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Topology-Preserving Conditions for 2D Digital Images Under Rigid Transformations

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Abstract

In the continuous domain \(\mathbb{R}^{n}\), rigid transformations are topology-preserving operations. Due to digitization, this is not the case when considering digital images, i.e., images defined on \(\mathbb{Z}^{n}\). In this article, we begin to investigate this problem by studying conditions for digital images to preserve their topological properties under all rigid transformations on \(\mathbb{Z}^{2}\). Based on (i) the recently introduced notion of DRT graph, and (ii) the notion of simple point, we propose an algorithm for evaluating digital images topological invariance.

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Notes

  1. The term digital refers to the digitization process of numeric images and transformations for such images, while the term discrete refers to the non-continuous structure of these transformations.

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Acknowledgements

The research leading to these results has received partial funding from the French Agence Nationale de la Recherche (Grant Agreement ANR-10-BLAN-0205 03).

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Authors and Affiliations

  1. LIGM, UPEMLV-ESIEE-CNRS, Université Paris-Est, Paris, France

    Phuc Ngo, Yukiko Kenmochi & Hugues Talbot

  2. CReSTIC, Université de Reims Champagne-Ardenne, Reims, France

    Nicolas Passat

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  1. Phuc Ngo
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  2. Yukiko Kenmochi
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  4. Hugues Talbot
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Correspondence to Phuc Ngo.

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Ngo, P., Kenmochi, Y., Passat, N. et al. Topology-Preserving Conditions for 2D Digital Images Under Rigid Transformations. J Math Imaging Vis 49, 418–433 (2014). https://doi.org/10.1007/s10851-013-0474-z

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