  This paper proposes a new framework and algorithms to address the problem of
diffeomorphic registration on a general class of geometric objects that can be
described as discrete distributions of local direction vectors. It builds on
both the large deformation diffeomorphic metric mapping (LDDMM) model and the
concept of oriented varifolds introduced in previous works like [Kaltenmark
2017]. Unlike previous approaches in which varifold representations are only
used as surrogates to define and evaluate fidelity terms, the specificity of
this paper is to derive direct deformation models and corresponding matching
algorithms for discrete varifolds. We show that it gives on the one hand an
alternative numerical setting for curve and surface matching but that it can
also handle efficiently more general shape structures, including
multi-directional objects or multi-modal images represented as distributions of
unit gradient vectors.
