Abstract

In this paper, we present a simple and effective scene-based nonuniformity correction (NUC) method for infrared focal plane arrays based on interframe registration. This method estimates the global translation between two adjacent frames and minimizes the mean square error between the two properly registered images to make any two detectors with the same scene produce the same output value. In this way, the accumulation of the registration error can be avoided and the NUC can be achieved. The advantages of the proposed algorithm lie in its low computational complexity and storage requirements and ability to capture temporal drifts in the nonuniformity parameters. The performance of the proposed technique is thoroughly studied with infrared image sequences with simulated nonuniformity and infrared imagery with real nonuniformity. It shows a significantly fast and reliable fixed-pattern noise reduction and obtains an effective frame-by-frame adaptive estimation of each detector’s gain and offset.

© 2011 Optical Society of America

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References

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  1. D. A. Scribner, M. Kruer, and J. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
    [CrossRef]
  2. D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
    [CrossRef]
  3. A. Friedenberg and I. Goldbatt, “Nonuniformity two-point linear correction errors in infrared focal plane arrays,” Opt. Eng. 37, 1251-1253 (1998).
    [CrossRef]
  4. E. Gurevich and A. Fein, “Maintaining uniformity of IR focal plane arrays by updating offset correction coefficients,” Proc. SPIE 4820, 809-820 (2003).
    [CrossRef]
  5. M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763-777 (1995).
    [CrossRef]
  6. O. Riou, S. Berrebi, and P. Bremond, “Nonuniformity correction and thermal drift compensation of thermal infrared camera,” Proc. SPIE 5405, 294-302 (2004).
    [CrossRef]
  7. D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
    [CrossRef]
  8. J. G. Harris and Y. M. Chiang, “Nonuniformity correction using constant-statistics constraint: analog and digital implementations,” Proc. SPIE 3061, 895-905 (1997).
    [CrossRef]
  9. D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
    [CrossRef]
  10. S. N. Torres, R. A. Reeves, and M. M. Hayat, “Scene-based nonuniformity correction method using constant-range: performance and analysis,” in Proceedings of 6th World Multiconference on Systemics, Cybernetics and Informatics (2002), pp. 224-229
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [PubMed]
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    [CrossRef]
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    [CrossRef]
  16. C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
    [CrossRef]
  17. R. Hardie, F. Baxley, B. Brys, and P. Hytla, “Scene-based nonuniformity correction with reduced ghosting using a gated LMS algorithm,” Opt. Express 17, 14918-14933 (2009).
    [CrossRef] [PubMed]
  18. J. Harris and Y. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
    [CrossRef]
  19. D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859(1993).
    [CrossRef]
  20. C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference of the Cybernetics Society (1975), pp. 163-165.
  21. B. Marcel, M. Briot, and R. Murrieta, “Calcul de translation et rotation par la transformation de Fourier,” Traitement du Signal 14, 135-149 (1997).
  22. M. Guizar-Sicairos, S. T. Thurman, and J. R. Fienup, “Efficient subpixel image registration algorithms,” Opt. Lett. 33, 156-158(2008).
    [CrossRef] [PubMed]

2011 (1)

C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
[CrossRef]

2009 (1)

2008 (1)

2004 (1)

O. Riou, S. Berrebi, and P. Bremond, “Nonuniformity correction and thermal drift compensation of thermal infrared camera,” Proc. SPIE 5405, 294-302 (2004).
[CrossRef]

2003 (3)

2002 (1)

2000 (1)

1998 (2)

A. Friedenberg and I. Goldbatt, “Nonuniformity two-point linear correction errors in infrared focal plane arrays,” Opt. Eng. 37, 1251-1253 (1998).
[CrossRef]

J. Harris and Y. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

1997 (2)

B. Marcel, M. Briot, and R. Murrieta, “Calcul de translation et rotation par la transformation de Fourier,” Traitement du Signal 14, 135-149 (1997).

