This paper describes the generation of large deformation diffeomorphisms ph
i : Omega = [0, 1](3) <-> for landmark matching generated as solutions to t
he transport equation d phi(x,t)/dt = nu(phi(x,t),t),t epsilon [0,1] and ph
i(x,0) = x, with the image map defined as phi(, 1) and therefore controlled
via the velocity field nu(., t),t epsilon [0, 1], Imagery are assumed char
acterized via sets of landmarks {x(n), y(n), n = 1, 2,..., N}. The optimal
diffeomorphic match is constructed to minimize a running smoothness cost pa
rallel to L nu parallel to(2) associated with a linear differential operato
r L on the velocity field generating the diffeomorphism while simultaneousl
y minimizing the matching end point condition of the landmarks,
Both inexact and exact Landmark matching is studied here. Given noisy landm
arks x(n) matched to y(n) measured with error covariances Sigma(n) then the
matching problem is solved generating the optimal diffeomorphism <(phi)ove
r cap>(x, 1) = integral(0)(1) <(nu)over cap>(<(phi)over cap>(x,t), t) dt x where
<(nu)over cap>(.) = arg min(nu(.)) integral(0)(1) integral(Omega) parallel
to L nu(x,t)parallel to(2) dx dt + Sigma(n=1)(N) [yn-phi(xn,1)](T)Sigma(n)(
-1)[yn-phi(x(n),1)]. (1)
Conditions for the existence of solutions in the space of diffeomorphisms a
re established, with a gradient algorithm provided for generating the optim
al flow solving the minimum problem. Results on matching two-dimensional (2
-D) and three-dimensional (3-D) imagery are presented in the the macaque mo
nkey.