We introduce a stochastic model of diffeomorphisms, whose action on a variety
of data types descends to stochastic evolution of shapes, images and landmarks.
The stochasticity is introduced in the vector field which transports the data
in the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework for
shape analysis and image registration. The stochasticity thereby models errors
or uncertainties of the flow in following the prescribed deformation velocity.
The approach is illustrated in the example of finite dimensional landmark
manifolds, whose stochastic evolution is studied both via the Fokker-Planck
equation and by numerical simulations. We derive two approaches for inferring
parameters of the stochastic model from landmark configurations observed at
discrete time points. The first of the two approaches matches moments of the
Fokker-Planck equation to sample moments of the data, while the second approach
employs an Expectation-Maximisation based algorithm using a Monte Carlo bridge
sampling scheme to optimise the data likelihood. We derive and numerically test
the ability of the two approaches to infer the spatial correlation length of
the underlying noise.