  We present an algorithm for computing the barcode of the image of a morphisms
in persistent homology induced by an inclusion of filtered finite-dimensional
chain complexes. These algorithms make use of the clearing optimization and can
be applied to inclusion-induced maps in persistent absolute homology and
persistent relative cohomology for filtrations of pairs of simplicial
complexes. They form the basis for our implementation for Vietoris-Rips
complexes in the framework of the software Ripser.
