DocumentCode :
1363855
Title :
Landmark matching via large deformation diffeomorphisms
Author :
Joshi, Sarang C. ; Miller, Michael I.
Author_Institution :
North Carolina Univ., Chapel Hill, NC, USA
Volume :
9
Issue :
8
fYear :
2000
fDate :
8/1/2000 12:00:00 AM
Firstpage :
1357
Lastpage :
1370
Abstract :
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 1Ω||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
Keywords :
covariance analysis; differential equations; gradient methods; image matching; image sequences; mathematical operators; medical image processing; minimisation; noise; 2D imagery matching; 3D imagery matching; anatomical images; error covariances; exact landmark matching; gradient algorithm; inexact landmark matching; large deformation diffeomorphisms; linear differential operator; macaque monkey; matching end point condition; medical imaging; noisy landmarks; optimal diffeomorphic match; optimal flow generation; running smoothness cost minimisation; transport equation solution; velocity field; Anatomy; Area measurement; Biology computing; Biomedical imaging; Computed tomography; Equations; Image matching; Length measurement; Shape measurement; X-ray imaging;
fLanguage :
English
Journal_Title :
Image Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1057-7149
Type :
jour
DOI :
10.1109/83.855431
Filename :
855431
Link To Document :
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