Neuroimaging at the group level requires spatial normalization of individual structural data. We propose a geometric approach that consists in matching a series of cortical surfaces through diffeomorphic registration of their sulcal imprints. The resulting 3D transforms naturally extends to the entire MRI volumes. The Diffeomorphic Sulcal-based COrtical (DISCO) registration integrates two recent technical outcomes: 1) the automatic extraction, identification and simplification of numerous sulci from T1-weighted MRI data series hereby revealing the sulcal imprint and 2) the measure-based diffeomorphic registration of those crucial anatomical landmarks. We show how the DISCO registration may be used to elaborate a sulcal template which optimizes the distribution of constraints over the entire cortical ribbon. DISCO was evaluated through a group of 20 individual brains. Quantitative and qualitative indices attest how this approach may improve both alignment of sulcal folds and overlay of gray and white matter volumes at the group level.