37, 855–866 (1971).

Al-Ajlouni, S.

C. S. Fraser and S. Al-Ajlouni, “Zoom-dependent camera calibration in digital close-range photogrammetry,” Photogramm. Eng. Remote Sensing 72, 1017–1026 (2006).

Beyer, H. A.

M. R. Shortis, S. Robson, and H. A. Beyer, “Principal point behaviour and calibration parameter models for Kodak DCS cameras,” Photogramm. Rec. 16(92), 165–186 (1998).
[CrossRef]

Brown, D. C.

D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. Remote Sensing 37, 855–866 (1971).

Bucklew, J.

D. Sebald and J. Bucklew, “Support vector machines and the multiple hypothesis test problem,” IEEE T, Signal Process. 49, 2865–2872 (2001).
[CrossRef]

Cao, H.

Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
[CrossRef]

Choi, K. S.

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
[CrossRef] [PubMed]

Clarke, T. A.

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[CrossRef]

Davis, L. S.

C. Huang, L. S. Davis, and J. R. G. Townshend, “An assessment of support vector machines for land cover classification,” Int. J. Remote Sens. 23(4), 725–749 (2002).
[CrossRef]

Dou, Y.

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

Foody, G. M.

A. Mathur and G. M. Foody, “Crop classification by support vector machines with intelligently selected training data for an operational application,” Int. J. Remote Sens. 29(8), 2227–2240 (2008).
[CrossRef]

Fraser, C.

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogramm. Remote Sens. XXXVI(5), 309–314 (2006).

Fraser, C. S.

C. S. Fraser and S. Al-Ajlouni, “Zoom-dependent camera calibration in digital close-range photogrammetry,” Photogramm. Eng. Remote Sensing 72, 1017–1026 (2006).

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. 52(4), 149–159 (1997).
[CrossRef]

C. S. Fraser and M. R. Shortis, “Variation of distortion within the photographic field,” Photogramm. Eng. Remote Sensing 58, 851–855 (1992).

C. S. Fraser, “On the use of non-metric cameras in analytical non-metric photogrammetry,” Int. Arch. Photogramm. Remote Sens. 24, 156–166 (1982).

Fryer, J. G.

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[CrossRef]

Gao, Y.

J. Meng, Y. Gao, and Y. Shi, “Support vector regression model for measuring the permittivity of asphalt concrete,” IEEE Microw. Wirel. Co. 17(12), 819–821 (2007).
[CrossRef]

Huang, C.

C. Huang, L. S. Davis, and J. R. G. Townshend, “An assessment of support vector machines for land cover classification,” Int. J. Remote Sens. 23(4), 725–749 (2002).
[CrossRef]

Jiang, J.

Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
[CrossRef]

Lam, E. Y.

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
[CrossRef] [PubMed]

Mathur, A.

A. Mathur and G. M. Foody, “Crop classification by support vector machines with intelligently selected training data for an operational application,” Int. J. Remote Sens. 29(8), 2227–2240 (2008).
[CrossRef]

Meng, J.

J. Meng, Y. Gao, and Y. Shi, “Support vector regression model for measuring the permittivity of asphalt concrete,” IEEE Microw. Wirel. Co. 17(12), 819–821 (2007).
[CrossRef]

Mi, H.

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

Pan, Y.

Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
[CrossRef]

Remondino, F.

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogramm. Remote Sens. XXXVI(5), 309–314 (2006).

Ren, Y. L.

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

Robson, S.

M. R. Shortis, S. Robson, and H. A. Beyer, “Principal point behaviour and calibration parameter models for Kodak DCS cameras,” Photogramm. Rec. 16(92), 165–186 (1998).
[CrossRef]

Schölkopf, B.

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14(3), 199–222 (2004).
[CrossRef]

Sebald, D.

D. Sebald and J. Bucklew, “Support vector machines and the multiple hypothesis test problem,” IEEE T, Signal Process. 49, 2865–2872 (2001).
[CrossRef]

Shi, Y.

J. Meng, Y. Gao, and Y. Shi, “Support vector regression model for measuring the permittivity of asphalt concrete,” IEEE Microw. Wirel. Co. 17(12), 819–821 (2007).
[CrossRef]

Shortis, M. R.

