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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 20, Iss. 5 — May. 1, 2003
  • pp: 797–816

Cramér–Rao analysis of orientation estimation: viewing geometry influences on the information conveyed by target features

David R. Gerwe and Paul S. Idell  »View Author Affiliations


JOSA A, Vol. 20, Issue 5, pp. 797-816 (2003)
http://dx.doi.org/10.1364/JOSAA.20.000797


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Abstract

A methodology for analyzing an imaging sensor’s ability to assess target properties is developed. By the application of a Cramér–Rao covariance analysis to a statistical model relating the sensor measurements to the target, a lower bound can be calculated on the accuracy with which any unbiased algorithm can form estimates of target properties. Such calculations are important in understanding how a sensor’s design influences its performance for a given assessment task and in performing feasibility studies or system architecture design studies between sensor designs and sensing modalities. A novel numerical model relating a sensor’s measurements to a target’s three-dimensional geometry is developed in order to overcome difficulties in accurately performing the required numerical computations. The accuracy of the computations is verified against simple test cases that can be solved in closed form. Examples are presented in which the approach is used to investigate the influence of viewing perspective on orientation accuracy limits. These examples are also used to examine the potential accuracy improvement that could be gained by fusing multiperspective data.

© 2003 Optical Society of America

OCIS Codes
(100.2960) Image processing : Image analysis
(100.5010) Image processing : Pattern recognition

History
Original Manuscript: May 20, 2002
Revised Manuscript: December 9, 2002
Manuscript Accepted: December 9, 2002
Published: May 1, 2003

Citation
David R. Gerwe and Paul S. Idell, "Cramér–Rao analysis of orientation estimation: viewing geometry influences on the information conveyed by target features," J. Opt. Soc. Am. A 20, 797-816 (2003)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-5-797


