Spatiotemporal Modeling for Image Time Series with Appearance Change: Application to Early Brain Development

There has been considerable research effort into image registration and regression, which address the problem of determining correspondence primarily through estimating models of structural change. There has been far less focus into methods which model both structural and intensity change. However, medical images often exhibit intensity changes over time. Of particular interest is MRI of the early developing brain, where such intensity change encodes rich information about development, such as rapidly increasing white matter intensity during the first years of life. In this paper, we develop a new spatiotemporal model which takes into account both structural and appearance changes jointly. This will not only lead to improved regression accuracy and data-matching in the presence of longitudinal intensity changes, but also facilitate the study of development by direct analysis of appearance change models. We propose to combine a diffeomorphic model of structural change with a Gompertz intensity model, which captures intensity trajectories with 3 intuitive parameters of asymptote, delay, and speed. We propose an optimization scheme which allows to control the balance between structural and intensity change via two data-matching terms. We show that Gompertz parameter maps show great promise to characterize regional patterns of development.