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Bayesian model of computational anatomy
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<p>Computational anatomy (CA) is a discipline within <a href="/facts/Medical_imaging/pL6JyJEp">medical imaging</a> focusing on the study of anatomical shape and form at the visible or <a href="/facts/Gross_anatomy/SMek20Yh">gross anatomical</a> scale of <a href="/facts/Morphology_(biology)/Nl3B0myy">morphology</a>. The field is broadly defined and includes foundations in <a href="/facts/Anatomy/p8TCWJuV">anatomy</a>, <a href="/facts/Applied_mathematics/qyqklXXm">applied mathematics</a> and <a href="/facts/Pure_mathematics/V29nQC1C">pure mathematics</a>, including <a href="/facts/Medical_imaging/pL6JyJEp">medical imaging</a>, <a href="/facts/Neuroscience/o5RV8Cas">neuroscience</a>, <a href="/facts/Physics/a7aH2y08">physics</a>, <a href="/facts/Probability/fgYvMhwb">probability</a>, and <a href="/facts/Statistics/DNPsKGYU">statistics</a>. It focuses on the anatomical structures being imaged, rather than the medical imaging devices. The central focus of the sub-field of <a href="/facts/Computational_anatomy/8lA9YzSB">computational anatomy</a> within <a href="/facts/Medical_imaging/pL6JyJEp">medical imaging</a> is mapping information across anatomical coordinate systems most often dense information measured within a <a href="/facts/Magnetic_resonance_imaging/Vh9yG9qq">magnetic resonance image</a> (MRI). The introduction of flows into CA, which are akin to the equations of motion used in fluid dynamics, exploit the notion that dense coordinates in image analysis follow the <a href="/facts/Lagrangian_and_Eulerian_specification_of_the_flow_field/sYLvgboC">Lagrangian and Eulerian</a> equations of motion. In models based on Lagrangian and Eulerian flows of diffeomorphisms, the constraint is associated to topological properties, such as open sets being preserved, coordinates not crossing implying uniqueness and existence of the inverse mapping, and connected sets remaining connected. The use of diffeomorphic methods grew quickly to dominate the field of mapping methods post Christensen's original paper, with fast and symmetric methods becoming available. </p>