Abstract

Source camera identification refers to the task of matching digital images with the cameras that are responsible for producing these images. This is an important task in image forensics, which in turn is a critical procedure in law enforcement. Unfortunately, few digital cameras are equipped with the capability of producing watermarks for this purpose. In this paper, we demonstrate that it is possible to achieve a high rate of accuracy in the identification by noting the intrinsic lens radial distortion of each camera. To reduce manufacturing cost, the majority of digital cameras are equipped with lenses having rather spherical surfaces, whose inherent radial distortions serve as unique fingerprints in the images. We extract, for each image, parameters from aberration measurements, which are then used to train and test a support vector machine classifier. We conduct extensive experiments to evaluate the success rate of a source camera identification with five cameras. The results show that this is a viable approach with high accuracy. Additionally, we also present results on how the error rates may change with images captured using various optical zoom levels, as zooming is commonly available in digital cameras.

© 2006 Optical Society of America

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References

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  1. R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE Journal of Robotics and Automation 3(4), 323-344 (1987).
    [CrossRef]
  2. F. Devernay and O. Faugeras, "Automatic calibration and removal of distortion from scenes of structured environments," in Investigative and Trial Image Processing, vol. 2567 of Proc. SPIE, pp. 62-67 (1995).
    [CrossRef]
  3. J. Pers and S. Kovacic, "Nonparametric, model-based radial lens distortion correction using tilted camera assumption," inProceedings of the Computer Vision Winter Workshop 2002, pp. 286-295 (2002).
  4. J. Adams, K. Parulski, and K. Spaulding, "Color processing in digital cameras," IEEE Micro 18(6), 20-30 (1998).
    [CrossRef]
  5. M. Kharrazi, H. T. Sencar, and N. Memon, "Blind source camera identification," in IEEE International Conference on Image Processing, pp. 709-712 (2004).
  6. I. Avcibas, N. Memon, and B. Sankur, "Steganalysis using image quality metrics," IEEE Transactions on Image Processing 12(2), 221-229 (2003).
    [CrossRef]
  7. S. Bayram, H. T. Sencar, N. Memon, and I. Avcibas, "Source camera identification based on CFA interpolation," in IEEE International Conference on Image Processing, vol. 3, pp. 69-72 (2005).
  8. Y. Long and Y. Huang, "Image based source camera identification using demosaicking," in IEEE International Workshop on Multimedia Signal Processing, vol. 3 (2006).
  9. J. Lukas, J. Fridrich, and M. Goljan, "Determining digital image origin using sensor imperfections," in Image and Video Communications and Processing, vol. 5685 of Proc. SPIE, pp. 16-20 (2005).
  10. R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, New York, 2001).
  11. K. S. Choi, E. Y. Lam, and K. K. Y. Wong, "Source camera identification using footprints from lens aberration," in Digital Photography II, vol. 6069 of Proc. SPIE, pp. 155-162 (2006).
  12. K. S. Choi, E. Y. Lam, and K. K. Y. Wong, "Feature selection in source camera identification," in IEEE International Conference on Systems, Man and Cybernetics, pp. 3176-3180 (2006).
  13. E. Y. Lam, "Image restoration in digital photography," IEEE Transactions on Consumer Electronics 49(2), 269- 274 (2003).
    [CrossRef]
  14. E. Hecht, Optics (Addison Wesly, San Francisco, California, 2002).
  15. B. Tordoff and D. W. Murray, "Violating rotating camera geometry: the effect of radial distortion on selfcalibration," in Proc. 15th International Conference on Pattern Recognition, vol. 1, pp. 423-427 (2000).
  16. P. D. Kovesi, Matlab and octave functions for computer vision and image processing. Software available at http://www.csse.uwa.edu.au/~pk/research/matlabfns/.
  17. C.-C. Chang and C.-J. Lin, LIBSVM: a library for support vector machines (2001). Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm.
  18. M. Li and J.-M. Lavest, "Some aspects of zoom lens camera calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence 18(11), 1105-1110 (1996).
    [CrossRef]
  19. Y.-S. Chen, S.-W. Shih, Y.-P. Hung, and C.-S. Fuh, "The JPEG still picture compression standard," in Proc. Of 15th International Conference on Pattern Recognition, vol. 4, pp. 495-498 (2000).

2003

I. Avcibas, N. Memon, and B. Sankur, "Steganalysis using image quality metrics," IEEE Transactions on Image Processing 12(2), 221-229 (2003).
[CrossRef]

E. Y. Lam, "Image restoration in digital photography," IEEE Transactions on Consumer Electronics 49(2), 269- 274 (2003).
[CrossRef]

2002

J. Pers and S. Kovacic, "Nonparametric, model-based radial lens distortion correction using tilted camera assumption," inProceedings of the Computer Vision Winter Workshop 2002, pp. 286-295 (2002).

