  We compare two state-of-the-art non-linear techniques for nonparametric
function estimation via piecewise constant approximation: the taut string and
the Unbalanced Haar methods. While it is well-known that the latter is
multiscale, it is not obvious that the former can also be interpreted as
multiscale. We provide a unified multiscale representation for both methods,
which offers an insight into the relationship between them as well as
suggesting lessons both methods can learn from each other.
