Abstract

We deal with the problem of restoration of images blurred by relative motion between the camera and the object of interest. This problem is common when the imaging system is in moving vehicles or held by human hands, and in robot vision. For correct restoration of the degraded image, it is useful to know the point-spread function (PSF) of the blurring system. We propose a straightforward method to restore motion-blurred images given only the blurred image itself. The method first identifies the PSF of the blur and then uses it to restore the blurred image. The blur identification here is based on the concept that image characteristics along the direction of motion are affected mostly by the blur and are different from the characteristics in other directions. By filtering the blurred image, we emphasize the PSF correlation properties at the expense of those of the original image. Experimental results for image restoration are presented for both synthetic and real motion blur.

© 1998 Optical Society of America

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References

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  1. M. P. Ekstrom, ed., Digital Image Processing Techniques (Academic, Orlando, Fla., 1984).
  2. A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 2.
  3. H. Lim, K. C. Tan, B. T. G. Tan, “Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment,” CVGIP: Graph. Models Image Process. 53, 186–195 (1991).
  4. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  5. M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58–63 (1976).
    [CrossRef]
  6. S. C. Som, “Analysis of the effect of linear smear on photographic images,” J. Opt. Soc. Am. 61, 859–864 (1971).
    [CrossRef]
  7. O. Hadar, S. R. Rotman, N. S. Kopeika, “Target acquisition modeling of forward-motion considerations for airborne reconnaissance over hostile territory,” Opt. Eng. 33, 3106–3117 (1994).
    [CrossRef]
  8. O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer function and experimental verification,” Opt. Eng. 33, 566–578 (1994).
    [CrossRef]
  9. A. K. Katsaggelos, ed., Digital Image Restoration (Springer-Verlag, New York, 1991).
  10. R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990).
    [CrossRef]
  11. G. Pavlovic, A. M. Tekalp, “Maximum likelihood parametric blur identification based on a continuous spatial domain model,” IEEE Trans. Image Process. 1, 496–504 (1992).
    [CrossRef] [PubMed]
  12. A. E. Savakis, H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2, 141–151 (1993).
    [CrossRef] [PubMed]
  13. Y. Yitzhaky, N. S. Kopeika, “Identification of blur parameters from motion blurred images,” CVGIP: Graph. Models Image Process. 59, 310–320 (1997).
  14. D. F. Mix, J. G. Sheppard, “Average correlation functions in on-line testing of linear systems,” IEEE Trans. Aerosp. Electron. Syst. AES-9, 665–669 (1973).
    [CrossRef]
  15. R. J. Schalkoff, Digital Image Processing and Computer Vision (Wiley, New York, 1989).
  16. A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 7.
  17. B. Gold, C. M. Rader, Digital Processing of Signals (McGraw-Hill, New York, 1969).
  18. M. Bellanger, Digital Processing of Signals (Wiley, New York, 1984).

1997 (1)

Y. Yitzhaky, N. S. Kopeika, “Identification of blur parameters from motion blurred images,” CVGIP: Graph. Models Image Process. 59, 310–320 (1997).

1994 (2)

O. Hadar, S. R. Rotman, N. S. Kopeika, “Target acquisition modeling of forward-motion considerations for airborne reconnaissance over hostile territory,” Opt. Eng. 33, 3106–3117 (1994).
[CrossRef]

O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer function and experimental verification,” Opt. Eng. 33, 566–578 (1994).
[CrossRef]

1993 (1)

A. E. Savakis, H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2, 141–151 (1993).
[CrossRef] [PubMed]

1992 (1)

G. Pavlovic, A. M. Tekalp, “Maximum likelihood parametric blur identification based on a continuous spatial domain model,” IEEE Trans. Image Process. 1, 496–504 (1992).
[CrossRef] [PubMed]

1991 (1)

H. Lim, K. C. Tan, B. T. G. Tan, “Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment,” CVGIP: Graph. Models Image Process. 53, 186–195 (1991).

1990 (1)

R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990).
[CrossRef]

1976 (1)

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58–63 (1976).
[CrossRef]

1973 (1)

D. F. Mix, J. G. Sheppard, “Average correlation functions in on-line testing of linear systems,” IEEE Trans. Aerosp. Electron. Syst. AES-9, 665–669 (1973).
[CrossRef]

1971 (1)

Bellanger, M.

M. Bellanger, Digital Processing of Signals (Wiley, New York, 1984).

Biemond, J.

R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990).
[CrossRef]

Cannon, M.

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58–63 (1976).
[CrossRef]

Dror, I.

