23 September 2003 Multivariate histogram shaping and statistically independent principle components
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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 principle components analysis, the resulting components are not only uncorrelated, as would be expected, but are statistically independent as well.
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Jeffrey P. Kern, Jeffrey P. Kern, J. Scott Tyo, J. Scott Tyo, } "Multivariate histogram shaping and statistically independent principle components", Proc. SPIE 5093, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery IX, (23 September 2003); doi: 10.1117/12.487475; https://doi.org/10.1117/12.487475
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