Abstract

Image motion causes a blur that changes features of objects and therefore complicates the task of automatic recognition. In this work we develop two recognition methods for motion-blurred images. For the first method we assume that the motion function and direction during the exposure are given. We develop the relation between the blurred-image moments and the original-image moments based on the motion function only. The recognition is carried out by comparing the moments of the restored image against the moments of the image database. In the second method the motion function is not known. In this case image moments that are invariant with respect to the motion blur are identified, and only these moments are used for recognition. The advantage of the suggested methods is that no time-consuming image restoration is required prior to recognition.

© 2002 Optical Society of America

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References

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  1. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Optical Engineering Press, Bellingham, Wash., 1998) Chap. 18.
  2. A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments and its implementation in image restoration,” in Digital Image Recovery and Synthesis III, P. S. Idell, T. J. Schultz, eds., Proc. SPIE2827, 191–202 (1996).
    [CrossRef]
  3. A. K. Jain, Fundamentals of Digital Image Processing (Prentice-Hall, Englewood Cliffs, N.J., 1989).
  4. M. Sonka, V. Hlavac, R. Boyle, Image Processing, Analysis and Machine Vision (Chapman & Hall, London, 1993).
    [CrossRef]
  5. R. L. Lagendijk, Iterative Identification and Restoration of Images (Kluwer Academic Publishers, Boston, 1991).
    [CrossRef]
  6. S. Dudani, K. Breeding, R. McGhee, “Aircraft identification by moment invariants,” IEEE Trans. Comput. 1, 39–45 (1977).
    [CrossRef]
  7. M. K. Hu, “Visual pattern recognition by moment invariants,” in Computer Methods in Image Analysis, J. K. Aggarwal, R. O. Duda, A. Rosenfeld, eds. (IEEE Computer Society, Los Angeles, 1977).
  8. R. Wong, E. Hall, “Scene matching with moment invariants,” Comput. Graph. Image Process. 8, 16–24 (1978).
    [CrossRef]
  9. D. Casasent, D. Psaltis, “Hybrid processor to compute invariant moments for pattern recognition,” J. Opt. Soc. Am. 5, 395–397 (1980).
  10. J. Flusser, T. Suk, S. Saic, “Recognition of blurred images by the method of moments,” IEEE Trans. on Im. Proc. 5, 533–538 (1996).
    [CrossRef]
  11. Y. Ytzhaky, I. Mor, A. Lantzman, N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A 15, 1512–1519 (1998).
    [CrossRef]
  12. K. J. Barnard, C. E. White, A. E. Absi, “Two-dimensional restoration of motion-degraded intensified CCD imagery,” Appl. Opt. 38, 1942–1952 (1999).
    [CrossRef]
  13. O. Hadar, I. Dror, N. S. Kopeika, “Image resolution limits resulting from mechanical vibration, part IV: real time numerical calculation of optical transfer functions and experimental verification,” Opt. Eng. 33, 566–578 (1994).
    [CrossRef]
  14. N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Optical Engineering, Bellingham, Wash., 1998) Chap. 14.
  15. J. Teuber, Digital Image Processing (Prentice-Hall, New York, 1993), pp. 213–216.
  16. A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments,” J. Opt. Soc. Am. A 14, 388–396 (1997).
    [CrossRef]

1999 (1)

1998 (1)

1997 (1)

1996 (1)

J. Flusser, T. Suk, S. Saic, “Recognition of blurred images by the method of moments,” IEEE Trans. on Im. Proc. 5, 533–538 (1996).
[CrossRef]

1994 (1)

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

1980 (1)

D. Casasent, D. Psaltis, “Hybrid processor to compute invariant moments for pattern recognition,” J. Opt. Soc. Am. 5, 395–397 (1980).

1978 (1)

R. Wong, E. Hall, “Scene matching with moment invariants,” Comput. Graph. Image Process. 8, 16–24 (1978).
[CrossRef]

1977 (1)

S. Dudani, K. Breeding, R. McGhee, “Aircraft identification by moment invariants,” IEEE Trans. Comput. 1, 39–45 (1977).
[CrossRef]

Absi, A. E.

Barnard, K. J.

Boyle, R.

M. Sonka, V. Hlavac, R. Boyle, Image Processing, Analysis and Machine Vision (Chapman & Hall, London, 1993).
[CrossRef]

Breeding, K.

S. Dudani, K. Breeding, R. McGhee, “Aircraft identification by moment invariants,” IEEE Trans. Comput. 1, 39–45 (1977).
[CrossRef]

Casasent, D.

D. Casasent, D. Psaltis, “Hybrid processor to compute invariant moments for pattern recognition,” J. Opt. Soc. Am. 5, 395–397 (1980).

