OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 19, Iss. 2 — Jan. 15, 1980
  • pp: 228–235

Three-parameter probability distribution density for statistical image analysis

H. C. Schau  »View Author Affiliations

Applied Optics, Vol. 19, Issue 2, pp. 228-235 (1980)

View Full Text Article

Enhanced HTML    Acrobat PDF (735 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Statistical analysis of 2-D image data or data gathered from a scanning radiometer requires that both the non-Gaussian nature and finite sample size of the process be considered. To aid the statistical analysis of this data, a higher moment description density function has been defined, and parameters have been identified with the estimated moments of the data. It is shown that the first two moments may be computed from a knowledge of the Weiner spectrum, whereas all higher moments require the complex spatial frequency spectrum. Parameter identification is carried out for a three-parameter density function and applied to a scene in the IR region, 8–14 μm. Results indicate that a three-parameter distribution density generally provides different probabilities than does a two-parameter Gaussian description if maximum entropy (minimum bias) forms are sought.

© 1980 Optical Society of America

Original Manuscript: July 21, 1979
Published: January 15, 1980

H. C. Schau, "Three-parameter probability distribution density for statistical image analysis," Appl. Opt. 19, 228-235 (1980)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. Roberts, “Signal Processing Techniques,” Interstate Electronics Corp., Anaheim, Calif. (1977).
  2. W. D. Montgomery, P. W. Broome, J. Opt. Soc. Am. 52, 1259 (1962). [CrossRef]
  3. Y. S. Itakura, S. Tsutsumi, T. Takagi, Infrared Phys. 14, 17 (1974). [CrossRef]
  4. J. R. Maxwell, L. Wilkins, IRIS Proc. 22, 101 (1978).
  5. D. Middleton, An Introduction to Statistical Communications Theory (McGraw-Hill, New York, 1960).
  6. A. J. Devaney, R. Chidlaw, J. Opt. Soc. Am. 68, 1352 (1978). [CrossRef]
  7. A. H. Greenaway, Opt. Lett. 1, 10 (1977). [CrossRef] [PubMed]
  8. C. Stein, “Approximation of Improper Prior Measures by Prior Probability Measures,” Department of Statistics, Stanford University Tech. Rept. 12 (1964).
  9. S. J. Dunning, S. R. Robinson, Appl. Opt. 18, 1507 (1979). [CrossRef]
  10. A. K. Majumdar, J. Opt. Soc. Am. 69, 199 (1979). [CrossRef]
  11. P. M. Lewis, Inf. Control 2, 214 (1959). [CrossRef]
  12. W. D. Montgomery, IEEE Trans. Inf. Theory 10, 2 (1964). [CrossRef]
  13. M. Abramowitz, I. R. Stegun, Eds., Handbook of Mathematical Functions (Dover, New York, 1968, Chap. 14.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited