Abstract
In ℝ2, rigid transformations are topology-preserving operations. However, this property is generally no longer true when considering digital images instead of continuous ones, due to digitization effects. In this article, we investigate this issue by studying discrete rigid transformations (DRTs) on ℤ2. More precisely, we define conditions under which digital images preserve their topological properties under any arbitrary DRTs. Based on the recently introduced notion of DRT graph and the classical notion of simple point, we first identify a family of local patterns that authorize topological invariance under DRTs. These patterns are then involved in a local analysis process that guarantees topological invariance of whole digital images in linear time.
Keywords
- 2D digital image
- discrete rigid transformation
- topology
- simple point
- DRT graph
- Eulerian model
The research leading to these results has received funding from the French Agence Nationale de la Recherche (Grant Agreement ANR-2010-BLAN-0205 03).
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Ngo, P., Kenmochi, Y., Passat, N., Talbot, H. (2013). Sufficient Conditions for Topological Invariance of 2D Images under Rigid Transformations. 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_14
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DOI: https://doi.org/10.1007/978-3-642-37067-0_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37066-3
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