The textural content of FDG-PET brain images has been shown to be useful for the diagnosis of Alzheimer's disease (AD) and Mild Cognitive Impairment (MCI). In this paper, we investigate the use of the textons method [1], a powerful texture extraction procedure that uses a full statistical representation of the response of the image to a set of filters. We also extend the MR8 filter bank used in [1] to 3D in order to match the dimensionality of FDG-PET images, while maintaining important properties such as invariance to rotation and a low dimensionality of the filter response space. We propose two methods to tackle difficulties inherent to the extraction and classification of texture from images whose appearance varies over space and to the fact that most regions of the image are not affected by AD or MCI. The first method selects only the voxels with the most discriminative filter responses, while the second method focuses on brain regions manually labeled by an expert physician. Experiments showed that the proposed approaches outperformed the more common one that uses voxel intensities directly as features both in the diagnosis of AD and MCI. It was also observed that the discriminative power of certain brain regions increased significantly when the texton based analysis was performed.