1998

J. Adams, K. Parulski, and K. Spaulding, "Color processing in digital cameras," IEEE Micro 18(6), 20-30 (1998).
[CrossRef]

1996

M. Li and J.-M. Lavest, "Some aspects of zoom lens camera calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence 18(11), 1105-1110 (1996).
[CrossRef]

1987

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE Journal of Robotics and Automation 3(4), 323-344 (1987).
[CrossRef]

Adams, J.

J. Adams, K. Parulski, and K. Spaulding, "Color processing in digital cameras," IEEE Micro 18(6), 20-30 (1998).
[CrossRef]

Avcibas, I.

I. Avcibas, N. Memon, and B. Sankur, "Steganalysis using image quality metrics," IEEE Transactions on Image Processing 12(2), 221-229 (2003).
[CrossRef]

Kovacic, S.

J. Pers and S. Kovacic, "Nonparametric, model-based radial lens distortion correction using tilted camera assumption," inProceedings of the Computer Vision Winter Workshop 2002, pp. 286-295 (2002).

Lam, E. Y.

E. Y. Lam, "Image restoration in digital photography," IEEE Transactions on Consumer Electronics 49(2), 269- 274 (2003).
[CrossRef]

Lavest, J.-M.

M. Li and J.-M. Lavest, "Some aspects of zoom lens camera calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence 18(11), 1105-1110 (1996).
[CrossRef]

Li, M.

M. Li and J.-M. Lavest, "Some aspects of zoom lens camera calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence 18(11), 1105-1110 (1996).
[CrossRef]

Memon, N.

I. Avcibas, N. Memon, and B. Sankur, "Steganalysis using image quality metrics," IEEE Transactions on Image Processing 12(2), 221-229 (2003).
[CrossRef]

Parulski, K.

J. Adams, K. Parulski, and K. Spaulding, "Color processing in digital cameras," IEEE Micro 18(6), 20-30 (1998).
[CrossRef]

Pers, J.

J. Pers and S. Kovacic, "Nonparametric, model-based radial lens distortion correction using tilted camera assumption," inProceedings of the Computer Vision Winter Workshop 2002, pp. 286-295 (2002).

Sankur, B.

I. Avcibas, N. Memon, and B. Sankur, "Steganalysis using image quality metrics," IEEE Transactions on Image Processing 12(2), 221-229 (2003).
[CrossRef]

Spaulding, K.

J. Adams, K. Parulski, and K. Spaulding, "Color processing in digital cameras," IEEE Micro 18(6), 20-30 (1998).
[CrossRef]

Tsai, R. Y.

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE Journal of Robotics and Automation 3(4), 323-344 (1987).
[CrossRef]

IEEE Journal of Robotics and Automation

R. Y. Tsai, "A versatile camera calibration technique for high-accuracy 3D machine vision metrology using off-the-shelf TV cameras and lenses," IEEE Journal of Robotics and Automation 3(4), 323-344 (1987).
[CrossRef]

IEEE Micro

J. Adams, K. Parulski, and K. Spaulding, "Color processing in digital cameras," IEEE Micro 18(6), 20-30 (1998).
[CrossRef]

IEEE Transactions on Consumer Electronics

E. Y. Lam, "Image restoration in digital photography," IEEE Transactions on Consumer Electronics 49(2), 269- 274 (2003).
[CrossRef]

IEEE Transactions on Image Processing

I. Avcibas, N. Memon, and B. Sankur, "Steganalysis using image quality metrics," IEEE Transactions on Image Processing 12(2), 221-229 (2003).
[CrossRef]

IEEE Transactions on Pattern Analysis and Machine Intelligence

M. Li and J.-M. Lavest, "Some aspects of zoom lens camera calibration," IEEE Transactions on Pattern Analysis and Machine Intelligence 18(11), 1105-1110 (1996).
[CrossRef]

Proceedings of the Computer Vision Winter Workshop

J. Pers and S. Kovacic, "Nonparametric, model-based radial lens distortion correction using tilted camera assumption," inProceedings of the Computer Vision Winter Workshop 2002, pp. 286-295 (2002).

Other

Y.-S. Chen, S.-W. Shih, Y.-P. Hung, and C.-S. Fuh, "The JPEG still picture compression standard," in Proc. Of 15th International Conference on Pattern Recognition, vol. 4, pp. 495-498 (2000).

E. Hecht, Optics (Addison Wesly, San Francisco, California, 2002).

B. Tordoff and D. W. Murray, "Violating rotating camera geometry: the effect of radial distortion on selfcalibration," in Proc. 15th International Conference on Pattern Recognition, vol. 1, pp. 423-427 (2000).

