Abstract

Target tracking in forward-looking infrared (FLIR) video sequences is a challenging problem because of various limitations such as low signal-to-noise ratio (SNR), image blurring, partial occlusion, and low texture information, which often leads to missing targets or tracking nontarget objects. To alleviate these problems, we developed a novel algorithm that involves local-deviation-based image preprocessing as well as fringe-adjusted joint-transform-correlation- (FJTC) and template-matching- (TM) based target detection and tracking. The local-deviation-based preprocessing technique is used to suppress smooth texture such as background and to enhance target edge information. However, for complex situations such as the target blending with background, partial occlusion of the target, or proximity of the target to other similar nontarget objects, FJTC may produce a false alarm. For such cases, the TM-based detection technique is used to compensate FJTC breaking points by use of cross-correlation coefficients. Finally, a robust tracking algorithm is developed by use of both FJTC and TM techniques, which is called FJTC-TM technique. The performance of the proposed FJTC-TM algorithm is tested with real-life FLIR image sequences.

© 2004 Optical Society of America

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References

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  1. H. Shekarforoush, R. Chellappa, “A multi-fractal formalism for stabilization, object detection and tracking in FLIR sequences,” IEEE Int. Conf. Image Proc. 3, 78–81 (2000).
  2. J. Y. Chen, I. S. Reed, “A detection algorithm for optical targets in clutter,” IEEE Trans. Aerosp. Electron. Syst. 23, 46–59 (1987).
    [CrossRef]
  3. A. Yilmaz, K. Shafique, M. Shah, “Target tracking in airborne forward looking infrared imagery,” Image Vision Comput. 21, 623–635 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  7. M. S. Alam, D. Chain, “Efficient multiple target recognition using a wavelet transform processor,” Opt. Eng. 39, 1203–1210 (2000).
    [CrossRef]
  8. M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
    [CrossRef]
  9. M. S. Alam, “Phase-encoded fringe-adjusted joint transform correlation,” Opt. Eng. 39, 1169–1176 (2000).
    [CrossRef]
  10. M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
    [CrossRef]
  11. Y. Wu, T. S. Huang, “Non-stationary color tracking for vision-based human-computer interaction,” IEEE Trans. Neural Netw. 13, 948–960 (2002).
    [CrossRef]
  12. E. Oron, A. Kumar, Y. Barshalom, “Precision tracking with segmentation for imaging sensors,” IEEE Trans. Aerosp. Electron. Syst. 29, 977–987 (1993).
    [CrossRef]
  13. A. K. Rastogi, B. N. Chatterji, A. K. Ray, “Design of real-time tracking system for fast moving objects,” IETE J. Res. 43, 359–369 (1997).
  14. K. S. Gudmundsson, A. A. S. Awwal, “Sub-imaging technique to improve phase only filter search capability,” Appl. Opt. 42, 4709–4717 (2003).
    [CrossRef] [PubMed]
  15. K. Brunnstrom, B. N. Schenkman, B. Jacobson, “Object detection in cluttered infrared images,” Opt. Eng. 42, 388–399 (2003).
    [CrossRef]
  16. S. Sun, H. W. Park, “Automatic target recognition using boundary partitioning and invariant features in forward-looking infrared images,” Opt. Eng. 42, 524–533 (2003).
    [CrossRef]
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    [CrossRef] [PubMed]
  18. S. K. Rogers, J. D. Cline, M. Kabrisky, “New binarization techniques for joint transform correlation,” Opt. Eng. 29, 1018–1093 (1990).
  19. M. S. Alam, “Deblurring using fringe-adjusted joint transform correlation,” Opt. Eng. 37, 556–564 (1998).
    [CrossRef]
  20. M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
    [CrossRef]
  21. F. T. S. Yu, F. Cheng, T. Nagata, D. A. Gregory, “Effects of fringe binarization of multiobject joint transform correlation,” Appl. Opt. 28, 2988–2990 (1989).
    [CrossRef] [PubMed]
  22. B. V. K. V. Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
    [CrossRef] [PubMed]
  23. R. Singh, B. V. Kumar, “Performance of the extended maximum average correlation height (EMACH) filter and the polynomial distance classifier correlation filter (PDCCF) for multiclass SAR detection and classification,” in Algorithms for Synthetic Aperture Radar Imagery IX, E. G. Zelnio, ed., Proc. SPIE4727, 265–276 (2002).
    [CrossRef]
  24. A. Mahalanobis, A. R. Sims, A. V. Nevel, “Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis,” Opt. Eng. 42, 1144–1151 (2003).
    [CrossRef]