J. G. Harris and Y. M. Chiang, “Nonuniformity correction using constant-statistics constraint: analog and digital implementations,” Proc. SPIE 3061, 895-905 (1997).
[CrossRef]

1995 (1)

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

1993 (1)

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859(1993).
[CrossRef]

1991 (2)

D. A. Scribner, M. Kruer, and J. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

1990 (1)

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

Armstrong, E. E.

Baxley, F.

Berrebi, S.

O. Riou, S. Berrebi, and P. Bremond, “Nonuniformity correction and thermal drift compensation of thermal infrared camera,” Proc. SPIE 5405, 294-302 (2004).
[CrossRef]

Bremond, P.

O. Riou, S. Berrebi, and P. Bremond, “Nonuniformity correction and thermal drift compensation of thermal infrared camera,” Proc. SPIE 5405, 294-302 (2004).
[CrossRef]

Briot, M.

B. Marcel, M. Briot, and R. Murrieta, “Calcul de translation et rotation par la transformation de Fourier,” Traitement du Signal 14, 135-149 (1997).

Brys, B.

Caldfield, J.

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Caldwell, L.

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

Caulfield, J.

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

Chen, Q.

C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
[CrossRef]

Chiang, Y.

J. Harris and Y. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

Chiang, Y. M.

J. G. Harris and Y. M. Chiang, “Nonuniformity correction using constant-statistics constraint: analog and digital implementations,” Proc. SPIE 3061, 895-905 (1997).
[CrossRef]

Colbert, M.

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Dereniak, E. L.

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859(1993).
[CrossRef]

Descour, M.

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Fein, A.

E. Gurevich and A. Fein, “Maintaining uniformity of IR focal plane arrays by updating offset correction coefficients,” Proc. SPIE 4820, 809-820 (2003).
[CrossRef]

Fienup, J. R.

Friedenberg, A.

A. Friedenberg and I. Goldbatt, “Nonuniformity two-point linear correction errors in infrared focal plane arrays,” Opt. Eng. 37, 1251-1253 (1998).
[CrossRef]

Goldbatt, I.

A. Friedenberg and I. Goldbatt, “Nonuniformity two-point linear correction errors in infrared focal plane arrays,” Opt. Eng. 37, 1251-1253 (1998).
[CrossRef]

Gridley, C.

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

Gu, G.

C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
[CrossRef]

Guizar-Sicairos, M.

Gurevich, E.

E. Gurevich and A. Fein, “Maintaining uniformity of IR focal plane arrays by updating offset correction coefficients,” Proc. SPIE 4820, 809-820 (2003).
[CrossRef]

Hardie, R.

Hardie, R. C.

Harris, J.

J. Harris and Y. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

Harris, J. G.

J. G. Harris and Y. M. Chiang, “Nonuniformity correction using constant-statistics constraint: analog and digital implementations,” Proc. SPIE 3061, 895-905 (1997).
[CrossRef]

Hayat, M. M.

Hines, D. C.

C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference of the Cybernetics Society (1975), pp. 163-165.

Hunt, J.

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Hytla, P.

Katz, G.

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

Killiany, J.

D. A. Scribner, M. Kruer, and J. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

Kruer, M.

D. A. Scribner, M. Kruer, and J. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Kuglin, C. D.

C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference of the Cybernetics Society (1975), pp. 163-165.

Marcel, B.

B. Marcel, M. Briot, and R. Murrieta, “Calcul de translation et rotation par la transformation de Fourier,” Traitement du Signal 14, 135-149 (1997).

Murrieta, R.

B. Marcel, M. Briot, and R. Murrieta, “Calcul de translation et rotation par la transformation de Fourier,” Traitement du Signal 14, 135-149 (1997).

O'Neil, W. F.

W. F. O'Neil, “Dithered scan detector compensation,” in Proceedings of the 1993 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, 1993).
[PubMed]

Perry, D. L.

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859(1993).
[CrossRef]

Pezoa, J. E.

Qian, W.

C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
[CrossRef]

Ratliff, B. M.

Reeves, R. A.

S. N. Torres, R. A. Reeves, and M. M. Hayat, “Scene-based nonuniformity correction method using constant-range: performance and analysis,” in Proceedings of 6th World Multiconference on Systemics, Cybernetics and Informatics (2002), pp. 224-229

Riou, O.