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References

  1. S. M. Hannon, J. H. Shapiro, “Laser radar target detection with a multipixel joint range-intensity processor,” in Laser Radar III, R. J. Becherer, ed., Proc. SPIE999, 162–175 (1988). [CrossRef]
  2. S. M. Hannon, J. H. Shapiro, “Active-passive detection of multipixel targets,” in Laser Radar V, R. J. Becherer, ed., Proc. SPIE1222, 2–23 (1990). [CrossRef]
  3. T. J. Green, J. H. Shapiro, “Maximum-likelihood laser radar range profiling with the expectation-maximization algorithm,” Opt. Eng. 31, 2343–2354 (1992). [CrossRef]
  4. J. Zhao, S. Ahalt, C. B. Stribling, “3-D orientation vector estimation from satellite imagery,” in Signal Processing, Sensor Fusion, and Target Recognition V, I. Kadar, V. Libby, eds., Proc. SPIE2755, 472–483 (1996). [CrossRef]
  5. L. Hassebrook, M. Lhamon, M. Wang, J. Chatterjee, “Postprocessing of correlation for orientation estimation,” Opt. Eng. 36, 2710–2718 (1997). [CrossRef]
  6. X. Du, S. Ahalt, B. Stribling, “Three-dimensional vector estimation for subcomponents of space object imagery,” Opt. Eng. 37, 798–807 (1998). [CrossRef]
  7. B. Li, Q. Zheng, S. Der, R. Chellappa, N. M. Nasrabadi, L. A. Chhan, L.-C. Wang, “Experimental evaluation of neural, statistical and model-based approaches to FLIR ATR,” in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE3371, 388–397 (1998). [CrossRef]
  8. A. E. Koksal, J. H. Shapiro, W. M. Wells, “Model-based object recognition using laser radar range imagery,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE3718, 256–266 (1999). [CrossRef]
  9. R. Li, “Model-based target recognition using laser radar,” Opt. Eng. 31, 322–327 (1992). [CrossRef]
  10. T. J. Green, J. H. Shapiro, “Detecting objects in three-dimensional laser radar range images,” Opt. Eng. 33, 865–874 (1994). [CrossRef]
  11. M. I. Miller, A. Srivastava, U. Grenander, “Conditional-mean estimation via jump-diffusion processes in multiple target tracking/recognition,” IEEE Trans. Signal Process. 43, 2678–2690 (1995). [CrossRef]
  12. M. I. Miller, U. Grenander, J. A. O’Sullivan, D. L. Snyder, “Automatic target recognition organized via jump-diffusion algorithms,” IEEE Trans. Image Process. 6, 157–174 (1997). [CrossRef] [PubMed]
  13. A. D. Lanterman, M. I. Miller, D. L. Snyder, “General Metropolis–Hastings jump diffusions for automatic target recognition in infrared scenes,” Opt. Eng. 36, 1123–1137 (1997). [CrossRef]
  14. M. Cooper, U. Grenander, M. I. Miller, A. Srivastava, “Accommodating geometric and thermodynamic variability for forward-looking infrared sensors,” in Algorithms for Synthetic Aperture Radar Imagery IV, E. G. Zelnio, ed., Proc. SPIE3070, 162–172 (1997). [CrossRef]
  15. J. Kostakis, M. Cooper, T. Green, M. Miller, J. O’Sullivan, J. Shapiro, D. Snyder, “Multispectral active-passive sensor fusion for ground-based target orientation estimation,” in Automatic Target Recognition VIII, F. A. Sadjadi, ed., Proc. SPIE3371, 500–507 (1998). [CrossRef]
  16. J. Kostakis, M. Cooper, T. Green, M. Miller, J. O’Sullivan, J. Shapiro, D. Snyder, “Multispectral sensor fusion for ground-based target orientation estimation: FLIR, LADAR, HRR,” in Automatic Target Recognition IX, F. A. Sadjadi, ed., Proc. SPIE3718, 14–24 (1999). [CrossRef]
  17. A. Srivastava, U. Grenander, G. R. Jensen, M. I. Miller, “Jump-diffusion Markov processes on orthogonal groups for object pose estimation,” J. Stat. Plann. Infer. 103, 15–37 (2002). [CrossRef]
  18. H. L. Van Trees, Detection, Estimation, and Modulation Theory: Part 1 (Wiley, New York, 1968).
  19. S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  20. E. Weinstein, A. J. Weiss, “A general class of lower bounds in parameter estimation,” IEEE Trans. Inf. Theory 34, 338–342 (1988). [CrossRef]
  21. A. Srivastava, U. Grenander, “Metrics for target recognition,” in Applications of Artificial Neural Networks in Image Processing III, N. M. Nasrabadi, A. K. Katsaggelos, eds., Proc. SPIE3307, 29–36 (1998). [CrossRef]
  22. U. Grenander, M. I. Miller, A. Srivastava, “Hilbert–Schmidt lower bounds for estimators on matrix Lie groups,” IEEE Trans. Pattern Anal. Mach. Intell. 20, 790–801 (1998). [CrossRef]
  23. U. Grenander, A. Srivastava, M. I. Miller, “Asymptotic performance analysis on Bayesian target recognition,” IEEE Trans. Inf. Theory 46, 1658–1665 (2000). [CrossRef]
  24. M. L. Cooper, M. Miller, “Information measures for object recognition accommodating signature variability,” IEEE Trans. Inf. Theory 46, 1896–1907 (2000). [CrossRef]
  25. H. Hendriks, “A Cramér–Rao type lower bound for estimators with values in a manifold,” J. Multivar. Analy. 38, 245–261 (1991). [CrossRef]
  26. As long as the noise of each measurement and sensor is statistically independent, which is true in a large number of situations, the joint pdf is simply the product of the pdfs corresponding to the individual measurements.
  27. J. V. D. R. Gerwe, P. S. Idell, “Cramer–Rao bound analysis of target characterization accuracy limits for imaging systems,” in Multifrequency Electronic/Photonic Devices and Systems for Dual-Use Applications, A. R. Pirich, P. L. Repak, P. S. Idell, S. R. Czyzak, eds., Proc. SPIE4490, 245–255 (2001). [CrossRef]
  28. A. D. Lanterman, M. I. Miller, D. L. Snyder, “Representations of thermodynamic variability in the automated understanding of FLIR scenes,” in Automatic Object Recognition VI, F. A. Sadjadi, ed., Proc. SPIE2756, 26–37 (1996). [CrossRef]
  29. The bound given in relation (4) corresponds to the lowest MMSE achievable by an optimal estimator for the specific value of ξ used in the calculations. Another, more global bound can be calculated by averaging Eq. (3) over all values of ξ and weighted by the a prioridistribution p(ξ).This Bayesian bound gives the minimum-mean-square accuracy achievable by any estimator including those that are biased. See pp. 72–73 and 84–85 of Van Trees.18
  30. D. Snyder, D. Angelisanti, W. Smith, G.-M. Dai, “Correction for nonuniform flat-field response in focal-plane arrays,” in Digital Image Recovery and Synthesis III, P. S. Idell, T. J. Schulz, eds., Proc. SPIE2827, 60–67 (1996). [CrossRef]
  31. D. Snyder, C. Helstrom, A. Lanterman, M. Faisal, R. White, “Compensation for readout noise in CCD images,” J. Opt. Soc. Am. A 12, 272–283 (1995). [CrossRef]
  32. D. Snyder, A. M. Hammoud, R. L. White, “Image recovery from data acquired with a charge-coupled-device camera,” J. Opt. Soc. Am. A 10, 1014–1023 (1993). [CrossRef] [PubMed]
  33. R. E. Blahut, Principles and Practice of Information Theory (Addison-Wesley, Reading, Mass., 1987).
  34. J. Riker, R. Butts, G. Crockett, C. Baer, G. Kroncke, G. Cochran, D. Briscoe, M. Stephens, R. Suizu, D. Clark, “Tracking for anti-satellite (TASAT) systems simulation. Vol. II—Physical models,” (Research and Development Associates Logicon, 105 East Vermijo, Suite 450, Colorado Springs, CO, 1989).
  35. Such a comparison was performed after the compilation of this paper. The details of the calculations are too long to include here but were similar to those presented in Section 4 and Appendix B. It was found that the numerical CRLB calculations were generally 5%–20% larger than that indicated by the closed-form expression. This difference is too small relative to the potential inaccuracies in the numerical calculations to infer much about how the obscuration effects influence the Fisher information. It does, however, provide an indication that the overall effect is fairly small and that the relative location of target edges dominates the Fisher information.
  36. The described modifications to the rendering algorithm were implemented subsequent to the compilation of this paper. Tests indicate that as a complex 3-D target was rotated, the pixel values in the vicinity of obscuration edges changed smoothly and continuously. A rigorous evaluation of the accuracy of the approach for computing CRLBs has not been performed, but preliminary results are promising.
  37. A. E. Siegman, Lasers (University Science Books, Mill Valley, Calif., 1986).

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