2003 (5)

A. Yilmaz, K. Shafique, M. Shah, “Target tracking in airborne forward looking infrared imagery,” Image Vision Comput. 21, 623–635 (2003).
[CrossRef]

K. Brunnstrom, B. N. Schenkman, B. Jacobson, “Object detection in cluttered infrared images,” Opt. Eng. 42, 388–399 (2003).
[CrossRef]

S. Sun, H. W. Park, “Automatic target recognition using boundary partitioning and invariant features in forward-looking infrared images,” Opt. Eng. 42, 524–533 (2003).
[CrossRef]

A. Mahalanobis, A. R. Sims, A. V. Nevel, “Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis,” Opt. Eng. 42, 1144–1151 (2003).
[CrossRef]

K. S. Gudmundsson, A. A. S. Awwal, “Sub-imaging technique to improve phase only filter search capability,” Appl. Opt. 42, 4709–4717 (2003).
[CrossRef] [PubMed]

2002 (1)

Y. Wu, T. S. Huang, “Non-stationary color tracking for vision-based human-computer interaction,” IEEE Trans. Neural Netw. 13, 948–960 (2002).
[CrossRef]

2000 (4)

M. S. Alam, D. Chain, “Efficient multiple target recognition using a wavelet transform processor,” Opt. Eng. 39, 1203–1210 (2000).
[CrossRef]

M. S. Alam, “Phase-encoded fringe-adjusted joint transform correlation,” Opt. Eng. 39, 1169–1176 (2000).
[CrossRef]

M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
[CrossRef]

H. Shekarforoush, R. Chellappa, “A multi-fractal formalism for stabilization, object detection and tracking in FLIR sequences,” IEEE Int. Conf. Image Proc. 3, 78–81 (2000).

1999 (1)

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

1998 (1)

M. S. Alam, “Deblurring using fringe-adjusted joint transform correlation,” Opt. Eng. 37, 556–564 (1998).
[CrossRef]

1997 (1)

A. K. Rastogi, B. N. Chatterji, A. K. Ray, “Design of real-time tracking system for fast moving objects,” IETE J. Res. 43, 359–369 (1997).

1994 (1)

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

1993 (3)

1992 (1)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

1990 (2)

S. K. Rogers, J. D. Cline, M. Kabrisky, “New binarization techniques for joint transform correlation,” Opt. Eng. 29, 1018–1093 (1990).

B. V. K. V. Kumar, L. Hassebrook, “Performance measures for correlation filters,” Appl. Opt. 29, 2997–3006 (1990).
[CrossRef] [PubMed]

1989 (1)

1988 (1)

1987 (1)

J. Y. Chen, I. S. Reed, “A detection algorithm for optical targets in clutter,” IEEE Trans. Aerosp. Electron. Syst. 23, 46–59 (1987).
[CrossRef]

Alam, M. S.

M. S. Alam, “Phase-encoded fringe-adjusted joint transform correlation,” Opt. Eng. 39, 1169–1176 (2000).
[CrossRef]

M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
[CrossRef]

M. S. Alam, D. Chain, “Efficient multiple target recognition using a wavelet transform processor,” Opt. Eng. 39, 1203–1210 (2000).
[CrossRef]

M. S. Alam, “Deblurring using fringe-adjusted joint transform correlation,” Opt. Eng. 37, 556–564 (1998).
[CrossRef]

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

Awwal, A. A. S.

Barshalom, Y.

E. Oron, A. Kumar, Y. Barshalom, “Precision tracking with segmentation for imaging sensors,” IEEE Trans. Aerosp. Electron. Syst. 29, 977–987 (1993).
[CrossRef]

Bognar, J. G.

M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
[CrossRef]

Brunnstrom, K.

K. Brunnstrom, B. N. Schenkman, B. Jacobson, “Object detection in cluttered infrared images,” Opt. Eng. 42, 388–399 (2003).
[CrossRef]

Chain, D.

M. S. Alam, D. Chain, “Efficient multiple target recognition using a wavelet transform processor,” Opt. Eng. 39, 1203–1210 (2000).
[CrossRef]

Chatterji, B. N.

A. K. Rastogi, B. N. Chatterji, A. K. Ray, “Design of real-time tracking system for fast moving objects,” IETE J. Res. 43, 359–369 (1997).

