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This paper deals with the concepts of persistence diagram and matching distance. These are two of the main ingredients of Topological Persistence, which has proven to be a promising framework for shape comparison. Persistence diagrams are descriptors providing a signature of the shapes under study, while the matching distance is a metric to compare them. One drawback in the application of these tools is the computational cost for the evaluation of the matching distance. The aim of the presentdoi:10.6092/unibo/amsacta/3498 fatcat:qsjsjuderbfgte2vzythx3cv4q