About: Riemannian metric and Lie bracket in computational anatomy

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Computational anatomy (CA) is the study of shape and form in medical imaging. The study of deformable shapes in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form . In CA, this orbit is in general considered a smooth Riemannian manifoldsince at every point of the manifold there is an inner product inducing the norm on the tangent spacethat varies smoothly from point to point in the manifold of shapes . This is generated by viewing thegroup of diffeomorphisms as a Riemannian manifold with , associated to the tangent space at . This induces the norm and metric on the orbit under the action from the group of diffeomorphisms.

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rdfs:label	Riemannian metric and Lie bracket in computational anatomy (en)
rdfs:comment	Computational anatomy (CA) is the study of shape and form in medical imaging. The study of deformable shapes in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form . In CA, this orbit is in general considered a smooth Riemannian manifoldsince at every point of the manifold there is an inner product inducing the norm on the tangent spacethat varies smoothly from point to point in the manifold of shapes . This is generated by viewing thegroup of diffeomorphisms as a Riemannian manifold with , associated to the tangent space at . This induces the norm and metric on the orbit under the action from the group of diffeomorphisms. (en)
dcterms:subject	Computational anatomy Neural engineering Geometry Biomedical engineering Fluid mechanics
Wikipage page ID	49400436 (xsd:integer)
Wikipage revision ID	1123961638 (xsd:integer)
Link from a Wikipage to another Wikipage	Computational anatomy Neural engineering Computational anatomy Matrix (mathematics) Medical imaging Sobolev space Hamilton's principle Tangent space Geometry Riemannian manifold Invertible matrix Biomedical engineering Fluid mechanics Large deformation diffeomorphic metric mapping Inner product space Lie bracket of vector fields Hamilton's principal of least action LDDMM Lie bracket
sameAs	Riemannian metric and Lie bracket in computational anatomy Riemannian metric and Lie bracket in computational anatomy
dbp:wikiPageUsesTemplate	dbt:COI dbt:Further_information dbt:Hidden dbt:Main dbt:NumBlk dbt:Reflist dbt:Short_description dbt:EquationRef dbt:EquationNote
has abstract	Computational anatomy (CA) is the study of shape and form in medical imaging. The study of deformable shapes in computational anatomy rely on high-dimensional diffeomorphism groups which generate orbits of the form . In CA, this orbit is in general considered a smooth Riemannian manifoldsince at every point of the manifold there is an inner product inducing the norm on the tangent spacethat varies smoothly from point to point in the manifold of shapes . This is generated by viewing thegroup of diffeomorphisms as a Riemannian manifold with , associated to the tangent space at . This induces the norm and metric on the orbit under the action from the group of diffeomorphisms. (en)
prov:wasDerivedFrom	wikipedia-en:Riemannian_metric_and_Lie_bracket_in_computational_anatomy?oldid=1123961638&ns=0
page length (characters) of wiki page	21524 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Riemannian_metric_and_Lie_bracket_in_computational_anatomy
is Link from a Wikipage to another Wikipage of	Riemannian Metric and Lie-Bracket in Computational Anatomy Riemannian metric and Lie-bracket in computational anatomy Riemannian metric and lie-bracket in computational anatomy The Riemannian Metric and Lie-Bracket in Computational Anatomy Riemannian Metric and Lie-Bracket Interpretation of the Euler Equation on Geodesics Riemannian Metric and Lie-Bracket for Euler Equation for Computational Anatomy Riemannian Metric and Lie-Bracket for the Euler-Lagrange Equation on Geodesics in the Orbit of Shapes in Computational Anatomy
is Wikipage redirect of	Riemannian Metric and Lie-Bracket in Computational Anatomy Riemannian metric and Lie-bracket in computational anatomy Riemannian metric and lie-bracket in computational anatomy The Riemannian Metric and Lie-Bracket in Computational Anatomy Riemannian Metric and Lie-Bracket Interpretation of the Euler Equation on Geodesics Riemannian Metric and Lie-Bracket for Euler Equation for Computational Anatomy Riemannian Metric and Lie-Bracket for the Euler-Lagrange Equation on Geodesics in the Orbit of Shapes in Computational Anatomy
is foaf:primaryTopic of	wikipedia-en:Riemannian_metric_and_Lie_bracket_in_computational_anatomy

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