A Unified Topological Framework for Digital Imaging
Identifieur interne : 002783 ( Main/Exploration ); précédent : 002782; suivant : 002784A Unified Topological Framework for Digital Imaging
Auteurs : Loïc Mazo [France] ; Nicolas Passat [France] ; Michel Couprie [France] ; Christian Ronse [France]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
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 ( $\mathbb{F}^n$ ).
Url:
DOI: 10.1007/978-3-642-19867-0_14
Affiliations:
- France
- Alsace (région administrative), Grand Est, Île-de-France
- Paris, Strasbourg
- Université de Strasbourg
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type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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 ( $\mathbb{F}^n$ ).</div></front></TEI><affiliations><list><country><li>France</li></country><region><li>Alsace (région administrative)</li><li>Grand Est</li><li>Île-de-France</li></region><settlement><li>Paris</li><li>Strasbourg</li></settlement><orgName><li>Université de Strasbourg</li></orgName></list><tree><country name="France"><region name="Grand Est"><name sortKey="Mazo, Loic" sort="Mazo, Loic" uniqKey="Mazo L" first="Loïc" last="Mazo">Loïc Mazo</name></region><name sortKey="Couprie, Michel" sort="Couprie, Michel" uniqKey="Couprie M" first="Michel" last="Couprie">Michel Couprie</name><name sortKey="Couprie, Michel" sort="Couprie, Michel" uniqKey="Couprie M" first="Michel" last="Couprie">Michel Couprie</name><name sortKey="Mazo, Loic" sort="Mazo, Loic" uniqKey="Mazo L" first="Loïc" last="Mazo">Loïc Mazo</name><name sortKey="Mazo, Loic" sort="Mazo, Loic" uniqKey="Mazo L" first="Loïc" last="Mazo">Loïc Mazo</name><name sortKey="Passat, Nicolas" sort="Passat, Nicolas" uniqKey="Passat N" first="Nicolas" last="Passat">Nicolas Passat</name><name sortKey="Passat, Nicolas" sort="Passat, Nicolas" uniqKey="Passat N" first="Nicolas" last="Passat">Nicolas Passat</name><name sortKey="Ronse, Christian" sort="Ronse, Christian" uniqKey="Ronse C" first="Christian" last="Ronse">Christian Ronse</name><name sortKey="Ronse, Christian" sort="Ronse, Christian" uniqKey="Ronse C" first="Christian" last="Ronse">Christian Ronse</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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