Chellappa, R.

H. Shekarforoush, R. Chellappa, “A multi-fractal formalism for stabilization, object detection and tracking in FLIR sequences,” IEEE Int. Conf. Image Proc. 3, 78–81 (2000).

Chen, J. Y.

J. Y. Chen, I. S. Reed, “A detection algorithm for optical targets in clutter,” IEEE Trans. Aerosp. Electron. Syst. 23, 46–59 (1987).
[CrossRef]

Cheng, F.

Cline, J. D.

S. K. Rogers, J. D. Cline, M. Kabrisky, “New binarization techniques for joint transform correlation,” Opt. Eng. 29, 1018–1093 (1990).

Fiebig, M.

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

Gregory, D. A.

Gudmundsson, K. S.

Hamlyn, G.

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

Hardie, R. C.

M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
[CrossRef]

Hassebrook, L.

Huang, T. S.

Y. Wu, T. S. Huang, “Non-stationary color tracking for vision-based human-computer interaction,” IEEE Trans. Neural Netw. 13, 948–960 (2002).
[CrossRef]

Jacobson, B.

K. Brunnstrom, B. N. Schenkman, B. Jacobson, “Object detection in cluttered infrared images,” Opt. Eng. 42, 388–399 (2003).
[CrossRef]

Javidi, B.

Kabrisky, M.

S. K. Rogers, J. D. Cline, M. Kabrisky, “New binarization techniques for joint transform correlation,” Opt. Eng. 29, 1018–1093 (1990).

Karim, M. A.

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

Kumar, A.

E. Oron, A. Kumar, Y. Barshalom, “Precision tracking with segmentation for imaging sensors,” IEEE Trans. Aerosp. Electron. Syst. 29, 977–987 (1993).
[CrossRef]

Kumar, B. V.

R. Singh, B. V. Kumar, “Performance of the extended maximum average correlation height (EMACH) filter and the polynomial distance classifier correlation filter (PDCCF) for multiclass SAR detection and classification,” in Algorithms for Synthetic Aperture Radar Imagery IX, E. G. Zelnio, ed., Proc. SPIE4727, 265–276 (2002).
[CrossRef]

Kumar, B. V. K. V.

Kuo, C.

Mahalanobis, A.

A. Mahalanobis, A. R. Sims, A. V. Nevel, “Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis,” Opt. Eng. 42, 1144–1151 (2003).
[CrossRef]

Miller, P. C.

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

Nagata, T.

Nevel, A. V.

A. Mahalanobis, A. R. Sims, A. V. Nevel, “Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis,” Opt. Eng. 42, 1144–1151 (2003).
[CrossRef]

Oron, E.

E. Oron, A. Kumar, Y. Barshalom, “Precision tracking with segmentation for imaging sensors,” IEEE Trans. Aerosp. Electron. Syst. 29, 977–987 (1993).
[CrossRef]

Park, H. W.

S. Sun, H. W. Park, “Automatic target recognition using boundary partitioning and invariant features in forward-looking infrared images,” Opt. Eng. 42, 524–533 (2003).
[CrossRef]

Rastogi, A. K.

A. K. Rastogi, B. N. Chatterji, A. K. Ray, “Design of real-time tracking system for fast moving objects,” IETE J. Res. 43, 359–369 (1997).

Ray, A. K.

A. K. Rastogi, B. N. Chatterji, A. K. Ray, “Design of real-time tracking system for fast moving objects,” IETE J. Res. 43, 359–369 (1997).

Reed, I. S.

J. Y. Chen, I. S. Reed, “A detection algorithm for optical targets in clutter,” IEEE Trans. Aerosp. Electron. Syst. 23, 46–59 (1987).
[CrossRef]

Rogers, S. K.

S. K. Rogers, J. D. Cline, M. Kabrisky, “New binarization techniques for joint transform correlation,” Opt. Eng. 29, 1018–1093 (1990).

Royce, M.

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

Schenkman, B. N.

K. Brunnstrom, B. N. Schenkman, B. Jacobson, “Object detection in cluttered infrared images,” Opt. Eng. 42, 388–399 (2003).
[CrossRef]

Shafique, K.

A. Yilmaz, K. Shafique, M. Shah, “Target tracking in airborne forward looking infrared imagery,” Image Vision Comput. 21, 623–635 (2003).
[CrossRef]

Shah, M.