O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer function and experimental verification,” Opt. Eng. 33, 566–578 (1994).
[CrossRef]

Gold, B.

B. Gold, C. M. Rader, Digital Processing of Signals (McGraw-Hill, New York, 1969).

Hadar, O.

O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer function and experimental verification,” Opt. Eng. 33, 566–578 (1994).
[CrossRef]

O. Hadar, S. R. Rotman, N. S. Kopeika, “Target acquisition modeling of forward-motion considerations for airborne reconnaissance over hostile territory,” Opt. Eng. 33, 3106–3117 (1994).
[CrossRef]

Jain, A. K.

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

Kak, A. C.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 2.

Kopeika, N. S.

Y. Yitzhaky, N. S. Kopeika, “Identification of blur parameters from motion blurred images,” CVGIP: Graph. Models Image Process. 59, 310–320 (1997).

O. Hadar, S. R. Rotman, N. S. Kopeika, “Target acquisition modeling of forward-motion considerations for airborne reconnaissance over hostile territory,” Opt. Eng. 33, 3106–3117 (1994).
[CrossRef]

O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer function and experimental verification,” Opt. Eng. 33, 566–578 (1994).
[CrossRef]

Lagendijk, R. L.

R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990).
[CrossRef]

Lim, H.

H. Lim, K. C. Tan, B. T. G. Tan, “Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment,” CVGIP: Graph. Models Image Process. 53, 186–195 (1991).

Mix, D. F.

D. F. Mix, J. G. Sheppard, “Average correlation functions in on-line testing of linear systems,” IEEE Trans. Aerosp. Electron. Syst. AES-9, 665–669 (1973).
[CrossRef]

Oppenheim, A. V.

A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 7.

Pavlovic, G.

G. Pavlovic, A. M. Tekalp, “Maximum likelihood parametric blur identification based on a continuous spatial domain model,” IEEE Trans. Image Process. 1, 496–504 (1992).
[CrossRef] [PubMed]

Rader, C. M.

B. Gold, C. M. Rader, Digital Processing of Signals (McGraw-Hill, New York, 1969).

Rosenfeld, A.

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 2.

Rotman, S. R.

O. Hadar, S. R. Rotman, N. S. Kopeika, “Target acquisition modeling of forward-motion considerations for airborne reconnaissance over hostile territory,” Opt. Eng. 33, 3106–3117 (1994).
[CrossRef]

Savakis, A. E.

A. E. Savakis, H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2, 141–151 (1993).
[CrossRef] [PubMed]

Schafer, R. W.

A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 7.

Schalkoff, R. J.

R. J. Schalkoff, Digital Image Processing and Computer Vision (Wiley, New York, 1989).

Sheppard, J. G.

D. F. Mix, J. G. Sheppard, “Average correlation functions in on-line testing of linear systems,” IEEE Trans. Aerosp. Electron. Syst. AES-9, 665–669 (1973).
[CrossRef]

Som, S. C.

Tan, B. T. G.

H. Lim, K. C. Tan, B. T. G. Tan, “Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment,” CVGIP: Graph. Models Image Process. 53, 186–195 (1991).

Tan, K. C.

H. Lim, K. C. Tan, B. T. G. Tan, “Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment,” CVGIP: Graph. Models Image Process. 53, 186–195 (1991).

Tekalp, A. M.

G. Pavlovic, A. M. Tekalp, “Maximum likelihood parametric blur identification based on a continuous spatial domain model,” IEEE Trans. Image Process. 1, 496–504 (1992).
[CrossRef] [PubMed]

R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990).
[CrossRef]

Trussell, H. J.

A. E. Savakis, H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2, 141–151 (1993).
[CrossRef] [PubMed]

Yitzhaky, Y.

Y. Yitzhaky, N. S. Kopeika, “Identification of blur parameters from motion blurred images,” CVGIP: Graph. Models Image Process. 59, 310–320 (1997).

CVGIP: Graph. Models Image Process. (2)

H. Lim, K. C. Tan, B. T. G. Tan, “Edge errors in inverse and Wiener filter restorations of motion-blurred images and their windowing treatment,” CVGIP: Graph. Models Image Process. 53, 186–195 (1991).

Y. Yitzhaky, N. S. Kopeika, “Identification of blur parameters from motion blurred images,” CVGIP: Graph. Models Image Process. 59, 310–320 (1997).

