Bayesian estimation of templates in computational anatomy: Difference between revisions

Revision as of 15:35, 21 February 2019

Revision as of 17:12, 17 March 2019

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The central group acting CA defined on volumes in <math>{\mathbb R}^3</math> are the [[diffeomorphisms]] <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>.

[[Group (mathematics)|Group]]s and [[groupGroup actionsaction (mathematics)|group]] are familiar to the Engineering community with the universal popularization and standardization of [[linear algebra]] as a basic model

A popular [[groupGroup actionsaction (mathematics)|group action]] is on scalar images, <math>I(x),x \in {\mathbb R}^3</math>, with action on the right via the inverse.

:<math>