Abstract
In this article, a tractable modus operandi is proposed to model a (binary) digital image (i.e., an image defined on \(\mathbb Z^n\) and equipped with a standard pair of adjacencies) as an image defined in the space of cubical complexes (\(\mathbb F^n\)). In particular, it is shown that all the standard pairs of adjacencies in \(\mathbb Z^n\) can then be correctly modelled in \(\mathbb F^n\). Moreover, it is established that the digital fundamental group of a digital image in \(\mathbb Z^n\) is isomorphic to the fundamental group of its corresponding image in \(\mathbb F^n\), thus proving the topological correctness of the proposed approach. From these results, it becomes possible to establish links between topology-oriented methods developed either in classical digital spaces (\(\mathbb Z^n\)) or cubical complexes (\(\mathbb{F}^n\)).
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Mazo, L., Passat, N., Couprie, M., Ronse, C. (2011). A Unified Topological Framework for Digital Imaging. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2011. Lecture Notes in Computer Science, vol 6607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19867-0_14
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