Abstract

We address the issue of distinguishing point objects from a cluttered background and estimating their position by image processing. We are interested in the specific context in which the object’s signature varies significantly relative to its random subpixel location because of aliasing. The conventional matched filter neglects this phenomenon and causes a consistent degradation of detection performance. Thus alternative detectors are proposed, and numerical results show the improvement brought by approximate and generalized likelihood-ratio tests compared with pixel-matched filtering. We also study the performance of two types of subpixel position estimator. Finally, we put forward the major influence of sensor design on both estimation and point object detection.

© 2004 Optical Society of America

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  1. C. D. Wang, “Adaptive spatial/temporal/spectral filters for background clutter suppression and target detection,” Opt. Eng. 21, 1033–1038 (1982).
    [CrossRef]
  2. A. Margalit, I. S. Reed, R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. 21, 394–405 (1985).
    [CrossRef]
  3. T. Soni, J. R. Zeidler, W. H. Ku, “Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data,” IEEE Trans. Image Process. 2, 327–340 (1993).
    [CrossRef] [PubMed]
  4. X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
    [CrossRef] [PubMed]
  5. E. A. Ashton, “Detection of subpixel anomalies in multispectral infrared imagery using an adaptive Bayesian classifier,” IEEE Trans. Geosci. Remote Sens. 36, 506–517 (1998).
    [CrossRef]
  6. I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. 19, 898–905 (1983).
    [CrossRef]
  7. S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
    [CrossRef]
  8. J. M. Mooney, J. Silverman, C. E. Caefer, “Point target detection in consecutive frame staring infrared imagery with evolving cloud clutter,” Opt. Eng. 34, 2772–2784 (1995).
    [CrossRef]
  9. H. L. Van Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968), Part 1.
  10. D. Manolakis, G. Shaw, “Detection algorithms for hyperspectral imaging applications,” Signal Process. Mag. 19, 29–43 (2002).
    [CrossRef]
  11. J. W. Goodman, Introduction à l’Optique de Fourier et à l’Holographie (Masson, Paris, 1972).
  12. R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
    [CrossRef]
  13. The ppmforge software is an open-source program originally designed by John Walker and included with the PBMPLUS and NetPBM raster image utilities; ppmforge generates random fractal forgeries of clouds, planets, and starry skies. A manual page can be found at http://netpbm.sourceforge.net/doc/ppmforge.html , and the source code is available, for example, at the following web address: http://www.ehynan.com/java_applet/fractal_applet/FractApplet/ppmfcprt/ .
  14. K. A. Winick, “Cramer-Rao lower bounds on the performance of charge-coupled-device optical position estimators,” J. Opt. Soc. Am. A 3, 1809–1815 (1986).
    [CrossRef]

2002 (1)

D. Manolakis, G. Shaw, “Detection algorithms for hyperspectral imaging applications,” Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

1998 (2)

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

E. A. Ashton, “Detection of subpixel anomalies in multispectral infrared imagery using an adaptive Bayesian classifier,” IEEE Trans. Geosci. Remote Sens. 36, 506–517 (1998).
[CrossRef]

1997 (1)

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

1995 (1)

J. M. Mooney, J. Silverman, C. E. Caefer, “Point target detection in consecutive frame staring infrared imagery with evolving cloud clutter,” Opt. Eng. 34, 2772–2784 (1995).
[CrossRef]

1993 (1)

T. Soni, J. R. Zeidler, W. H. Ku, “Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data,” IEEE Trans. Image Process. 2, 327–340 (1993).
[CrossRef] [PubMed]

1991 (1)

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

1986 (1)

1985 (1)

A. Margalit, I. S. Reed, R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. 21, 394–405 (1985).
[CrossRef]

1983 (1)

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. 19, 898–905 (1983).
[CrossRef]

1982 (1)

C. D. Wang, “Adaptive spatial/temporal/spectral filters for background clutter suppression and target detection,” Opt. Eng. 21, 1033–1038 (1982).
[CrossRef]

Armstrong, E. E.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

Ashton, E. A.

E. A. Ashton, “Detection of subpixel anomalies in multispectral infrared imagery using an adaptive Bayesian classifier,” IEEE Trans. Geosci. Remote Sens. 36, 506–517 (1998).
[CrossRef]

Barnard, K. J.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

Blostein, S. D.

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

Bognar, J. G.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

Caefer, C. E.

J. M. Mooney, J. Silverman, C. E. Caefer, “Point target detection in consecutive frame staring infrared imagery with evolving cloud clutter,” Opt. Eng. 34, 2772–2784 (1995).
[CrossRef]

Chen, A. M.

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

Gagliardi, R. M.

