Computing Large Deformation Metric Mappings via Geodesic Flows of Diffeomorphisms

摘要

This 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 I 0, I 1 are given and connected via the diffeomorphic change of coordinates I 0○ϕ−1=I 1 where ϕ=Φ1 is the end point at t= 1 of curve Φ t , t∈[0, 1] satisfying .Φ t =v t (Φ t ), t∈ [0,1] with Φ0=id. The variational problem takes the form