  This paper explores a novel connection between two areas: shape analysis of
surfaces and unbalanced optimal transport. Specifically, we characterize the
square root normal field (SRNF) shape distance as the pullback of the
Wasserstein-Fisher-Rao (WFR) unbalanced optimal transport distance. In
addition, we propose a new algorithm for computing the WFR distance and present
numerical results that highlight the effectiveness of this algorithm. As a
consequence of our results we obtain a precise method for computing the SRNF
shape distance directly on piecewise linear surfaces and gain new insights
about the degeneracy of this distance.
