Moment evolution equations and moment matching for stochastic image EPDiff
This work addresses the need for statistical inference in stochastic image deformation models, particularly for longitudinal medical image analysis, but it is incremental as it builds on existing LDDMM models.
The paper tackled the problem of estimating parameters in stochastic image deformation models by developing moment evolution equations and moment matching for a stochastic EPDiff equation, resulting in successful estimation of spatial correlation parameters for noise fields on images using efficient automatic differentiation tools.
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random subject specific variation. Focusing on a stochastic extension of the LDDMM models with evolutions governed by a stochastic EPDiff equation, we use moment approximations of the corresponding Itô diffusion to construct estimators for statistical inference in the full stochastic model. We show that this approach, when efficiently implemented with automatic differentiation tools, can successfully estimate parameters encoding the spatial correlation of the noise fields on the image.