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Langevin equations for landmark image registration with uncertainty

Presented by: 
Stephen Marsland Massey University
Wednesday 13th December 2017 - 11:30 to 12:30
INI Seminar Room 1
Co-author: Tony Shardlow (University of Bath)

Pairs of images can be brought into alignment (registered) by finding corresponding points on the two images and deforming one of them so that the points match. This can be carried out as a Hamiltonian boundary-value problem, and then provides 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. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons