Activation detection in functional Magnetic Resonance Imaging (fMRI) datasets is usually performed by thresholding activation maps in the brain volume or, better, on the cortical surface. However, basing the analysis on a site-by-site statistical decision may be detrimental both to the interpretation of the results and to the sensitivity of the analysis, because a perfect point-to-point correspondence of brain surfaces from multiple subjects cannot be guaranteed in practice. In this paper, we propose a new approach that first defines anatomical regions such as cortical gyri outlined on the cortical surface, and then segments these regions into functionally homogeneous structures using a parcellation procedure that includes an explicit between-subject variability model, i.e. random effects. We show that random effects inference can be performed in this framework. Our procedure allows an exact control of the specificity using permutation techniques, and we show that the sensitivity of this approach is higher than the sensitivity of voxel- or cluster-level random effects tests performed on the cortical surface.