This Python code accompanies the paper Langevin equations for landmark image registration with uncertainty, S. Marsland and T. Shardlow (2016).
Registration of images parameterised by landmarks provides a useful method of
describing shape variations by computing the minimum-energy time-dependent deformation
field that flows 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.
Example sets and further explanation about the code are found in the supplement.