  We introduce \emph{ReMatching}, a novel shape correspondence solution based
on the functional maps framework. Our method, by exploiting a new and
appropriate \emph{re}-meshing paradigm, can target shape-\emph{matching} tasks
even on meshes counting millions of vertices, where the original functional
maps does not apply or requires a massive computational cost. The core of our
procedure is a time-efficient remeshing algorithm which constructs a
low-resolution geometry while acting conservatively on the original topology
and metric. These properties allow translating the functional maps optimization
problem on the resulting low-resolution representation, thus enabling efficient
computation of correspondences with functional map approaches. Finally, we
propose an efficient technique for extending the estimated correspondence to
the original meshes. We show that our method is more efficient and effective
through quantitative and qualitative comparisons, outperforming
state-of-the-art pipelines in quality and computational cost.
