Abstract
The inherent dimensionality of a spectral image can be estimated in a number of ways, primarily based on statistical
measures of the data cloud in the hyperspace. Methods using the eigenvalues from a Principal Components
Analysis, a Minimum Noise Fraction transformation, or the Virtual Dimensionality algorithm are widely used
as applied to entire images typically with the goal of reducing the dimensionality of an image in its entirety.
However, it is desirable to understand the dimensionality of individual components within a hyperspectral scene,
as there is no a priori reason to expect all distinct material classes in the scene to have the same inherent dimensionality.
Additionally, in complex scenes containing non-natural materials, the lack of multivariate normality
of the data set implies that a statistically based estimation is less than optimal. Here, a geometric approach is
developed based on the local estimation of dimensionality in the native data hyperspace. It will be shown that
the dimensionality of a collection of data points (k) in the full n dimensions (where n is the number of spectral
channels measured) can be estimated by calculating the change in point density as a function of distance in the
full n dimensional hyperspace. Simple simulated examples to demonstrate the concept will be shown, as well as
applications to real hyperspectral imagery collected with the HyMAP sensor.
