  Specific data compression techniques, formalized by the concept of coresets,
proved to be powerful for many optimization problems. In fact, while tightly
controlling the approximation error, coresets may lead to significant speed up
of the computations and hence allow to extend algorithms to much larger problem
sizes. The present paper deals with a weight-balanced clustering problem from
imaging in materials science. Here, the class of desired coresets is naturally
confined to those which can be viewed as lowering the resolution of the data.
Hence one would expect that such resolution coresets are inferior to
unrestricted coreset. We show, however, that the restrictions are more than
compensated by utilizing the underlying structure of the data. In particular,
we prove bounds for resolution coresets which improve known bounds in the
relevant dimensions and also lead to significantly faster algorithms practice.
