Structural and functional brain images are playing an important role in helping us understand the changes associated with neurological disorders such as Alzheimer's disease (AD). Recent efforts have now started investigating their utility for diagnosis purposes. This line of research has shown promising results where methods from machine learning (such as Support Vector Machines) have been used to identify AD-related patterns from images, for use in diagnosing new individual subjects. In this paper, we propose a new framework for AD classification which makes use of the Linear Program (LP) boosting with novel additional regularization based on spatial "smoothness" in 3D image coordinate spaces. The algorithm formalizes the expectation that since the examples for training the classifier are images, the voxels eventually selected for specifying the decision boundary must constitute spatially contiguous chunks, i.e., "regions" must be preferred over isolated voxels. This prior belief turns out to be useful for significantly reducing the space of possible classifiers and leads to substantial benefits in generalization. In our method, the requirement of spatial contiguity (of selected discriminating voxels) is incorporated within the optimization framework directly. Other methods have made use of similar biases as a pre- or post-processing step, however, our model incorporates this emphasis on spatial smoothness directly into the learning step. We report on extensive evaluations of our algorithm on MR and FDG-PET images from the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset, and discuss the relationship of the classification output with the clinical and cognitive biomarker data available within ADNI.