  We present a novel method to model and calculate deformation fields between
shapes embedded in $\mathbb{R}^D$. Our framework combines naturally
interpolating the two input shapes and calculating correspondences at the same
time. The key idea is to compute a divergence-free deformation field
represented in a coarse-to-fine basis using the Karhunen-Lo\`eve expansion. The
advantages are that there is no need to discretize the embedding space and the
deformation is volume-preserving. Furthermore, the optimization is done on
downsampled versions of the shapes but the morphing can be applied to any
resolution without a heavy increase in complexity. We show results for shape
correspondence, registration, inter- and extrapolation on the TOSCA and FAUST
data sets.
