Image registration is undoubtedly one of the most active areas of research in medical imaging. Within inter-individual comparison, registration should align images as well as cortical and external structures such as sulcal lines and fibers. While using image-based registration[1], neural fibers appear uniformly white giving no information to the registration. Tensor-based registration was recently proposed to improve white-matter alignment[2,3], however misregistration may also persist in regions where the tensor field appears uniform[4]. We propose an hybrid approach by extending the Diffeomorphic Demons(D)[5] registration to incorporate geometric constrains. Combining the deformation field induce 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.