  We show that the recently introduced L1TV functional can be used to
explicitly compute the flat norm for co-dimension one boundaries. While this
observation alone is very useful, other important implications for image
analysis and shape statistics include a method for denoising sets which are not
boundaries or which have higher co-dimension and the fact that using the flat
norm to compute distances not only gives a distance, but also an informative
decomposition of the distance. This decomposition is made to depend on scale
using the "flat norm with scale" which we define in direct analogy to the L1TV
functional. We illustrate the results and implications with examples and
figures.
