Riemannian geometry

Concepts

• LDDMM 10 exercisesLDDMM (Large Deformation Diffeomorphic Metric Mapping) is a registration framework that looks for a smooth diffeomorphic deformat…
• Smooth diffeomorphic deformation 11 exercisesA smooth diffeomorphic deformation φ is a bijective, smooth transformation whose inverse is also smooth.
• Minimum energy 11 exercisesThe minimum energy E_min is the lowest cost among admissible deformations; in LDDMM it measures how much effort the field generat…
• Diffeomorphic flow 11 exercisesA diffeomorphic flow φ_t is a family of deformations parametrized by time t, where at each instant the transformation remains inv…
• Velocity field 11 exercisesA velocity field v_t is a vector field that changes with time: at each instant t it assigns to every point the velocity at which…
• Time derivative 11 exercisesThe time derivative φ_t describes how a deformation changes as the time parameter t varies.
• Composition and inverse from Set theory 30 exercisesThe composition g∘ f applies f first and then g. The inverse f^-1 exists when f is bijective and undoes its action.