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There is a relative paucity of studies that seek to nonparametrically describe or categorize hyperspectral image (HSI)
data in the most natural context within which those data are best represented: n-dimensional (n-D) hyperspace, where n
is the number of bands in an HSI data cube. Statistical techniques-and specifically those based on second-order
statistics-are predominant and generally do not provide (nor are they utilized to provide or 'leave behind') an
understanding of the distribution of spectra in hyperspace for the purpose of discovering patterns, comparing data sets,
developing a deeper understanding of HSI data, etc. With the terabytes of HSI data in archives today representing a huge
diversity of geographical settings, it seems natural to enquire as to whether there are universal patterns among HSI data
sets. If such patterns exist, new techniques may be developed to exploit them, e.g., to enhance information extraction
speed and accuracy. Since an understanding of the nature of HSI data has rarely gone beyond cursory, visual
assessments of geographical setting; i.e., assessments of whether the data are of desert, forest, urban, littoral, etc.,
environments, it is perhaps worthwhile to develop methods to probe n-D hyperspace with the intent to identify and
describe universal data commonalities, differences, classifications, and patterns. Building upon earlier work (Resmini,
2003 [1], 2006 [2]), an algorithm was created to describe the volume (and label the individual volume elements) of
hyperspace occupied by an HSI data set. The algorithm essentially discretizes hyperspace assigning addresses to boxes
in which data points (i.e., spectra) reside. The algorithm has been applied to visible/near-infrared to shortwave infrared
(VNIR/SWIR) and longwave infrared (LWIR) HSI data cubes. Implemented in C code, the algorithm may also be used
to calculate the fractal dimension of any array of points in any n-D hyperspace because it is essentially an
implementation of box counting. The algorithm is described as are results of its application to actual HSI data sets. The
fractal dimension of HSI data derived from the algorithm are also presented and compared to principal componentsbased
estimates of data dimensionality. Application of the algorithm for developing a deeper understanding of the nature
of HSI data as viewed as points in hyperspace is discussed as are practical applications for 'traditional' HSI exploitation
activities such as anomaly and target detection.
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