Dror, I.

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

Dudani, S.

S. Dudani, K. Breeding, R. McGhee, “Aircraft identification by moment invariants,” IEEE Trans. Comput. 1, 39–45 (1977).
[CrossRef]

Flusser, J.

J. Flusser, T. Suk, S. Saic, “Recognition of blurred images by the method of moments,” IEEE Trans. on Im. Proc. 5, 533–538 (1996).
[CrossRef]

Hadar, O.

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

Hall, E.

R. Wong, E. Hall, “Scene matching with moment invariants,” Comput. Graph. Image Process. 8, 16–24 (1978).
[CrossRef]

Hlavac, V.

M. Sonka, V. Hlavac, R. Boyle, Image Processing, Analysis and Machine Vision (Chapman & Hall, London, 1993).
[CrossRef]

Hu, M. K.

M. K. Hu, “Visual pattern recognition by moment invariants,” in Computer Methods in Image Analysis, J. K. Aggarwal, R. O. Duda, A. Rosenfeld, eds. (IEEE Computer Society, Los Angeles, 1977).

Jain, A. K.

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

Kopeika, N. S.

Y. Ytzhaky, I. Mor, A. Lantzman, N. S. Kopeika, “Direct method for restoration of motion-blurred images,” J. Opt. Soc. Am. A 15, 1512–1519 (1998).
[CrossRef]

A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments,” J. Opt. Soc. Am. A 14, 388–396 (1997).
[CrossRef]

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

A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments and its implementation in image restoration,” in Digital Image Recovery and Synthesis III, P. S. Idell, T. J. Schultz, eds., Proc. SPIE2827, 191–202 (1996).
[CrossRef]

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Optical Engineering Press, Bellingham, Wash., 1998) Chap. 18.

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Optical Engineering, Bellingham, Wash., 1998) Chap. 14.

Lagendijk, R. L.

R. L. Lagendijk, Iterative Identification and Restoration of Images (Kluwer Academic Publishers, Boston, 1991).
[CrossRef]

Lantzman, A.

McGhee, R.

S. Dudani, K. Breeding, R. McGhee, “Aircraft identification by moment invariants,” IEEE Trans. Comput. 1, 39–45 (1977).
[CrossRef]

Mor, I.

Psaltis, D.

D. Casasent, D. Psaltis, “Hybrid processor to compute invariant moments for pattern recognition,” J. Opt. Soc. Am. 5, 395–397 (1980).

Saic, S.

J. Flusser, T. Suk, S. Saic, “Recognition of blurred images by the method of moments,” IEEE Trans. on Im. Proc. 5, 533–538 (1996).
[CrossRef]

Sonka, M.

M. Sonka, V. Hlavac, R. Boyle, Image Processing, Analysis and Machine Vision (Chapman & Hall, London, 1993).
[CrossRef]

Stern, A.

A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments,” J. Opt. Soc. Am. A 14, 388–396 (1997).
[CrossRef]

A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments and its implementation in image restoration,” in Digital Image Recovery and Synthesis III, P. S. Idell, T. J. Schultz, eds., Proc. SPIE2827, 191–202 (1996).
[CrossRef]

Suk, T.

J. Flusser, T. Suk, S. Saic, “Recognition of blurred images by the method of moments,” IEEE Trans. on Im. Proc. 5, 533–538 (1996).
[CrossRef]

Teuber, J.

J. Teuber, Digital Image Processing (Prentice-Hall, New York, 1993), pp. 213–216.

White, C. E.

Wong, R.

R. Wong, E. Hall, “Scene matching with moment invariants,” Comput. Graph. Image Process. 8, 16–24 (1978).
[CrossRef]

Ytzhaky, Y.

Appl. Opt. (1)

Comput. Graph. Image Process. (1)

R. Wong, E. Hall, “Scene matching with moment invariants,” Comput. Graph. Image Process. 8, 16–24 (1978).
[CrossRef]

IEEE Trans. Comput. (1)

S. Dudani, K. Breeding, R. McGhee, “Aircraft identification by moment invariants,” IEEE Trans. Comput. 1, 39–45 (1977).
[CrossRef]

IEEE Trans. on Im. Proc. (1)

J. Flusser, T. Suk, S. Saic, “Recognition of blurred images by the method of moments,” IEEE Trans. on Im. Proc. 5, 533–538 (1996).
[CrossRef]

J. Opt. Soc. Am. (1)

D. Casasent, D. Psaltis, “Hybrid processor to compute invariant moments for pattern recognition,” J. Opt. Soc. Am. 5, 395–397 (1980).

