Support vector machines (SVM) are increasingly used in brain image analyses since they allow capturing complex multivariate relationships in the data. Moreover, when the kernel is linear, SVMs can be used to localize spatial patterns of discrimination between two groups of subjects. However, the features' spatial distribution is not taken into account. As a consequence, the optimal margin hyperplane is often scattered and lacks spatial coherence, making its anatomical interpretation difficult. This paper introduces a framework to spatially regularize SVM for brain image analysis. We show that Laplacian regularization provides a flexible framework to integrate various types of constraints and can be applied to both cortical surfaces and 3D brain images. The proposed framework is applied to the classification of MR images based on gray matter concentration maps and cortical thickness measures from 30 patients with Alzheimer's disease and 30 elderly controls. The results demonstrate that the proposed method enables natural spatial and anatomical regularization of the classifier.