Multidimensional persistent modules do not admit a concise representation analogous to that provided by persistence diagrams for real-valued functions. However, there is no obstruction for multidimensional persistent Betti numbers to admit one. Therefore, it is reasonable to look for a generalization of persistence diagrams concerning those properties that are related only to persistent Betti numbers. In this paper, the persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense. Furthermore, it is presented a method to visualize topological features of a shape via persistence spaces. Finally, it is shown that this method is resistant to perturbations of the input data. © 2013 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Cerri, A., & Landi, C. (2013). The persistence space in multidimensional persistent homology. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7749 LNCS, pp. 180–191). Springer Verlag. https://doi.org/10.1007/978-3-642-37067-0_16
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