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Group actions in computational anatomy
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<p><a href="/facts/Group_action_(mathematics)/Vh9VtUUw">Group actions</a> are central to <a href="/facts/Riemannian_geometry/pPEzjyQC">Riemannian geometry</a> and defining <a href="/facts/Orbit_(control_theory)/RLESThsQ">orbits (control theory)</a>. The orbits of <a href="/facts/Computational_anatomy/8lA9YzSB">computational anatomy</a> consist of <a href="/facts/Computational_anatomy/8lA9YzSB">anatomical shapes and medical images</a>; the anatomical shapes are submanifolds of <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a> consisting of points, curves, surfaces and subvolumes,. This generalized the ideas of the more familiar orbits of <a href="/facts/Linear_algebra/8VaB4VWk">linear algebra</a> which are <a href="/facts/Vector_space/M1pxMLx2">linear vector spaces</a>. Medical images are scalar and tensor images from <a href="/facts/Medical_imaging/pL6JyJEp">medical imaging</a>. The group actions are used to define models of human shape which accommodate variation. These orbits are deformable templates as originally formulated more abstractly in <a href="/facts/Pattern_theory/sBIjR1cz">pattern theory</a>. </p>