<sod>For the study of deformable shape in CA, a more general diffeomorphism group has been the group of choice, which is the infinite dimensional analogue. The high-dimensional differeomorphism groups used in Computational Anatomy are generated via smooth flows   which satisfy the Lagrangian and Eulerian specification of the flow fields satisfying the ordinary differential equation: Showing the Lagrangian flow of coordinates  with associated vector fields  satisfying ordinary differential equation .<eod>
<sod>For the study of deformable shape in CA, a more general diffeomorphism group has been the group of choice, which is the infinite dimensional analogue. The high-dimensional differeomorphism groups used in Computational Anatomy are generated via smooth flows   which satisfy the Lagrangian and Eulerian specification of the flow fields satisfying the ordinary differential equation: <eod>