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Journal of the Optical Society of America

Journal of the Optical Society of America

  • Vol. 65, Iss. 2 — Feb. 1, 1975
  • pp: 191–196

Planimetric analysis of color images using least-squares and related algorithms

D. Lee and H. Stark  »View Author Affiliations

JOSA, Vol. 65, Issue 2, pp. 191-196 (1975)

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A least-squares approach to the planimetric analysis of color scenes is furnished. The technique involves parallel processing in that all image points are involved simultaneously at every step of the processing. It is assumed that each object in the color scene has a unique spectral (color) signature. The end result of the processing is a vector whose components are the areas covered by the different objects in the scene. The technique requires only a simple optical system and can be easily automated. Procedures for finding the signatures that minimize the error variance are investigated. The theory is illustrated with a laboratory example.

D. Lee and H. Stark, "Planimetric analysis of color images using least-squares and related algorithms," J. Opt. Soc. Am. 65, 191-196 (1975)

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  1. K. S. Fu, D. A. Landgrebe, and T. L. Phillips, IEEE Proc. 57, 639 (1969).
  2. H. Stark, R. C. Barker, and D. Lee, Appl. Opt. 11, 2540 (1972).
  3. M. R. Holter, in Remote Sensing (National Academy of Sciences, Washington, D. C., 1970), Ch. 3.
  4. As one reviewer pointed out, Eq. (1) must be modified in the case of high-altitude imagery such as is obtained with ERTS observation satellites. In that case, the modification takes the form WT(λ)=S(λ)ρ(λ)ρ(λ)+WA(λ),where WT(λ) is the total irradiance and WA(λ) is a component of irradiance scattered into the sensor by the atmosphere between the sensor and the subject. Techniques for obtaining WA(λ) are furnished by R. H. Rogers and K. Peacock in Vol. I of Symposium on Significant Results Obtained from ERTS-1, NASA SP-327, March 1973, pp. 1115–1122. Provided that WA(λ) is relatively free from statistical fluctuations, we can write W(λ) =WT(λ)- WA(λ)=S(λ)ρ(λ)Ƭ(λ)and apply the theory developed in this paper. If WA(λ) contains strong statistical fluctuations, then the average bias can be subtracted from WT(λ) and the zero-mean fluctuations can be lumped with the other zero-mean fluctuations in W(λ). Processing of ERTS-type data must take into account the seasonal variatio ns in spectral reflectances, and variations in atmospheric and illtlminating conditions.
  5. R. Deutsch, Estimation Theory (Prentice–Hall, Englewood Cliffs, N. J., 1965), p. 59.
  6. Reference 5, p. 62.
  7. R. A. Holmes and R. B. McDonald, IEEE Proc. 57, 629 (1969).

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