Diffeomorphic sulcal shape analysis for cortical surface registration

We present an intrinsic framework for constructing sulcal shape atlases on the human cortex. We propose the analysis of sulcal and gyral patterns by representing them by continuous open curves in R³. The space of such curves, also termed as the shape manifold is equipped with a Riemannian L² metric on the tangent space, and shows desirable properties while matching shapes of sulci. On account of the spherical nature of the shape space, geodesics between shapes can be computed analytically. Additionally, we also present an optimization approach that computes geodesics in the quotient space of shapes modulo rigid rotations and reparameterizations. We also integrate the elastic shape model into a surface registration framework for a population of 176 subjects, and show a considerable improvement in the constructed surface atlases.