In this paper we present a new way of measuring brain variability based on the registration of sulcal lines sets in the large deformation framework. Lines are modelled geometrically as currents, avoiding then matchings based on point correspondences. At the end we retrieve a globally consistent deformation of the underlying brain space that best matches the lines. Thanks to this framework the measured variability is defined everywhere whereas a previous method introduced by P. Fillard requires tensors extrapolation. Evaluating both methods on the same database, we show that our new approach enables to describe different details of the variability and to highlight the major trends of deformation in the database thanks to a Tangent-PCA analysis.