A. Yilmaz, K. Shafique, M. Shah, “Target tracking in airborne forward looking infrared imagery,” Image Vision Comput. 21, 623–635 (2003).
[CrossRef]

Shekarforoush, H.

H. Shekarforoush, R. Chellappa, “A multi-fractal formalism for stabilization, object detection and tracking in FLIR sequences,” IEEE Int. Conf. Image Proc. 3, 78–81 (2000).

Sims, A. R.

A. Mahalanobis, A. R. Sims, A. V. Nevel, “Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis,” Opt. Eng. 42, 1144–1151 (2003).
[CrossRef]

Singh, R.

R. Singh, B. V. Kumar, “Performance of the extended maximum average correlation height (EMACH) filter and the polynomial distance classifier correlation filter (PDCCF) for multiclass SAR detection and classification,” in Algorithms for Synthetic Aperture Radar Imagery IX, E. G. Zelnio, ed., Proc. SPIE4727, 265–276 (2002).
[CrossRef]

Sun, S.

S. Sun, H. W. Park, “Automatic target recognition using boundary partitioning and invariant features in forward-looking infrared images,” Opt. Eng. 42, 524–533 (2003).
[CrossRef]

Tang, Q.

Virgo, P.

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

Wu, Y.

Y. Wu, T. S. Huang, “Non-stationary color tracking for vision-based human-computer interaction,” IEEE Trans. Neural Netw. 13, 948–960 (2002).
[CrossRef]

Yasuda, B. J.

M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
[CrossRef]

Yilmaz, A.

A. Yilmaz, K. Shafique, M. Shah, “Target tracking in airborne forward looking infrared imagery,” Image Vision Comput. 21, 623–635 (2003).
[CrossRef]

Yu, F. T. S.

Appl. Opt. (6)

IEEE Int. Conf. Image Proc. (1)

H. Shekarforoush, R. Chellappa, “A multi-fractal formalism for stabilization, object detection and tracking in FLIR sequences,” IEEE Int. Conf. Image Proc. 3, 78–81 (2000).

IEEE Trans. Aerosp. Electron. Syst. (2)

J. Y. Chen, I. S. Reed, “A detection algorithm for optical targets in clutter,” IEEE Trans. Aerosp. Electron. Syst. 23, 46–59 (1987).
[CrossRef]

E. Oron, A. Kumar, Y. Barshalom, “Precision tracking with segmentation for imaging sensors,” IEEE Trans. Aerosp. Electron. Syst. 29, 977–987 (1993).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

M. S. Alam, J. G. Bognar, R. C. Hardie, B. J. Yasuda, “Infrared image registration and high resolution reconstruction using multiple translationally shifted aliased video frames,” IEEE Trans. Instrum. Meas. 49, 915–923 (2000).
[CrossRef]

IEEE Trans. Neural Netw. (1)

Y. Wu, T. S. Huang, “Non-stationary color tracking for vision-based human-computer interaction,” IEEE Trans. Neural Netw. 13, 948–960 (2002).
[CrossRef]

IETE J. Res. (1)

A. K. Rastogi, B. N. Chatterji, A. K. Ray, “Design of real-time tracking system for fast moving objects,” IETE J. Res. 43, 359–369 (1997).

Image Vision Comput. (1)

A. Yilmaz, K. Shafique, M. Shah, “Target tracking in airborne forward looking infrared imagery,” Image Vision Comput. 21, 623–635 (2003).
[CrossRef]

Opt. Eng. (9)

S. K. Rogers, J. D. Cline, M. Kabrisky, “New binarization techniques for joint transform correlation,” Opt. Eng. 29, 1018–1093 (1990).

M. S. Alam, “Deblurring using fringe-adjusted joint transform correlation,” Opt. Eng. 37, 556–564 (1998).
[CrossRef]

P. C. Miller, M. Royce, P. Virgo, M. Fiebig, G. Hamlyn, “Evaluation of an optical correlator automatic target recognition system for acquisition and tracking in densely cluttered natural scenes,” Opt. Eng. 38, 1814–1825 (1999).
[CrossRef]

M. S. Alam, D. Chain, “Efficient multiple target recognition using a wavelet transform processor,” Opt. Eng. 39, 1203–1210 (2000).
[CrossRef]

M. S. Alam, M. A. Karim, “Multiple target detection using a modified fringe-adjusted joint transform correlator,” Opt. Eng. 33, 1610–1617 (1994).
[CrossRef]