O. Riou, S. Berrebi, and P. Bremond, “Nonuniformity correction and thermal drift compensation of thermal infrared camera,” Proc. SPIE 5405, 294-302 (2004).
[CrossRef]

Sarkady, K.

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Schulz, M.

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

Scribner, D.

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

Scribner, D. A.

D. A. Scribner, M. Kruer, and J. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

Thurman, S. T.

Torres, S. N.

Yasuda, B.

Zuo, C.

C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
[CrossRef]

Appl. Opt. (2)

Infrared Phys. Technol. (1)

M. Schulz and L. Caldwell, “Nonuniformity correction and correctability of infrared focal plane arrays,” Infrared Phys. Technol. 36, 763-777 (1995).
[CrossRef]

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

Opt. Eng. (2)

D. L. Perry and E. L. Dereniak, “Linear theory of nonuniformity correction in infrared staring sensors,” Opt. Eng. 32, 1854-1859(1993).
[CrossRef]

A. Friedenberg and I. Goldbatt, “Nonuniformity two-point linear correction errors in infrared focal plane arrays,” Opt. Eng. 37, 1251-1253 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Opt. Rev. (1)

C. Zuo, Q. Chen, G. Gu, and W. Qian, “New temporal high-pass filter nonuniformity correction based on bilateral filter,” Opt. Rev. 18, 197-202 (2011).
[CrossRef]

Proc. IEEE (1)

D. A. Scribner, M. Kruer, and J. Killiany, “Infrared focal plane array technology,” Proc. IEEE 79, 66-85 (1991).
[CrossRef]

Proc. SPIE (6)

D. Scribner, K. Sarkady, J. Caulfield, M. Kruer, G. Katz, and C. Gridley, “Non-uniformity correction for staring focal plane arrays using scene-based techniques,” Proc. SPIE 1308, 224-233(1990).
[CrossRef]

E. Gurevich and A. Fein, “Maintaining uniformity of IR focal plane arrays by updating offset correction coefficients,” Proc. SPIE 4820, 809-820 (2003).
[CrossRef]

O. Riou, S. Berrebi, and P. Bremond, “Nonuniformity correction and thermal drift compensation of thermal infrared camera,” Proc. SPIE 5405, 294-302 (2004).
[CrossRef]

J. G. Harris and Y. M. Chiang, “Nonuniformity correction using constant-statistics constraint: analog and digital implementations,” Proc. SPIE 3061, 895-905 (1997).
[CrossRef]

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive nonuniformity correction for IR focal plane arrays using neural networks,” Proc. SPIE 1541, 100-109 (1991).
[CrossRef]

J. Harris and Y. Chiang, “Minimizing the 'ghosting' artifact in scene-based nonuniformity correction,” Proc. SPIE 3377, 106-113 (1998).
[CrossRef]

Traitement du Signal (1)

B. Marcel, M. Briot, and R. Murrieta, “Calcul de translation et rotation par la transformation de Fourier,” Traitement du Signal 14, 135-149 (1997).

Other (4)

C. D. Kuglin and D. C. Hines, “The phase correlation image alignment method,” in Proceedings of the International Conference of the Cybernetics Society (1975), pp. 163-165.

W. F. O'Neil, “Dithered scan detector compensation,” in Proceedings of the 1993 International Meeting of the Infrared Information Symposium Specialty Group on Passive Sensors (Infrared Information Analysis Center, 1993).
[PubMed]

S. N. Torres, R. A. Reeves, and M. M. Hayat, “Scene-based nonuniformity correction method using constant-range: performance and analysis,” in Proceedings of 6th World Multiconference on Systemics, Cybernetics and Informatics (2002), pp. 224-229

D. Scribner, K. Sarkady, M. Kruer, J. Caldfield, J. Hunt, M. Colbert, and M. Descour, “Adaptive retina-like preprocessing for imaging detector arrays,” in Proceedings of the IEEE International Conference on Neural Networks (Institute of Electrical and Electronics Engineers, 1993), pp. 1955-1960.
[CrossRef]

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Figures (13)

Fig. 1
Fig. 1

Schematic diagram of the overlay of two frames.

