In this paper we propose a new diagnostic feature for Alzheimer's Disease (AD) which is based on assessment of the degree of inter-hemispheric asymmetry using Single Photon Emission Computed Tomography (SPECT). The asymmetry measure used represents differences in 3D perfusion image patterns in the cerebral hemispheres. We start from the simplest descriptors of brain perfusion such as the mean intensity within pairs of brain lobes, gradually increasing the resolution up to five-dimensional co-occurrence matrices. Evaluation of the method was performed using SPECT scans of 79 subjects including 42 patients with clinical diagnosis of AD and 37 controls. It was found that combination of intensity and gradient features in co-occurrence matrices captures significant differences in asymmetry values between AD and normal controls (p < 0.00003 for all cerebral lobes). Our results suggest that the asymmetry feature is useful for discriminating AD patients from normal controls as detected by SPECT.