Current Alzheimer's disease diagnosis and cognitive assessment are based on medical history assessment and evaluation of cognitive score systems. They are time-consuming and subjective. A rapid and automated method is developed by processing positron emission tomography neuroimages and performing statistical analysis. The brain areas are firstly extracted from the neuroimages by an atlas-assisted approach, and then transformed piecewise into a common atlas space by dividing the brain into 18 cubic regions based on the landmarks identified automatically. The statistical models of stepwise regressions and discriminant classification are applied to predict the cognitive scores and make a diagnosis on Alzheimer's disease or mild cognitive impairment. The proposed method is fully automatic and has been tested on 400 cases. The preliminary testing results are promising. For a group of 250 cases which are the samples of the regressions and discriminant classification, the success rates of disease diagnosis are 73.7%, 54.9%, and 79.7% for the patients with Alzheimer's disease, mild cognitive impairment, and normal subjects, respectively. The average success rate for another group of 150 cases is 61.3%.