Non-linear image registration is one of the most challenging task in medical image analysis. In this work, we propose an extension of the well-established diffeomorphic Demons registration algorithm to take into account geometric constraints. Combining the deformation field induced by the image and the geometry, we define a mathematically sound framework to jointly register images and geometric descriptors such as fibers or sulcal lines. We demonstrate this framework by registering simultaneously T 1 images and 50 fiber bundles consistently extracted in 12 subjects. Results show the improvement of fibers alignment while maintaining, and sometimes improving image registration. Further comparisons with non-linear T 1 and tensor registration demonstrate the superiority of the Geometric Demons over their purely iconic counterparts.