An image warping approach to spatio-temporal modelling

In this article we present a spatio-temporal dynamic model that can be realized using image warping. Image warping is a non-linear deformation which maps every point in one image plane to a point in another image plane. Using thin-plate splines, these deformations are defined by how a small set of points is mapped, making the method computationally tractable. In our case the dynamics of the process is modelled by thin-plate spline deformations and how they vary in time. Thus we make no assumption of stationarity in time. Finding the deformation between two images in the space–time series is a trade-off between a good match of the images and a smooth, physically plausible, deformation. This is formulated as a penalized likelihood problem, where the likelihood measures how good the match is and the penalty comes from a prior model on the deformation. The dynamic model we suggest can be used to make forecasts and also to estimate the uncertainties associated with these. An introduction to image warping and thin-plate splines is given as well as an application where the methodology is applied to the problem of nowcasting radar precipitation.