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Target detection in reflective hyperspectral imagery generally involves the application of a spectral matched filter on a per-pixel basis to create an image of the target likelihood of occupying each pixel. Stochastic (or unstructured) target detection techniques require the user to define an estimate of the background mean and covariance from which to separate out the desired targets in the image. Typically, scene-wide statistics are used, although it is simple to show that this methodology does not produce sufficiently multivariate normal backgrounds, nor does it necessarily represent the best suppression of likely false alarms. This technique can be improved on by segmentation methods that selectively choose which pixels best represent the background for a particular test pixel and / or target spectrum. Here, several spatial and spectral segmentation techniques are presented and improved target detection performance over scene-wide statistics is shown for a common target in two data sets with different scene content. Results are presented in the form of average false alarm rates and a chi-squared goodness of fit measure of the background multivariate normality. Improvements are possible using segmentation methods over global estimation of background mean and covariance. However, the best method of background characterization depends strongly on the spatial and spectral characteristics of the target of interest and scene content.