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Shape Analysis and Description Using Real Functions

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Topological and Statistical Methods for Complex Data

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

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Abstract

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 geometric/topological descriptors. As examples, we refer to Reeb graphs and persistence diagrams, encoding either the configuration of level sets or sub-level sets of functions. We then move to the case of vector-valued functions, encoding multi-dimensional properties of shapes, showing how this kind of information can be dealt with by means of persistence spaces. Experiments on the retrieval of textured 3D models are presented as a possible application of such tools.

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Acknowledgements

This work is partially funded by the EU project IQmulus under grant agreement no. FP7-ICT-2011-318787 and the CNR Flagship project INTEROMICS, InterOmics PB05, research unit WP 15.

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Authors and Affiliations

  1. CNR-IMATI, Via De Marini 6, Genova, Italy

    Silvia Biasotti, Andrea Cerri, Michela Spagnuolo & Bianca Falcidieno

Authors
  1. Silvia Biasotti
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  2. Andrea Cerri
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  3. Michela Spagnuolo
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  4. Bianca Falcidieno
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Corresponding author

Correspondence to Bianca Falcidieno .

Editor information

Editors and Affiliations

  1. Sandia National Laboratories, MS 9152, Livermore, California, USA

    Janine Bennett

  2. CEA CESTA, CS 60001, Le Barp CEDEX, France

    Fabien Vivodtzev

  3. School of Computing and SCI Institute, University of Utah, Salt Lake City, Utah, USA

    Valerio Pascucci

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Biasotti, S., Cerri, A., Spagnuolo, M., Falcidieno, B. (2015). Shape Analysis and Description Using Real Functions. In: Bennett, J., Vivodtzev, F., Pascucci, V. (eds) Topological and Statistical Methods for Complex Data. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44900-4_6

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