Authors: Peter Bajorski
Abstract: This paper deals with the max-min and min-max detectors that were introduced in our earlier paper as special cases of generalized detection fusion. Here we investigate theoretical properties of such detectors. For the case of a oneelement background space, we provide the detection region for the max-type detector for an arbitrary shape of the target space. We then show two theorems presenting scenarios when the maxtype detector and the GLR (generalized likelihood ratio) detector are equivalent. In the case when the background and the target spaces are composite, the max-min and min-max detectors may not be equivalent in general and their detection regions may take some complex shapes. Against this backdrop, we specify a fairly general case when the two detectors are equivalent and their detection region boundary is defined by a hyperplane.
Keywords: target detection, hyperspectral imagery, continuum fusion, max-type detector, max-min detector, generalized likelihood ratio detector