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.

翻译：视觉图像变形模型可以研究通过图像领域变形改变图像的时间-持续随机影响。 应用包括包含人口趋势和随机主题特定变异的纵向医学图像分析。 侧重于LDDMM模型的随机扩展,其演化由随机 EPDiff 等式调节,我们使用相应的It ⁇ o扩散瞬时近似值来构建完整视觉模型中统计推导的估测器。 我们显示,这种方法如果以自动分化工具有效运用,可以成功地估算图像上噪音场空间相关性的参数。