Abstract

This work describes several approaches to the estimation of target detection and identification probabilities as a function of target range. A Bayesian approach to estimation is adopted, whereby the posterior probability distributions associated with these probabilities are analytically derived. The parameter posteriors are then used to develop credible intervals quantifying the degree of uncertainty in the parameter estimates. In our first approach we simply show how these credible intervals evolve as a function of range. A second approach, also following the Bayesian philosophy, attempts to directly estimate the parameterized performance curves. This second approach makes efficient use of the available data and yields a distribution of probability versus range curves. Finally, we demonstrate both approaches using experimental data collected from wide field-of-view imagers focused on maritime targets.

© 2013 Optical Society of America

PDF Article

References

  • View by:
  • |
  • |
  • |

  1. R. G. Driggers, J. S. Taylor, and K. Krapels, “Probability of identification cycle criterion (N50/N90) for underwater mine target acquisition,” Opt. Eng. 46, 033201 (2007).
    [CrossRef]
  2. S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
    [CrossRef]
  3. R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
    [CrossRef]
  4. A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, 1974).
  5. J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
    [CrossRef]
  6. W. A. Link and R. J. Barker, Bayesian Inference with Ecological Examples (Academic, 2010).
  7. P. Walley, “Inferences from multinomial data: learning about a bag of marbles,” J. R. Statist. Soc. B 58, 3–57 (1996).
  8. W. L. Quirin, Probability and Statistics (Harper & Row, 1978).
  9. R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
    [CrossRef]
  10. V. Dhar and Z. Khan, “Comparison of modeled atmosphere-dependent range performance of long-wave and mid-wave ir iamgers,” Infrared Phys. Technol. 51, 520–527 (2008).
    [CrossRef]
  11. W. K. Hastings, “Monte carlo sampling methods using markov chains and their applications,” Biometrika 57, 97–109 (1970).
    [CrossRef]
  12. J. M. Nichols, M. Currie, F. Bucholtz, and W. A. Link, “Bayesian estimation of weak material dispersion: theory and experiment,” Opt. Express 18, 2076–2089 (2010).
    [CrossRef]
  13. A. N. Kolmogorov, Foundations of Probability (Chelsea, 1956).

2010 (1)

2008 (1)

V. Dhar and Z. Khan, “Comparison of modeled atmosphere-dependent range performance of long-wave and mid-wave ir iamgers,” Infrared Phys. Technol. 51, 520–527 (2008).
[CrossRef]

2007 (1)

R. G. Driggers, J. S. Taylor, and K. Krapels, “Probability of identification cycle criterion (N50/N90) for underwater mine target acquisition,” Opt. Eng. 46, 033201 (2007).
[CrossRef]

2006 (2)

S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
[CrossRef]

J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
[CrossRef]

2004 (1)

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
[CrossRef]

1998 (1)

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

1996 (1)

P. Walley, “Inferences from multinomial data: learning about a bag of marbles,” J. R. Statist. Soc. B 58, 3–57 (1996).

1970 (1)

W. K. Hastings, “Monte carlo sampling methods using markov chains and their applications,” Biometrika 57, 97–109 (1970).
[CrossRef]

Barker, R. J.

W. A. Link and R. J. Barker, Bayesian Inference with Ecological Examples (Academic, 2010).

Boes, D. C.

A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, 1974).

Bucholtz, F.

Cox, P. G.

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

Currie, M.

Deaver, D. M.

J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
[CrossRef]

Dhar, V.

V. Dhar and Z. Khan, “Comparison of modeled atmosphere-dependent range performance of long-wave and mid-wave ir iamgers,” Infrared Phys. Technol. 51, 520–527 (2008).
[CrossRef]

Driggers, R. G.

R. G. Driggers, J. S. Taylor, and K. Krapels, “Probability of identification cycle criterion (N50/N90) for underwater mine target acquisition,” Opt. Eng. 46, 033201 (2007).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
[CrossRef]

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

Edwards, T. C.

S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
[CrossRef]

Graybill, F. A.

A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, 1974).

Hastings, W. K.

