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Published in:
2013 | OriginalPaper | Chapter
The Persistence Space in Multidimensional Persistent Homology
Authors : Andrea Cerri, Claudia Landi
Published in: Discrete Geometry for Computer Imagery
Publisher: Springer Berlin Heidelberg
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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.