Fig. 2
Fig. 2

Block diagram of the proposed algorithm.

Fig. 3
Fig. 3

Mean absolute error of translation estimates for various levels of gain and offset nonuniformity in an 8   bit gray-scale image.

Fig. 4
Fig. 4

RMSE versus frame number using different learning rates.

Fig. 5
Fig. 5

Relationship between RMSE and average displacement d (after 300 times iteration, learning rate a = 0.05 ).

Fig. 6
Fig. 6

PSNR results of the synthetic noisy test sequence corrected using different NUC methods.

Fig. 7
Fig. 7

(Media 1) Simulated nonuniformity image results. (a) Image with simulated gain and offset nonuniformity ( PSNR = 23.6 dB ). (b) Corrected with GALMS 3 × 3 ( PSNR = 36.6 dB ). (c) Corrected with GALMS 21 × 21 ( PSNR = 34.7 dB ). (d) Corrected with MCA ( PSNR = 36.4 dB ). (e)  Corrected with IRLMS ( PSNR = 38.3 dB ).

Fig. 8
Fig. 8

Error images for (a) GALMS 3 × 3 ; (b) GALMS 21 × 21 ; (c) MCA; (d) IRLMS. All images are scaled to the same display range.

Fig. 9
Fig. 9

Sample images of the two test sequences. (a) Frame 1 of the first test sequence. (b) Frame 1 of the second test sequence.

Fig. 10
Fig. 10

(Media 2) NUC performance comparison of frame 50 of the first test sequence. (a) Unprocessed ( ρ = 2.059 × 10 3 ); (b) GALMS 3 × 3 ( ρ = 1.552 × 10 3 ); (c) GALMS 21 × 21 ( ρ = 1.419 × 10 3 ); (d) MCA ( ρ = 1.371 × 10 3 ); (e) IRLMS ( ρ = 1.355 × 10 3 ).

Fig. 11
Fig. 11

(Media 3) NUC performance comparison of frame 50 of the second test sequence. (a) Unprocessed ( ρ = 1.632 × 10 3 ); (b) GALMS 3 × 3 ( ρ = 1.251 × 10 3 ); (c) GALMS 21 × 21 ( ρ = 1.129 × 10 3 ); (d) MCA ( ρ = 0.971 × 10 3 ); (e) IRLMS ( ρ = 0.852 × 10 3 ).

Fig. 12
Fig. 12

(Media 2) NUC performance comparison of frame 150 of the first test sequence. (a) Unprocessed ( ρ = 1.769 × 10 3 ); (b) GALMS 3 × 3 ( ρ = 0.997 × 10 3 ); (c) GALMS 21 × 21 ( ρ = 0.929 × 10 3 ); (d) MCA ( ρ = 0.871 × 10 3 ); (e) IRLMS ( ρ = 0.855 × 10 3 ).

Fig. 13
Fig. 13

(Media 3) NUC performance comparison of frame 230 of the second test sequence. (a) Unprocessed ( ρ = 1.629 × 10 3 ); (b) GALMS 3 × 3 ( ρ = 0.677 × 10 3 ); (c) GALMS 21 × 21 ( ρ = 0.609 × 10 3 ); (d) MCA ( ρ = 0.681 × 10 3 ); (e) IRLMS ( ρ = 0.543 × 10 3 ).

Tables (2)

Tables Icon

Table 1 Average CPU Time Consumed per Frame for GALMS and IRLMS

Tables Icon

Table 2 Mean Roughness ρ ( × 10 3 ) Results for the Two Test Sequences

Equations (27)

