<sod>The central group in CA defined on volumes in  <math>{\mathbb R}^3</math> are the [[Computational anatomy#The diffeomorphism group of computational anatomy|The diffeomorphism group of Computational Anatomy]] <math>\mathcal{G} \doteq Diff</math> which are mappings with 3-components <math>\phi(\cdot) = (\phi_1(\cdot),\phi_2 (\cdot),\phi_3 (\cdot))</math>, law of composition of functions <math> \phi \circ \phi^\prime (\cdot)\doteq \phi (\phi^\prime(\cdot)) </math>, with inverse <math> \phi \circ \phi^{-1}(\cdot) =\phi ( \phi^{-1}(\cdot))= id</math>.<eod>
<sod>The central group in CA defined on volumes in  <math>{\mathbb R}^3</math> are the [[Computational anatomy#The diffeomorphism group of computational anatomy|the diffeomorphism group]]  <math>\mathcal{G} \doteq Diff</math> which are mappings with 3-components <math>\phi(\cdot) = (\phi_1(\cdot),\phi_2 (\cdot),\phi_3 (\cdot))</math>, law of composition of functions <math> \phi \circ \phi^\prime (\cdot)\doteq \phi (\phi^\prime(\cdot)) </math>, with inverse <math> \phi \circ \phi^{-1}(\cdot) =\phi ( \phi^{-1}(\cdot))= id</math>.<eod>