# Stability of persistence spaces of vector-valued continuous functions

@article{Cerri2013StabilityOP, title={Stability of persistence spaces of vector-valued continuous functions}, author={Andrea Cerri and Claudia Landi}, journal={ArXiv}, year={2013}, volume={abs/1305.6425} }

Multidimensional persistence 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…

## 4 Citations

The Persistence Space in Multidimensional Persistent Homology

- MathematicsDGCI
- 2013

The persistence space of a vector-valued continuous function is introduced to generalize the concept of persistence diagram in this sense and a method to visualize topological features of a shape via persistence spaces is presented.

Necessary conditions for discontinuities of multidimensional persistent Betti numbers

- Mathematics
- 2015

Topological persistence has proven to be a promising framework for dealing with problems concerning the analysis of data. In this context, it was originally introduced by taking into account…

Shape Analysis and Description Using Real Functions

- Computer ScienceTopological and Statistical Methods for Complex Data, Tackling Large-Scale, High-Dimensional, and Multivariate Data Spaces
- 2015

We discuss how the shape of an object can be analyzed according to the properties of real functions defined on it, and how these properties can be stored in compact and informative…

PHOG: Photometric and geometric functions for textured shape retrieval

- Computer ScienceSGP '13
- 2013

This paper shows how to include photometric information in the persistence homology setting, and introduces a generalization of the integral geodesic distance which fuses shape and color properties and adopts a purely geometric description.

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