Moment Evolution Equations and Moment Matching for Stochastic Image EPDiff

Models of stochastic image deformation allow study time-continuous effects transforming images by deforming the domain. Applications include longitudinal medical analysis with both population trends and random subject-specific variation. Focusing on a extension LDDMM models evolutions governed EPDiff equation, we use moment approximations corresponding Itô diffusion to construct estimators for statistical inference in full model. We show that this approach, when efficiently implemented automatic differentiation tools, can successfully estimate parameters encoding spatial correlation noise fields image.