Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012
This paper deals with the concepts of persistence diagrams and matching distance. They are two of... more This paper deals with the concepts of persistence diagrams and matching distance. They are two of the main ingredients of Topo- logical Persistence, which has proven to be a promising framework for shape comparison. Persistence diagrams are descriptors providing a sig- nature of the shapes under study, while the matching distance is a metric to compare them. One drawback in
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimi... more The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012
This paper deals with the concepts of persistence diagrams and matching distance. They are two of... more This paper deals with the concepts of persistence diagrams and matching distance. They are two of the main ingredients of Topo- logical Persistence, which has proven to be a promising framework for shape comparison. Persistence diagrams are descriptors providing a sig- nature of the shapes under study, while the matching distance is a metric to compare them. One drawback in
The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimi... more The concept of natural pseudo-distance has proven to be a powerful tool for measuring the dissimilarity between topological spaces endowed with continuous real-valued functions. Roughly speaking, the natural pseudo-distance is defined as the infimum of the change of the functions' values, when moving from one space to the other through homeomorphisms, if possible. In this paper, we prove the first available result about the existence of optimal homeomorphisms between closed curves, i.e. inducing a change of the function that equals the natural pseudo-distance.
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Papers by Barbara Fabio