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

Y n ( i , j ) = g n ( i , j ) · X n ( i , j ) + o n ( i , j ) .
X n ( i , j ) = w n ( i , j ) · Y n ( i , j ) + b n ( i , j ) ,
w n ( i , j ) = 1 g n ( i , j ) ,
b n ( i , j ) = o n ( i , j ) g n ( i , j ) .
f 2 ( x , y ) = f 1 ( x x 0 , y y 0 ) .
c ^ ( u , v ) = F 2 ( u , v ) F 1 * ( u , v ) | F 2 ( u , v ) F 1 * ( u , v ) | = e 2 π j ( u x 0 + v y 0 ) ,
( d i , d j ) = argmax i , j Re { FFT 1 ( Y ¯ n ( u , v ) · Y ¯ n 1 * ( u , v ) | Y ¯ n ( u , v ) · Y ¯ n 1 * ( u , v ) | ) } ,
Y n ( i , j ) = Y n 1 ( i d i , j d j ) = FFT 1 ( Y ¯ n 1 ( u , v ) e 2 π j ( u d i + v d j ) ) .
e n ( i , j ) = X ^ n 1 ( i d i , j d j ) X ^ n ( i , j ) .
e n ( i , j ) = T n ( i , j ) ( w n ( i , j ) · Y n ( i , j ) + b n ( i , j ) ) ,
T n ( i , j ) = FFT 1 ( X ^ ¯ n 1 ( u , v ) e 2 π j ( u d i + v d j ) ) .
e n ( i , j ) = ( w n ( i d i , j d j ) · Y n 1 ( i d i , j d j ) + b n ( i d i , j d j ) ) ( w n ( i , j ) · Y n ( i , j ) + b n ( i , j ) ) .
J ( i , j ) = n e n ( i , j ) 2 = n ( T n ( i , j ) ( w n ( i , j ) · Y n ( i , j ) + b n ( i , j ) ) ) 2 ,
w n + 1 ( i , j ) = { w n ( i , j ) + a · e n ( i , j ) · Y n ( i , j ) when pixel ( i , j ) is in the overlapped area w n ( i , j ) other ,
b n + 1 ( i , j ) = { b n ( i , j ) + a · e n ( i , j ) when pixel ( i , j ) is in the overlapped area b n ( i , j ) other ,
J ( i , j ) = n e n ( i , j ) 2 = n ( ( w n ( i d i , j d j ) · Y n 1 ( i d i , j d j ) + b n ( i d i , j d j ) ) ( w n ( i , j ) · Y n ( i , j ) + b n ( i , j ) ) ) 2 .
J ( i , j ) = n ( ( w n ( i d i , j d j ) · g n 1 ( i d i , j d j ) · X n 1 ( i d i , j d j ) + w n ( i d i , j d j ) o n 1 ( i d i , j d j ) + b n ( i d i , j d j ) ) ( w n ( i , j ) · g n ( i , j ) · X n ( i , j ) + w n ( i , j ) · o n ( i , j ) + b n ( i , j ) ) ) 2 .
X n 1 ( i d i , j d j ) = X n ( i , j ) .
w n ( i d i , j d j ) · g n 1 ( i d i , j d j ) = w n ( i , j ) · g n ( i , j ) , w n ( i d i , j d j ) · o n 1 ( i d i , j d j ) + b n ( i d i , j d j ) = w n ( i , j ) · o n ( i , j ) + b n ( i , j ) .
w n ( i , j ) · g n ( i , j ) = w n ( k , l ) · g n ( k , l ) , w n ( i , j ) · o n ( i , j ) + b n ( i , j ) = w n ( k , l ) · o n ( k , l ) + b n ( k , l ) , i , j , k , l Z , i , l M , j , k N .
w n ( i , j ) · g n ( i , j ) = 1 , w n ( i , j ) · o n ( i , j ) + b n ( i , j ) = 0 , i , j Z , i M , j N .
w n ( i , j ) = 1 g n ( i , j ) , b n ( i , j ) = o n ( i , j ) g n ( i , j ) .
RMSE = 1 M · N i , j ( X ( i , j ) X ^ ( i , j ) ) 2 ,
e n ( i , j ) = X ^ n k ( i d i , j d j ) X ^ n ( i , j ) .
d = n = 1 m d i ( n ) 2 + d j ( n ) 2 m ,
PSNR = 20 log 10 ( 2 b 1 RMSE ) ,
ρ = h 1 * I 1 + h 2 * I 1 I 1 ,

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