J. Opt. Soc. Am. A (2)

Opt. Eng. (1)

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

Other (8)

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Optical Engineering, Bellingham, Wash., 1998) Chap. 14.

J. Teuber, Digital Image Processing (Prentice-Hall, New York, 1993), pp. 213–216.

M. K. Hu, “Visual pattern recognition by moment invariants,” in Computer Methods in Image Analysis, J. K. Aggarwal, R. O. Duda, A. Rosenfeld, eds. (IEEE Computer Society, Los Angeles, 1977).

N. S. Kopeika, A System Engineering Approach to Imaging (SPIE Optical Engineering Press, Bellingham, Wash., 1998) Chap. 18.

A. Stern, N. S. Kopeika, “Analytical method to calculate optical transfer function for image motion and vibration using moments and its implementation in image restoration,” in Digital Image Recovery and Synthesis III, P. S. Idell, T. J. Schultz, eds., Proc. SPIE2827, 191–202 (1996).
[CrossRef]

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

M. Sonka, V. Hlavac, R. Boyle, Image Processing, Analysis and Machine Vision (Chapman & Hall, London, 1993).
[CrossRef]

R. L. Lagendijk, Iterative Identification and Restoration of Images (Kluwer Academic Publishers, Boston, 1991).
[CrossRef]

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Figures (9)

Fig. 1
Fig. 1

(a) Motion trajectory, (b) motion function S(t) in s direction, (c) motion PSF.

Fig. 2
Fig. 2

Image database.

Fig. 3
Fig. 3

Sixth image of the database in Fig. 2 (Pajama Cardinal fish) blurred by the motion function S(t) = (1000t,0) pixels and exposure time t e = 20 msec.

Fig. 4
Fig. 4

Distance ρ (on logarithmic scale) between the sixth unknown image (Fig. 3) and the i = 1 … N images of the database (Fig. 2).

Fig. 5
Fig. 5

Image No. 7 of the database (Piacasso fish) blurred by motion in the direction θ = -50°.

Fig. 6
Fig. 6

Log of the distance {log[ρ′(i)]} between the unknown observed image (image No. 7) and the nine images of the database (Fig. 2).

Fig. 7
Fig. 7

Six images of keys used as database that were used in the real experiment.

Fig. 8
Fig. 8

Keys in Fig. 7 blurred by manual motion.

Fig. 9
Fig. 9

(a) The log distance {log[ρ′(i)]} of the first three blurred images (Key #1, Key #2, Key #3) in Fig. 8 and each image of the database in Fig. 7, (b) the log distance {log[ρ′(i)]} between the last three blurred images (Key #4, Key #5, Key #6) and each image of the database.

Equations (13)

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

gx, y=fix, y*hx, y+nx, y,
hx, y=1tet0t0+te δx-sxt, y-sytdt,
μp,qg=i=0pj=0qpiqj μi,jhμp-i,q-jfi,
μp,qg=--x-m1,0gpy-m0,1gqgx, ydxdy,
m1,0g=-- xgx, ydxdy, m0,1g=-- ygx, ydxdy,
μp,qh=--x-m1,0hpy-m0,1hq1tet0t0+te×δx-sxt, y-sytdtdxdy =1tet0t0+tesxt-m1,0hpsyt-m0,1hqdtμp,qs
m1,0h=-- xsxtdxdy, m0,1h=-- ysytdxdy.
μp,qh=1tet0t0+testcos θ-m1,0hp×stsin θ-m0,1hqdt.
μˆ00fi=μ00gμ00s, μˆ10fi=μ10g-μ10sμˆ00fiμ00s, μˆ01fi=μ01g-μ01sμˆ00fiμ00s, μˆ11fi=μ11g-μ01sμˆ10fi-μ10sμˆ01fi-s11μˆ00fiμ00s, μˆ20fi=μ20g-2μ10sμˆ10fi-μ20sμˆ00fiμ00s, μˆ02fi=μ02g-2μ01sμˆ01fi-μ02sμˆ00fiμ00s, μˆ12fi=μ12g-2μ01sμˆ11fi-μ02sμˆ10fi-μ10sμˆ02fi-2μ1sμˆ01fi-μ12sμˆ00fiμ00s.
ρi=p,qMμˆpqfi/μˆ00fi-μpqfi/μ00fiμˆpqfi/μˆ00fi2 i=1N,
ηp,q=μp,qμ0,0γ, γ=p+q+2/2.
μp,qfi=r=0ps=0q-1k-sprqscos θp-r+s×sin θq+r-sμr+s,p+q-r-sfi.
ρi=q=2nμ0qg/μ00g-μp,qfi/μ00fiμ0qg/μ00g2 i=1N,

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