Multivariate histogram shaping and statistically independent principal components

Jeffrey P. Kern, J Scott Tyo

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In signal processing, signals are often treated as Gaussian random variables in order to simplify processing when, in fact, they are not. Similarly, in multispectral image processing, grayscale images from individual spectral bands do not have simple, predictable distributions nor are the bands independent from one another. Equalization and histogram shaping techniques have been used for many years to map signals and images to more desirable probability mass functions such as uniform or Gaussian. The ability to extend these techniques to multivariate random variables, i.e. jointly across multiple bands or channels, can be difficult due to an insufficient number of samples for constructing a multidimensional distribution. If successful, however, the resulting components can be made to be both uncorrelated and statistically independent. A method is presented here that achieves reasonably good equalization and Gaussian shaping in multispectral imagery. When combined with principal components analysis, the resulting components are not only uncorrelated, as would be expected, but are statistically independent as well.

Original languageEnglish (US)
Title of host publicationProceedings of SPIE - The International Society for Optical Engineering
EditorsS.S. Shen, P.E. Lewis
Pages263-274
Number of pages12
Volume5093
DOIs
StatePublished - 2003
Externally publishedYes
EventAlgorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX - Orlando, FL, United States
Duration: Apr 21 2003Apr 24 2003

Other

OtherAlgorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX
CountryUnited States
CityOrlando, FL
Period4/21/034/24/03

Fingerprint

random variables
Random variables
histograms
spectral bands
principal components analysis
imagery
Principal component analysis
image processing
signal processing
Signal processing
Image processing
Processing

Keywords

  • Independence
  • Multivariate histogram shaping
  • Mutual information matrix
  • Principal components analysis

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics

Cite this

Kern, J. P., & Tyo, J. S. (2003). Multivariate histogram shaping and statistically independent principal components. In S. S. Shen, & P. E. Lewis (Eds.), Proceedings of SPIE - The International Society for Optical Engineering (Vol. 5093, pp. 263-274) https://doi.org/10.1117/12.487475

Multivariate histogram shaping and statistically independent principal components. / Kern, Jeffrey P.; Tyo, J Scott.

Proceedings of SPIE - The International Society for Optical Engineering. ed. / S.S. Shen; P.E. Lewis. Vol. 5093 2003. p. 263-274.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kern, JP & Tyo, JS 2003, Multivariate histogram shaping and statistically independent principal components. in SS Shen & PE Lewis (eds), Proceedings of SPIE - The International Society for Optical Engineering. vol. 5093, pp. 263-274, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, Orlando, FL, United States, 4/21/03. https://doi.org/10.1117/12.487475
Kern JP, Tyo JS. Multivariate histogram shaping and statistically independent principal components. In Shen SS, Lewis PE, editors, Proceedings of SPIE - The International Society for Optical Engineering. Vol. 5093. 2003. p. 263-274 https://doi.org/10.1117/12.487475
Kern, Jeffrey P. ; Tyo, J Scott. / Multivariate histogram shaping and statistically independent principal components. Proceedings of SPIE - The International Society for Optical Engineering. editor / S.S. Shen ; P.E. Lewis. Vol. 5093 2003. pp. 263-274
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