  Surface comparison and matching is a challenging problem in computer vision.
While reparametrization-invariant Sobolev metrics provide meaningful elastic
distances and point correspondences via the geodesic boundary value problem,
solving this problem numerically tends to be difficult. Square root normal
fields (SRNF) considerably simplify the computation of certain elastic
distances between parametrized surfaces. Yet they leave open the issue of
finding optimal reparametrizations, which induce elastic distances between
unparametrized surfaces. This issue has concentrated much effort in recent
years and led to the development of several numerical frameworks. In this
paper, we take an alternative approach which bypasses the direct estimation of
reparametrizations: we relax the geodesic boundary constraint using an
auxiliary parametrization-blind varifold fidelity metric. This reformulation
has several notable benefits. By avoiding altogether the need for
reparametrizations, it provides the flexibility to deal with simplicial meshes
of arbitrary topologies and sampling patterns. Moreover, the problem lends
itself to a coarse-to-fine multi-resolution implementation, which makes the
algorithm scalable to large meshes. Furthermore, this approach extends readily
to higher-order feature maps such as square root curvature fields and is also
able to include surface textures in the matching problem. We demonstrate these
advantages on several examples, synthetic and real.
