Langevin equations for landmark image registration with uncertainty

Tony Shardlow, Stephen Marsland

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
125 Downloads (Pure)

Abstract

Registration of images parameterized by landmarks provides a useful method of describing shape variations by computing the minimum-energy time-dependent deformation field that flows from one landmark set to the other. This is sometimes known as the geodesic interpolating spline and can be solved via a Hamiltonian boundary-value problem to give a diffeomorphic registration between images. However, small changes in the positions of the landmarks can produce large changes in the resulting diffeomorphism. We formulate a Langevin equation for looking at small random perturbations of this registration. The Langevin equation and three computationally convenient approximations are introduced and used as prior distributions. A Bayesian framework is then used to compute a posterior distribution for the registration, and also to formulate an average of multiple sets of landmarks.
Original languageEnglish
Pages (from-to)782-807
Number of pages26
JournalSIAM Journal on Imaging Sciences
Volume10
Issue number2
Early online date25 May 2017
DOIs
Publication statusPublished - 31 Dec 2017

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