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Modelling deformation of anatomical objects observed in medical images canhelp describe disease progression patterns and variations in anatomy acrosspopulations. We apply a stochastic generalisation of the Large DeformationDiffeomorphic Metric Mapping (LDDMM) framework to model differences in theevolution of anatomical objects detected in populations of image data. Thecomputational challenges that are prevalent even in the deterministic LDDMMsetting are handled by extending the FLASH LDDMM representation to thestochastic setting keeping a finite discretisation of the infinite dimensionalspace of image deformations. In this computationally efficient setting, weperform estimation to infer parameters for noise correlations and localvariability in datasets of images. Fundamental for the optimisation procedureis using the finite dimensional Fourier representation to derive approximationsof the evolution of moments for the stochastic warps. Particularly, the firstmoment allows us to infer deformation mean trajectories. The second momentencodes variation around the mean, and thus provides information on the noisecorrelation. We show on simulated datasets of 2D MR brain images that theestimation algorithm can successfully recover parameters of the stochasticmodel.

Stochastic Image Deformation in Frequency Domain and Parameter Estimation using Moment Evolutions