  The square root velocity transform is a powerful tool for the efficient
computation of distances between curves. Also, after factoring out
reparametrisations, it defines a distance between shapes that only depends on
their intrinsic geometry but not the concrete parametrisation. Though
originally formulated for smooth curves, the square root velocity transform and
the resulting shape distance have been thoroughly analysed for the setting of
absolutely continuous curves using a relaxed notion of reparametrisations. In
this paper, we will generalise the square root velocity distance even further
to a class of discontinuous curves. We will provide an explicit formula for the
natural extension of this distance to curves of bounded variation and analyse
the resulting quotient distance on the space of unparametrised curves. In
particular, we will discuss the existence of optimal reparametrisations for
which the minimal distance on the quotient space is realised.
