A new theoretical framework is created for the class of detection problems traditionally addressed by the generalized likelihood ratio test. Absent prior knowledge that would permit implementation of the optimal detector, a family of optimal detectors is fused according to any one of a group of criteria. Geometrical solutions are presented to several specific problems motivated by hyperspectral signal processing. For the general case, a set of partial differential relations is derived. The generalized likelihood ratio test is shown to be equivalent to one of several flavors of continuum fusion detector.