  The theory of multidimensional persistent homology was initially developed in
the discrete setting, and involved the study of simplicial complexes filtered
through an ordering of the simplices. Later, stability properties of
multidimensional persistence have been proved to hold when topological spaces
are filtered by continuous functions, i.e. for continuous data. This paper aims
to provide a bridge between the continuous setting, where stability properties
hold, and the discrete setting, where actual computations are carried out. More
precisely, a stability preserving method is developed to compare rank
invariants of vector functions obtained from discrete data. These advances
confirm that multidimensional persistent homology is an appropriate tool for
shape comparison in computer vision and computer graphics applications. The
results are supported by numerical tests.
