An Image Warping Approach to SpatioTemporal Dynamic Modelling
Sofia Aberg, Finn Lindgren, Anders Malmberg, Jan Holst and Ulla Holst
Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,
2004
ISSN 14039338

Abstract:

In this work we present a spatiotemporal dynamic model that can be realized
using image warping. Image warping is a nonlinear deformation which maps
every point in one image plane to a point in another image plane. Using
thinplate 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 thinplate 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 spacetime series is a tradeoff
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 thinplate splines is given as
well as an application where the methodology is applied to the problem of
nowcasting radar precipitation.




Key words:

Dynamic models, spatiotemporal modelling, image warping, thinplate splines,
forecasting