IEEE Trans. Acoust. Speech Signal Process. (1)

M. Cannon, “Blind deconvolution of spatially invariant image blurs with phase,” IEEE Trans. Acoust. Speech Signal Process. ASSP-24, 58–63 (1976).
[CrossRef]

IEEE Trans. Aerosp. Electron. Syst. (1)

D. F. Mix, J. G. Sheppard, “Average correlation functions in on-line testing of linear systems,” IEEE Trans. Aerosp. Electron. Syst. AES-9, 665–669 (1973).
[CrossRef]

IEEE Trans. Image Process. (2)

G. Pavlovic, A. M. Tekalp, “Maximum likelihood parametric blur identification based on a continuous spatial domain model,” IEEE Trans. Image Process. 1, 496–504 (1992).
[CrossRef] [PubMed]

A. E. Savakis, H. J. Trussell, “Blur identification by residual spectral matching,” IEEE Trans. Image Process. 2, 141–151 (1993).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (1)

Opt. Eng. (3)

O. Hadar, S. R. Rotman, N. S. Kopeika, “Target acquisition modeling of forward-motion considerations for airborne reconnaissance over hostile territory,” Opt. Eng. 33, 3106–3117 (1994).
[CrossRef]

O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibrations. Part IV: real-time numerical calculation of optical transfer function and experimental verification,” Opt. Eng. 33, 566–578 (1994).
[CrossRef]

R. L. Lagendijk, A. M. Tekalp, J. Biemond, “Maximum likelihood image and blur identification: a unifying approach,” Opt. Eng. 29, 422–435 (1990).
[CrossRef]

Other (8)

R. J. Schalkoff, Digital Image Processing and Computer Vision (Wiley, New York, 1989).

A. V. Oppenheim, R. W. Schafer, Digital Signal Processing (Prentice-Hall, Englewood Cliffs, N.J., 1975), Chap. 7.

B. Gold, C. M. Rader, Digital Processing of Signals (McGraw-Hill, New York, 1969).

M. Bellanger, Digital Processing of Signals (Wiley, New York, 1984).

A. K. Katsaggelos, ed., Digital Image Restoration (Springer-Verlag, New York, 1991).

A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).

M. P. Ekstrom, ed., Digital Image Processing Techniques (Academic, Orlando, Fla., 1984).

A. Rosenfeld, A. C. Kak, Digital Picture Processing (Academic, New York, 1982), Vol. 2.

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Figures (13)

Fig. 1
Fig. 1

Image of the Earth horizontally blurred by accelerated motion with 20-pixel blur extent and different values of R.

Fig. 2
Fig. 2

Average of the autocorrelation functions of the blurred Earth image derivative lines in the motion direction for different values of R.

Fig. 3
Fig. 3

Comparison of the identified and true power spectra of acceleration motion blur PSF’s: (a) identified power spectra obtained by Fourier-transforming the ACF’s of Fig. 2, (b) true power spectra.

Fig. 4
Fig. 4

Blur function identification: (a) original image, (b) image blurred by accelerated motion with R=10 and 20-pixel blur extent, (c) true versus identified MTF, (d) true versus identified phase.

Fig. 5
Fig. 5

(a) True versus identified PSF, (b) restored image with use of the identified OTF.

Fig. 6
Fig. 6

Blur function identification from a noisy blurred image: (a) original image, (b) image blurred by accelerated motion with R =10 and 20-pixel blur extent and an additive noise forming a 30-dB signal-to-noise ratio, (c) true versus identified MTF, (d) true versus identified phase.

Fig. 7
Fig. 7

(a) True versus identified PSF, (b) restored image with use of the identified OTF.

Fig. 8
Fig. 8

Picture taken from a moving car.

Fig. 9
Fig. 9

(a) Identified MTF of the motion blur, (b) identified PTF of the motion blur.

Fig. 10
Fig. 10

Restored image with use of the identified OTF.

Fig. 11
Fig. 11

Picture taken from a moving car.

Fig. 12
Fig. 12

(a) Identified MTF, (b) identified PTF.

Fig. 13
Fig. 13

Restored image with use of the identified OTF.

Equations (12)

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

g(i, j)=mnh(i-m, j-n)f(m, n)+n(i, j),
OTF=MTF exp(j PTF),
[Δf(i, j)]k°=f(i, j) * d(i, j),
d(i, j)=-11-tan(k)0tan(k)
[I(Δg)]k°=1N-11M-1[Δg(i, j)]k°,
Rl(j)=i=-MMl(i+j)l(i),integerj[-M, M],
S¯Δf(u)SdPSF(u),
SdPSF(u)=|OTF(u)D(u)|2,
MTF(u)S¯Δf(u)/|D(u)|.
PTF(u)=-12π02π ln[MTF(α)]cotu-α2dα.
LSF(x)=1te(ν02+2ax)1/2,
R=ν02/a

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