Geodesic Image Interpolation: Parameterizing and Interpolating Spatiotemporal Images

We develop a practical, symmetric, data-driven formulation, geodesic image interpolation (GII), for interpolating images with respect to geometric and photometric variables. GII captures, in implementation, the desirable properties of symmetry that comes from the theory of diffeomorphisms and Grenander’s computational anatomy (CA). Geodesic diffeomorphisms are a desirable transformation model as they provide a symmetric deforming path connecting images or a series of images. Once estimated, this geodesic may be used to (re)parameterize and interpolate image sets in approximation of continuous, deforming dynamic processes. One may then closely recover the original continuous signal from a few samples. The method, based on our work in symmetric diffeomorphic image registration, generalizes the concept of point set reparameterization to the case where point sets are replaced by image sets. This problem differs from point reparameterization in that a variational image correspondence problem must be solved before resampling. Our image reparameterization method is applied to solve similar problems to point reparameterization: dense interpolation, matching and simulation of dynamic processes are illustrated.