Landmark matching via large deformation diffeomorphisms
Joshi, S.C.; Miller, M.I.
Image Processing, IEEE Transactions on
Volume 9, Issue 8, Aug 2000 Page(s):1357 - 1370
Digital Object Identifier 10.1109/83.855431
Summary:This paper describes the generation of large deformation
diffeomorphisms φ:Ω=[0,1]3&rlhar2;Ω for
landmark matching generated as solutions to the transport equation
dφ(x,t)/dt=ν(φ(x,t),t),t∈[0,1] and φ(x,0)=x, with
the image map defined as φ(·,1) and therefore controlled via
the velocity field ν(·,t),t∈[0,1]. Imagery are assumed
characterized via sets of landmarks {xn, yn, n=1,
2, ..., N}. The optimal diffeomorphic match is constructed to minimize a
running smoothness cost ||Lν||2 associated with a
linear differential operator L on the velocity field generating the
diffeomorphism while simultaneously minimizing the matching end point
condition of the landmarks. Both inexact and exact landmark matching is
studied here. Given noisy landmarks xn matched to yn
measured with error covariances Σn, then the
matching problem is solved generating the optimal diffeomorphism
φˆ(x,1)=∫01
νˆ(φˆ(x,t),t)dt+x where
νˆ(·)argminν(·)∫1
1∫Ω||Lν(x,t)||2dxdt
+Σn=1N[yn-φ(xn,1)]
TΣn-1[yn-φ(xn
,1)]. Conditions for the existence of solutions in the space of
diffeomorphisms are established, with a gradient algorithm provided for
generating the optimal flow solving the minimum problem. Results on
matching two-dimensional (2-D) and three-dimensional (3-D) imagery are
presented in the macaque monkey
View citation and abstract |
Cart
