Abstract
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.
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Cerri, A., Landi, C. (2013). The Persistence Space in Multidimensional Persistent Homology. In: Gonzalez-Diaz, R., Jimenez, MJ., Medrano, B. (eds) Discrete Geometry for Computer Imagery. DGCI 2013. Lecture Notes in Computer Science, vol 7749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37067-0_16
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DOI: https://doi.org/10.1007/978-3-642-37067-0_16
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Keywords
- Topological Feature
- Homology Class
- Lower Dimensional Space
- Persistent Homology
- Multidimensional Analogue
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
