  We derive an algorithm for compression of the currents and varifolds
representations of shapes, using the Nystrom approximation in Reproducing
Kernel Hilbert Spaces. Our method is faster than existing compression
techniques, and comes with theoretical guarantees on the rate of convergence of
the compressed approximation, as a function of the smoothness of the associated
shape representation. The obtained compression are shown to be useful for
down-line tasks such as nonlinear shape registration in the Large Deformation
Metric Mapping (LDDMM) framework, even for very high compression ratios. The
performance of our algorithm is demonstrated on large-scale shape data from
modern geometry processing datasets, and is shown to be fast and scalable with
rapid error decay.
