Complex sentence: The flows between coordinates in Computational anatomy are constrained to be geodesic flows satisfying the principle of least action for the Kinetic energy of the flow defined via a Sobolev smoothness norm with more than two finite square-integrable derivatives for each component of the velocity of flow.
Split into simpler sentences: The flows between coordinates in Computational anatomy are constrained to be geodesic flows satisfying the principle of least action for the Kinetic energy of the flow. The kinetic energy of the flows are defined via a Sobolev smoothness norm with more than two finite square-integrable derivatives for each component of the velocity of flow.