P. D. Kovesi, Matlab and octave functions for computer vision and image processing. Software available at http://www.csse.uwa.edu.au/~pk/research/matlabfns/.

C.-C. Chang and C.-J. Lin, LIBSVM: a library for support vector machines (2001). Software available at http://www.csie.ntu.edu.tw/~cjlin/libsvm.

S. Bayram, H. T. Sencar, N. Memon, and I. Avcibas, "Source camera identification based on CFA interpolation," in IEEE International Conference on Image Processing, vol. 3, pp. 69-72 (2005).

Y. Long and Y. Huang, "Image based source camera identification using demosaicking," in IEEE International Workshop on Multimedia Signal Processing, vol. 3 (2006).

J. Lukas, J. Fridrich, and M. Goljan, "Determining digital image origin using sensor imperfections," in Image and Video Communications and Processing, vol. 5685 of Proc. SPIE, pp. 16-20 (2005).

R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification (Wiley, New York, 2001).

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, "Source camera identification using footprints from lens aberration," in Digital Photography II, vol. 6069 of Proc. SPIE, pp. 155-162 (2006).

K. S. Choi, E. Y. Lam, and K. K. Y. Wong, "Feature selection in source camera identification," in IEEE International Conference on Systems, Man and Cybernetics, pp. 3176-3180 (2006).

M. Kharrazi, H. T. Sencar, and N. Memon, "Blind source camera identification," in IEEE International Conference on Image Processing, pp. 709-712 (2004).

F. Devernay and O. Faugeras, "Automatic calibration and removal of distortion from scenes of structured environments," in Investigative and Trial Image Processing, vol. 2567 of Proc. SPIE, pp. 62-67 (1995).
[CrossRef]

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Figures (8)

Fig. 1.
Fig. 1.

Block diagram of color processing pipeline in digital cameras.

Fig. 2.
Fig. 2.

Distortion of a rectangular grid. Left: Undistorted grid. Middle: Grid with barrel distortion. Right: Grid with pincushion distortion.

Fig. 3.
Fig. 3.

A rectangular grid taken by Casio. The grid has barrel distortion.

Fig. 4.
Fig. 4.

Sample images obtained using the Canon (A80).

Fig. 5.
Fig. 5.

The scatter plot of lens radial distortion parameters, k 1 and k 2, in Canon (A80) (×), Casio (o) and Ricoh (+) in our experiment. It can be seen that the lens radial distortion parameters can be clearly separable into three groups.

Fig. 6.
Fig. 6.

The scatter plot of lens radial distortion parameters, k 1 and k 2, in Canon (A80) (×), Casio (o), Ricoh (+), Canon (I55) (∇) and Olympus (Δ) in our experiment. It can be seen that the lens radial distortion parameters can be clearly separable into five groups.

Fig. 7.
Fig. 7.

The scatter plot of lens radial distortion parameters, k 1 and k 2, in Canon (A80), Casio, and Ricoh in our experiment. The distortion parameters were measured from images with various zoom intervals. The first zoom interval represents maximum zoom out (wide), whereas the fifth zoom interval represents maximum zoom in (tele). We can see that the distortion parameters from one camera can be clearly separable from another camera in some cases. However, the distortion parameters from 5th zoom interval of Canon (A80) have a considerable overlap with the parameters from Casio.

Fig. 8.
Fig. 8.

Top: An example image from Casio and its edge map. Only a few short straight lines appeared in the edge map. Bottom: Another example image from Casio and its edge map. Only one straight line in the middle of the image. Lines which are short or at the center may not provide useful information for distortion estimation. The k 2 and k 2 values from both examples are far from the majority of Casio images in fig. 5.

Tables (11)

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Table 1. Cameras used in experiments and their properties

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Table 2. The confusion matrix for camera identification with 60 testing images by lens radial distortion only.

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Table 3. The confusion matrix for camera identification with 60 testing images by features proposed by Kharrazi et al. only.

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Table 4. The confusion matrix for camera identification with 60 testing images by lens radial distortion and features proposed by Kharrazi et al.

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Table 5. The confusion matrix for camera identification with 100 testing images by lens radial distortion only.

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Table 6. The confusion matrix for camera identification with 100 testing images by features proposed by Kharrazi et al. only.

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Table 7. The confusion matrix for camera identification with 100 testing images by lens radial distortion and features proposed by Kharrazi et al.

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Table 8. The confusion matrix for five-camera identification by lens radial distortion only.

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Table 9. The confusion matrix for five-camera identification by features proposed by Kharrazi et al. only.

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Table 10. The confusion matrix for five-camera identification by lens radial distortion and features proposed by Kharrazi et al.

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Table 11. The confusion matrix for camera identification by lens radial distortion only.

Equations (1)

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r u = r d + k 1 r d 3 + k 2 r d 5

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