M. R. Shortis, S. Robson, and H. A. Beyer, “Principal point behaviour and calibration parameter models for Kodak DCS cameras,” Photogramm. Rec. 16(92), 165–186 (1998).
[CrossRef]

C. S. Fraser and M. R. Shortis, “Variation of distortion within the photographic field,” Photogramm. Eng. Remote Sensing 58, 851–855 (1992).

Smola, A. J.

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14(3), 199–222 (2004).
[CrossRef]

Townshend, J. R. G.

C. Huang, L. S. Davis, and J. R. G. Townshend, “An assessment of support vector machines for land cover classification,” Int. J. Remote Sens. 23(4), 725–749 (2002).
[CrossRef]

Wang, R.

Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
[CrossRef]

Wong, K. K. Y.

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
[CrossRef] [PubMed]

Zou, J. Y.

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

Zou, T. T.

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

Anal. Biochem. (1)

T. T. Zou, Y. Dou, H. Mi, J. Y. Zou, and Y. L. Ren, “Support vector regression for determination of component of compound oxytetracycline powder on near-infrared spectroscopy,” Anal. Biochem. 355(1), 1–7 (2006).
[CrossRef] [PubMed]

Chemometr. Intell. Lab. (1)

Y. Pan, J. Jiang, R. Wang, and H. Cao, “Advantages of support vector machine in QSPR studies for predicting auto-ignition temperatures of organic compounds,” Chemometr. Intell. Lab. 92(2), 169–178 (2008).
[CrossRef]

IEEE Microw. Wirel. Co. (1)

J. Meng, Y. Gao, and Y. Shi, “Support vector regression model for measuring the permittivity of asphalt concrete,” IEEE Microw. Wirel. Co. 17(12), 819–821 (2007).
[CrossRef]

IEEE T, (1)

D. Sebald and J. Bucklew, “Support vector machines and the multiple hypothesis test problem,” IEEE T, Signal Process. 49, 2865–2872 (2001).
[CrossRef]

Int. Arch. Photogramm. Remote Sens. (2)

F. Remondino and C. Fraser, “Digital camera calibration methods: considerations and comparisons,” Int. Arch. Photogramm. Remote Sens. XXXVI(5), 309–314 (2006).

C. S. Fraser, “On the use of non-metric cameras in analytical non-metric photogrammetry,” Int. Arch. Photogramm. Remote Sens. 24, 156–166 (1982).

Int. J. Remote Sens. (2)

A. Mathur and G. M. Foody, “Crop classification by support vector machines with intelligently selected training data for an operational application,” Int. J. Remote Sens. 29(8), 2227–2240 (2008).
[CrossRef]

C. Huang, L. S. Davis, and J. R. G. Townshend, “An assessment of support vector machines for land cover classification,” Int. J. Remote Sens. 23(4), 725–749 (2002).
[CrossRef]

ISPRS J. Photogramm. (1)

C. S. Fraser, “Digital camera self-calibration,” ISPRS J. Photogramm. 52(4), 149–159 (1997).
[CrossRef]

Opt. Express (1)

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, “Automatic source camera identification using the intrinsic lens radial distortion,” Opt. Express 14(24), 11551–11565 (2006).
[CrossRef] [PubMed]

Photogramm. Eng. Remote Sensing (3)

D. C. Brown, “Close-range camera calibration,” Photogramm. Eng. Remote Sensing 37, 855–866 (1971).

C. S. Fraser and M. R. Shortis, “Variation of distortion within the photographic field,” Photogramm. Eng. Remote Sensing 58, 851–855 (1992).

C. S. Fraser and S. Al-Ajlouni, “Zoom-dependent camera calibration in digital close-range photogrammetry,” Photogramm. Eng. Remote Sensing 72, 1017–1026 (2006).

Photogramm. Rec. (2)

M. R. Shortis, S. Robson, and H. A. Beyer, “Principal point behaviour and calibration parameter models for Kodak DCS cameras,” Photogramm. Rec. 16(92), 165–186 (1998).
[CrossRef]

T. A. Clarke and J. G. Fryer, “The development of camera calibration methods and models,” Photogramm. Rec. 16(91), 51–66 (1998).
[CrossRef]

Stat. Comput. (1)

A. J. Smola and B. Schölkopf, “A tutorial on support vector regression,” Stat. Comput. 14(3), 199–222 (2004).
[CrossRef]

Other (12)

B. Möller, and S. Posch, “Identifying lens distortions in image registration by learning from examples,” in Proceedings of British Machine Vision Conference (BMVC '07), University of Warwick, Coventry, UK. pp. 152–161 (2007).

