Moment evolution equations and moment matching for stochastic image EPDiff

TL;DR

This paper develops moment evolution equations and moment matching techniques for stochastic image deformation models, enabling efficient statistical inference of noise parameters in stochastic LDDMM frameworks.

Contribution

It introduces a novel moment approximation approach for stochastic EPDiff equations in image deformation, facilitating parameter estimation in complex stochastic models.

Findings

Successfully estimates spatial noise correlation parameters

Demonstrates effective use of automatic differentiation for inference

Validates approach on stochastic image deformation models

Abstract

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 It\^o 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.