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The purpose of this paper is to introduce a general type of detection fusion that allows combining a set of basic detectors into one more versatile detector. The fusion can be performed based on the spectral information contained in a pixel, the global characteristics of the background and target spaces, as well as spatial local information. As an example of generalized fusion, we introduce a new class of detectors called the directional segmented matched filters (DSMFs). We then concentrate on the more basic type of fusion that does not use the spatial local information. Our goal is to build a theoretical foundation for the future more sophisticated detectors. Within this setup, we define max-min and min-max types of fusion, which turn out to be equivalent to the geometric approach to continuum fusion already introduced in the literature. Nevertheless, this new framework allows natural formulation of other types of approaches, such as discrete fusion, without the continuity assumption. This new formalism also allows formulation of a general theorem about the relationship between the max-min and min-max detectors. We also provide experimental results that demonstrate the benefits of the new approach. We compare two new detectors with the global matched filter using two different targets in an AVIRIS (Airborne Visible/Infrared Imaging Spectrometer) image. The results show that various forms of the DSMFs dominate depending on the target type.