  Modelling deformation of anatomical objects observed in medical images can
help describe disease progression patterns and variations in anatomy across
populations. We apply a stochastic generalisation of the Large Deformation
Diffeomorphic Metric Mapping (LDDMM) framework to model differences in the
evolution of anatomical objects detected in populations of image data. The
computational challenges that are prevalent even in the deterministic LDDMM
setting are handled by extending the FLASH LDDMM representation to the
stochastic setting keeping a finite discretisation of the infinite dimensional
space of image deformations. In this computationally efficient setting, we
perform estimation to infer parameters for noise correlations and local
variability in datasets of images. Fundamental for the optimisation procedure
is using the finite dimensional Fourier representation to derive approximations
of the evolution of moments for the stochastic warps. Particularly, the first
moment allows us to infer deformation mean trajectories. The second moment
encodes variation around the mean, and thus provides information on the noise
correlation. We show on simulated datasets of 2D MR brain images that the
estimation algorithm can successfully recover parameters of the stochastic
model.
