# Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

@article{Beg2004ComputingLD, title={Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms}, author={Mirza Faisal Beg and Michael I. Miller and Alain Trouv{\'e} and Laurent Younes}, journal={International Journal of Computer Vision}, year={2004}, volume={61}, pages={139-157} }

AbstractThis paper examine the Euler-Lagrange equations for the solution of the large deformation diffeomorphic metric mapping problem studied in Dupuis et al. (1998) and Trouvé (1995) in which two images I0, I1 are given and connected via the diffeomorphic change of coordinates I0○ϕ−1=I1 where ϕ=Φ1 is the end point at t= 1 of curve Φt, t∈[0, 1] satisfying .Φt=vt (Φt), t∈ [0,1] with Φ0=id. The variational problem takes the form
$$\mathop {\arg {\text{m}}in}\limits_{\upsilon :\dot \phi _t…

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