W. K. Hastings, “Monte carlo sampling methods using markov chains and their applications,” Biometrika 57, 97–109 (1970).
[CrossRef]

Hixon, J. G.

S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
[CrossRef]

Jacobs, E.

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
[CrossRef]

Khan, Z.

V. Dhar and Z. Khan, “Comparison of modeled atmosphere-dependent range performance of long-wave and mid-wave ir iamgers,” Infrared Phys. Technol. 51, 520–527 (2008).
[CrossRef]

Kolmogorov, A. N.

A. N. Kolmogorov, Foundations of Probability (Chelsea, 1956).

Krapels, K.

R. G. Driggers, J. S. Taylor, and K. Krapels, “Probability of identification cycle criterion (N50/N90) for underwater mine target acquisition,” Opt. Eng. 46, 033201 (2007).
[CrossRef]

S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
[CrossRef]

Leachtenauer, J.

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

Link, W. A.

Mood, A. M.

A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, 1974).

Moyer, S.

S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
[CrossRef]

Nichols, J. M.

O’Conner, J. D.

J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
[CrossRef]

O’Shea, P.

J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
[CrossRef]

Palmer, J. E.

J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
[CrossRef]

Quirin, W. L.

W. L. Quirin, Probability and Statistics (Harper & Row, 1978).

Scribner, D. A.

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

Taylor, J. S.

R. G. Driggers, J. S. Taylor, and K. Krapels, “Probability of identification cycle criterion (N50/N90) for underwater mine target acquisition,” Opt. Eng. 46, 033201 (2007).
[CrossRef]

Vollmerhausen, R.

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

Vollmerhausen, R. H.

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
[CrossRef]

Walley, P.

P. Walley, “Inferences from multinomial data: learning about a bag of marbles,” J. R. Statist. Soc. B 58, 3–57 (1996).

Biometrika (1)

W. K. Hastings, “Monte carlo sampling methods using markov chains and their applications,” Biometrika 57, 97–109 (1970).
[CrossRef]

Infrared Phys. Technol. (1)

V. Dhar and Z. Khan, “Comparison of modeled atmosphere-dependent range performance of long-wave and mid-wave ir iamgers,” Infrared Phys. Technol. 51, 520–527 (2008).
[CrossRef]

J. R. Statist. Soc. B (1)

P. Walley, “Inferences from multinomial data: learning about a bag of marbles,” J. R. Statist. Soc. B 58, 3–57 (1996).

Opt. Eng. (4)

R. G. Driggers, J. S. Taylor, and K. Krapels, “Probability of identification cycle criterion (N50/N90) for underwater mine target acquisition,” Opt. Eng. 46, 033201 (2007).
[CrossRef]

S. Moyer, J. G. Hixon, T. C. Edwards, and K. Krapels, “Probability of identification of small hand-held objects for electro-optic forward-looking infrared systems,” Opt. Eng. 45, 063201 (2006).
[CrossRef]

R. H. Vollmerhausen, E. Jacobs, and R. G. Driggers, “New metric for predicting target acquisition performance,” Opt. Eng. 43, 2806–2818 (2004).
[CrossRef]

R. G. Driggers, P. G. Cox, J. Leachtenauer, R. Vollmerhausen, and D. A. Scribner, “Targeting and intelligence electro-optical recognition modeling: a juxtaposition of the probabilities of discrimination and the general image quality equation,” Opt. Eng. 37, 789–797 (1998).
[CrossRef]

Opt. Express (1)

Proc. SPIE (1)

J. D. O’Conner, P. O’Shea, J. E. Palmer, and D. M. Deaver, “Standard target sets for field sensor performance measurements,” Proc. SPIE 6207, 62070U (2006).
[CrossRef]

Other (4)

W. A. Link and R. J. Barker, Bayesian Inference with Ecological Examples (Academic, 2010).

W. L. Quirin, Probability and Statistics (Harper & Row, 1978).

A. M. Mood, F. A. Graybill, and D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, 1974).

A. N. Kolmogorov, Foundations of Probability (Chelsea, 1956).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Metrics