We introduce the concept of the metabolic centroid spectrum as the feature space to characterize the distribution of metabolic activity in three-dimensional brains. The method computes the metabolic centroid of a brain subvolume for each increment of metabolic activity occurring in the whole brain. The result is the metabolic spectral signature, a continuous three-dimensional curve whose shape reflects the distribution of metabolic rates in the brain. The method's sensitivity to metabolic distribution asymmetries is greatly increased over that of the metabolic centroid method, while retaining its advantages; it is almost invariant to head size, head positioning, photon scatter, and the positron emission tomography (PET) camera's full width at half-maximum. It does not require magnetic resonance, computed tomography, or x-ray images. To test the method we analyzed the metabolic PET images of 40 normal subjects and 20 schizophrenics. The results show a unification of several metabolic characteristics of schizophrenic brains, such as laterality, hypofrontality, cortical/subcortical abnormalities, and overall brain hypometabolism, which were identified by different laboratories in separate studies using differing methodologies. Here they are presented by a single automatic objective method.