A. Margalit, I. S. Reed, R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. 21, 394–405 (1985).
[CrossRef]

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. 19, 898–905 (1983).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction à l’Optique de Fourier et à l’Holographie (Masson, Paris, 1972).

Hardie, R. C.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

Hoff, L. E.

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

Huang, T. S.

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

Ku, W. H.

T. Soni, J. R. Zeidler, W. H. Ku, “Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data,” IEEE Trans. Image Process. 2, 327–340 (1993).
[CrossRef] [PubMed]

Manolakis, D.

D. Manolakis, G. Shaw, “Detection algorithms for hyperspectral imaging applications,” Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

Margalit, A.

A. Margalit, I. S. Reed, R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. 21, 394–405 (1985).
[CrossRef]

Mooney, J. M.

J. M. Mooney, J. Silverman, C. E. Caefer, “Point target detection in consecutive frame staring infrared imagery with evolving cloud clutter,” Opt. Eng. 34, 2772–2784 (1995).
[CrossRef]

Reed, I. S.

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

A. Margalit, I. S. Reed, R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. 21, 394–405 (1985).
[CrossRef]

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. 19, 898–905 (1983).
[CrossRef]

Shao, H. M.

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. 19, 898–905 (1983).
[CrossRef]

Shaw, G.

D. Manolakis, G. Shaw, “Detection algorithms for hyperspectral imaging applications,” Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

Silverman, J.

J. M. Mooney, J. Silverman, C. E. Caefer, “Point target detection in consecutive frame staring infrared imagery with evolving cloud clutter,” Opt. Eng. 34, 2772–2784 (1995).
[CrossRef]

Soni, T.

T. Soni, J. R. Zeidler, W. H. Ku, “Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data,” IEEE Trans. Image Process. 2, 327–340 (1993).
[CrossRef] [PubMed]

Stotts, L. B.

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968), Part 1.

Wang, C. D.

C. D. Wang, “Adaptive spatial/temporal/spectral filters for background clutter suppression and target detection,” Opt. Eng. 21, 1033–1038 (1982).
[CrossRef]

Watson, E. A.

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

Winick, K. A.

Yu, X.

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

Zeidler, J. R.

T. Soni, J. R. Zeidler, W. H. Ku, “Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data,” IEEE Trans. Image Process. 2, 327–340 (1993).
[CrossRef] [PubMed]

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

A. Margalit, I. S. Reed, R. M. Gagliardi, “Adaptive optical target detection using correlated images,” IEEE Trans. Aerosp. Electron. Syst. 21, 394–405 (1985).
[CrossRef]

I. S. Reed, R. M. Gagliardi, H. M. Shao, “Application of three-dimensional filtering to moving target detection,” IEEE Trans. Aerosp. Electron. Syst. 19, 898–905 (1983).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

E. A. Ashton, “Detection of subpixel anomalies in multispectral infrared imagery using an adaptive Bayesian classifier,” IEEE Trans. Geosci. Remote Sens. 36, 506–517 (1998).
[CrossRef]

IEEE Trans. Image Process. (2)

T. Soni, J. R. Zeidler, W. H. Ku, “Performance evaluation of 2-D adaptive prediction filters for detection of small objects in image data,” IEEE Trans. Image Process. 2, 327–340 (1993).
[CrossRef] [PubMed]

X. Yu, L. E. Hoff, I. S. Reed, A. M. Chen, L. B. Stotts, “Automatic target detection and recognition in multiband imagery: a unified ML detection and estimation approach,” IEEE Trans. Image Process. 6, 143–156 (1997).
[CrossRef] [PubMed]

IEEE Trans. Signal Process. (1)

S. D. Blostein, T. S. Huang, “Detecting small, moving objects in image sequences using sequential hypothesis testing,” IEEE Trans. Signal Process. 39, 1611–1629 (1991).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (3)

R. C. Hardie, K. J. Barnard, J. G. Bognar, E. E. Armstrong, E. A. Watson, “High-resolution image reconstruction from a sequence of rotated and translated frames and its application to an infrared imaging system,” Opt. Eng. 37, 247–260 (1998).
[CrossRef]

J. M. Mooney, J. Silverman, C. E. Caefer, “Point target detection in consecutive frame staring infrared imagery with evolving cloud clutter,” Opt. Eng. 34, 2772–2784 (1995).
[CrossRef]

C. D. Wang, “Adaptive spatial/temporal/spectral filters for background clutter suppression and target detection,” Opt. Eng. 21, 1033–1038 (1982).
[CrossRef]

Signal Process. Mag. (1)

D. Manolakis, G. Shaw, “Detection algorithms for hyperspectral imaging applications,” Signal Process. Mag. 19, 29–43 (2002).
[CrossRef]

Other (3)

J. W. Goodman, Introduction à l’Optique de Fourier et à l’Holographie (Masson, Paris, 1972).

The ppmforge software is an open-source program originally designed by John Walker and included with the PBMPLUS and NetPBM raster image utilities; ppmforge generates random fractal forgeries of clouds, planets, and starry skies. A manual page can be found at http://netpbm.sourceforge.net/doc/ppmforge.html , and the source code is available, for example, at the following web address: http://www.ehynan.com/java_applet/fractal_applet/FractApplet/ppmfcprt/ .