C. W. Hsu, C. C. Chang, and C. J. Lin, “A practical guide to support vector classification,” http://www.csie.ntu.edu.tw/~cjlin/papers/guide/guide.pdf .

B. E. Boser, I. M. Guyon, and V. Vapnik, “A training algorithm for optimum margin classifiers,” in Proceedings of the Fifth Annual Workshop on Computational Learning Theory 5, (ACM, 1992), pp. 144–152.

A. Gruen, and H. A. Beyer, “System calibration through self-calibration,”. Chapter 7 in Calibration and Orientation of Cameras in Computer Vision (Eds. A. Gruen and T.S. Huang), Springer Series in Information Sciences 34, Springer, Berlin. 235 pages: 163–194 (2001).

K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles Publishing, 1996).

V. N. Vapnik, The Nature of Statistical Learning Theory (Springer-Verlag, 1995).

J. Cardenal, E. Mata, P. Castro, J. Delgado, M. A. Hernandez, J. L. Perez, M. Ramos, and M. Torres, “Evaluation of a digital non metric camera (Canon D30) for the photogrammetric recording of historical buildings,” International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Istanbul, Turkey, 34, Part XXX (2004).

C. S. Fraser, M. R. Shortis, and G. Ganci, “Multi-sensor system self-calibration,” in Proceedings of Videometrics IV Conference (SPIE, 1995) 2598, pp 2–18.

S. Abraham, and T. Hau, “Towards autonomous high precision calibration of digital cameras,” in Proceedings of SPIE Annual Meeting, San Diego, 82–93 (1997).

C. Bellman, and M. R. Shortis, “A machine learning approach to building recognition in aerial photographs,” in Proceedings ISPRS Commission III Symposium on Photogrammetric Computer Vision 2002, Graz, Austria, 9–13 September, Part A, pp 50–54 (2002).

C. Bellman, and M. R. Shortis, “Using support vector machines for building recognition in aerial photographs,” presented at 11th Remote Sensing and Photogrammetry Conference on Images to Information, Brisbane, Australia, 2–6 Sept. 2002.

R. Mohamed, A. Ahmed, A. Eid, and A. Farag, “Support vector machines for camera calibration problem,” in Proceedings of IEEE International Conference on Image Processing (ICIP'06), Atlanta, USA. pp. 1029–1032 (2006).

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Figures (2)

Fig. 1
Fig. 1

Calibration using bundle adjustment with additional parameters for the 3D test field.

Fig. 2
Fig. 2

The illustration of SVM for linear regression problem.

Tables (6)

Tables Icon

Table 1 Performance analysis of support vector machines for the targets determined on the test field with different focal length settings.

Tables Icon

Table 2 RMSE values of projection centers estimated through bundle block adjustment with and without SVR processes and inner orientation parameters for 9mm focal length.

Tables Icon

Table 3 RMSE values of projection centers estimated through bundle block adjustment with and without SVR processes and inner orientation parameters for 18mm focal length.

Tables Icon

Table 4 RMSE values of projection centers estimated through bundle block adjustment with and without SVR processes and inner orientation parameters for 36mm focal length.

Tables Icon

Table 5 Summary of adjustment results for the 9mm, 18mm and 36mm lenses before SVM application. Coordinate discrepancies are shown as minimum and maximum values.

Tables Icon

Table 6 Summary of adjustment results for the 9mm, 18mm and 36mm lenses after SVM application. Coordinate discrepancies are shown as minimum and maximum values.

Equations (3)

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Minimize 1 2 w 2 + C i = 1 l ξ i + ξ i *
subject to { y i w x i b ε + ξ i w x i + b y i ε + ξ i * ξ i , ξ i * 0
f ( x ) = ( w ϕ ( x ) + b ) = i = 1 n ( α i α i * ) K ( x i , x ) + b

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