M. S. Alam, “Phase-encoded fringe-adjusted joint transform correlation,” Opt. Eng. 39, 1169–1176 (2000).
[CrossRef]

K. Brunnstrom, B. N. Schenkman, B. Jacobson, “Object detection in cluttered infrared images,” Opt. Eng. 42, 388–399 (2003).
[CrossRef]

S. Sun, H. W. Park, “Automatic target recognition using boundary partitioning and invariant features in forward-looking infrared images,” Opt. Eng. 42, 524–533 (2003).
[CrossRef]

A. Mahalanobis, A. R. Sims, A. V. Nevel, “Signal-to-clutter measure for measuring automatic target recognition performance using complimentary eigenvalue distribution analysis,” Opt. Eng. 42, 1144–1151 (2003).
[CrossRef]

Opt. Laser Tech. (1)

M. S. Alam, M. A. Karim, “Improved correlation discrimination in a multiobject bipolar joint transform correlator,” Opt. Laser Tech. 24, 45–50 (1992).
[CrossRef]

Other (1)

R. Singh, B. V. Kumar, “Performance of the extended maximum average correlation height (EMACH) filter and the polynomial distance classifier correlation filter (PDCCF) for multiclass SAR detection and classification,” in Algorithms for Synthetic Aperture Radar Imagery IX, E. G. Zelnio, ed., Proc. SPIE4727, 265–276 (2002).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Automatic target-tracking algorithm block diagram.

Fig. 2
Fig. 2

Example of segmentation process: (a) Reference target window segmentation, (b) 25 × 25 pixel subframe segmentation, (c) local deviation, normalization, and mean subtraction for 25 × 25 pixel subframe.

Fig. 3
Fig. 3

Basic optoelectronic FJTC architecture.

Fig. 4
Fig. 4

FJTC-based target-detection system.

Fig. 5
Fig. 5

TM process: (a) Subframe segmented a frame in sequence lwir_2214. (b) TM result in subframe.

Fig. 6
Fig. 6

PCE for correlation output plane obtaining by use of FJTC.

Fig. 7
Fig. 7

PSR for correlation output plane obtaining by use of FJTC.

Fig. 8
Fig. 8

Moving-target-tracking results. (a) Noise and smoke surrounding target tracking in a sequence lwir_1918, frames 26, 50, 100, 150, 200, 260. (b) Low contrast and blending with background target tracking in a sequence lwir_1807, frames 2, 50, 120, 150, 200, 259. (c) Fast target tracking in close approximate nontarget objects and smoky scenes in sequence lwir_1907, frames 119, 130, 150, 160, 180, and 195.

Tables (1)

Tables Icon

Table 1 Detection and Tracking Results of FJTC and FJTC-TM Algorithms for Five Different Sequences

Equations (15)

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

Lx=1|M|-1i=1|M|Ixi-Ix21/2,
fx, y=rx, y+y0+i=1n tix-xi, y-yi+nx, y-y0,
|Fu, v|2=|Ru, v|2+i=1n |Tiu, v|2+|Nu, v|2 +2 i=1n |Tiu, vRu, v|cosϕtiu, v-ϕru, v-uxi-vyi-2vy0+2|Ru, vNu, v|cosϕru, v-ϕnu, v+2vy0)+2 i=1n |Tiu, vNu, v|cosϕtiu, v-ϕnu, v-uxi-vyi+2 i=1nk=1kin |Tiu, vTku, v|cosϕtiu, v-ϕtku, v-uxi+uxk-vyi+vyk,
Pu, v=|Fu, v|2-|Tu, v|2-|Ru, v|2 =2 i=1n |Tiu, vRu, v|cosϕtiu, v-ϕru, v-uxi-vyi-2vy0+2|Ru, vNu, v|cosϕru, v-ϕnu, v-2vy0.
Hu, v=Cu, vDu, v+|Ru, v|2-1,
Hu, v|Ru, v|-2.
Ou, v=Hu, vPu, v|Ru, v|-2Pu, v.
ρx=|x-x¯|, ρy=|y-y¯|,
rmn=mnItm, n-μtIrm, n-μrmnItm, n-μt2mnIrm, n-μr21/2,
μ=1MN1N1M Im, n.
xˆ, ŷmaxrmn,
xn=xn-1+xˆ-Γ2+1, yn=yn-1+ŷ-Γ2+1,
PCE=|px, y|2Ep,
Ep=xy |px, y|2.
PSR=|px, y|-μσ,

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