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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 68, Iss. 2 — Feb. 1, 1978
  • pp: 157–166

Image mensuration by maximum a posteriori probability estimation

James W. Burnett and Thomas S. Huang  »View Author Affiliations

JOSA, Vol. 68, Issue 2, pp. 157-166 (1978)

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We present an algorithm for pulse width estimation from blurred and nonlinear observations in the presence of signal dependent noise. The main application is the accurate measurement of image sizes on film. The problem is approached by modeling the signal as a discrete position finite state Markov process, and then determining the transition location that maximizes the a posteriori probability. It turns out that the blurred signal can be represented by a trellis, and the maximum a posteriori probability (MAP) estimation is obtained by finding the minimum cost path through the trellis. The latter is done by the Viterbi algorithm. Several examples are presented. These include the measurement of the width of a road in an aerial photo taken at an altitude of 5000 ft. The resulting width estimate is accurate to within a few inches.

© 1978 Optical Society of America

James W. Burnett and Thomas S. Huang, "Image mensuration by maximum a posteriori probability estimation," J. Opt. Soc. Am. 68, 157-166 (1978)

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  1. A. Viterbi, "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm," IEEE Trans. Inf. Theory, IT-13, 260–269 (1967).
  2. G. Forney, "The Viterbi algorithm," Proc. IEEE, 61, 268–278 (1973).
  3. J. W. Burnett and T. S. Huang, "Image modeling with application to measurement," Technical Report TR-EE 77-11, School of Electrical Engineering, Purdue University (March 1977).
  4. H. Van Trees, Detection, Estimation, and Modulation, Part I, (Wiley, New York, 1968), p. 71.
  5. G. Roussas, A First Course in Mathematical Statistics (Addison- Wesley, Reading, Mass., 1973).
  6. R. Gonsalves, Cramer-Rao bounds on mensuration errors," Appl. Opt. 15, 1270–1275 (1976).
  7. B. Tuong-Phong, "Illumination for computer generated images," Technical Report C Sc-73-127, University of Utah (July 1973).
  8. R. Tarkington, "Kodak panchromatic negative films for aerial photography," Photogramm. Eng. 695–699 (December 1959).
  9. D. Paris, "Approximation of the sine wave response of photographic emulsions," J. Opt. Soc. Am. 51, 988–991 (1961).

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