Riemannian metric and Lie bracket in computational anatomy

Computational anatomy (CA) is the study of shape and form in medical imaging. The study of deformable shapes in CA rely on high-dimensional diffeomorphism groups Diff V {\displaystyle \operatorname {Diff} _{V}} which generate orbits of the form M ≐ { φ ⋅ m ∣ φ ∈ Diff V } {\displaystyle {\mathcal {M}}\doteq \{\varphi \cdot m\mid \varphi \in \operatorname {Diff} _{V}\}} .

Source: Wikipedia — Riemannian metric and Lie bracket in computational anatomy (CC BY-SA 4.0)