H. L. Van Trees, Detection, Estimation and Modulation Theory (Wiley, New York, 1968), Part 1.

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Figures (10)

Fig. 1
Fig. 1

Examples of image spots for several cross-marked subpixel positions (windows of size 5 × 5 pixels). Sensor design parameter r c is set to its common value of 2.44 (see Section 3).

Fig. 2
Fig. 2

Empirical distribution of the image-spot central pixel s [0, 0] for a uniformly random position U[-0.5,0.5)2 .

Fig. 3
Fig. 3

Examples of PMF theoretical ROC curves for several true subpixel positions (SNR, 15 dB): the ideal case, where * = 0 = (0, 0); * = (0.5, 0); and the worst case, where * = (0.5, 0.5). The mean curve was drawn for uniformly sampled *.

Fig. 4
Fig. 4

Left, radial PSF h o (u, v) (top) and slice along a diameter (bottom). Right, corresponding optical transfer function o (ν u , ν v ) and slice along a diameter (r c = 2.44).

Fig. 5
Fig. 5

Empirical ROC curves in the Gaussian white-noise case with common sensor design (r c = 2.44) for two different SNRs. These curves were obtained for 9 × 104 instances of noise.

Fig. 6
Fig. 6

Simulation of a cloud fractal image of 200 × 200 pixels (Hurst parameter, H = 0.7).

Fig. 7
Fig. 7

Empirical ROC curves obtained for the fractal image of Fig. 6 for a true (but assumed unknown) target amplitude α = 60 gray levels. The standard deviation of the correlated noise on the whole image is ∼104 gray levels, and the estimated innovation standard deviation is ∼4.6. The following generalized definition of the SNR, 10 log102ε s t R -1 s d), leads to an estimated SNR value of 18.1 dB.

Fig. 8
Fig. 8

Examples of image spots corresponding to a correctly sampled optics (r c = 0.5) to be compared with those of Fig. 1.

Fig. 9
Fig. 9

Empirical ROC curves in the Gaussian white-noise case with common sensor design (top, r c = 2.44) compared with correctly sampled optics (bottom, r c = 0.5) for the same SNR of 15 dB. These curves were obtained for 4 × 105 instances of noise.

Fig. 10
Fig. 10

Average MSEs of position estimators in the Gaussian white-noise case with common sensor design (top, r c = 2.44) compared with correctly sampled optics (bottom, r c = 0.5). MAP, maximum a posteriori.

Equations (21)

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si, j=i-0.5i+0.5j-0.5j+0.5 hou-1, v-2dudv,
H0 : z=n,H1 : z=αs+n,
pz|H0N0, R,pz|H1, α, Nαs, R.
pz|H1, α, pz|H0H1H0threshold.
αˆ=arg maxα pz|H1, α, =arg minαz-αstR-1z-αs=stR-1zstR-1s;
αˆ0T0z=|s0tR-1z|2s0tR-1s0.
gz=maxα,pz|H1, α, pz|H0=pz|H1, αˆML, ˆMLpz|H0threshold.
ˆML=arg maxε pz|H1, αˆ, =arg maxε|stR-1z|2stR-1s.
αˆMLTˆMLz=|sˆMLtR-1z|2sˆMLtR-1sˆML.
z=pz|H1pz|H0=ε pz|H1, α, pαpdαdpz|H0.
z  ε1stR-1s1/2exp|stR-1z|22stR-1sd.
az=¼f0|z+½k=14 fk|z+¼k=58 fk|z.
zSa+n=p=1P apsp+n,
âML=StR-1S-1StR-1z,
Dz=ztR-1SStR-1S-1StR-1z.
hou, v=1πJ1πρrcρ2, ρ=u2+v2.
i,j2si, j=2 hou, vdudv=1.
SNR=10 log10α2Eσ2, E=εi,j2si, j2d.
ˆPM=εp|H1, zd,
p|H1, z=pz|H1, ppz|H1 =ppz|H1 pz|H1, α, pαdα.
p|H1, z  1stR-1s1/2exp|stR-1z|22stR-1s.

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