New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces
A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove t...
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| Veröffentlicht in: | IEEE transactions on pattern analysis and machine intelligence 2009-04, Vol.31 (4), p.637-648 |
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| container_title | IEEE transactions on pattern analysis and machine intelligence |
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| creator | Couprie, M. Bertrand, G. |
| description | A point of a discrete object is called simple if it can be deleted from this object without altering topology. In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove these characterizations, we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension. This work is settled in the framework of cubical complexes, which provides a sound topological basis for image analysis, and allows to retrieve the main notions and results of digital topology, in particular the notion of simple point. |
| doi_str_mv | 10.1109/TPAMI.2008.117 |
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In this article, we present new characterizations of simple points which hold in dimensions 2, 3 and 4, and which lead to efficient algorithms for detecting such points. In order to prove these characterizations, we establish two confluence properties of the collapse operation which hold in the neighborhood of a point in spaces of low dimension. 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Computational geometry</topic><topic>Physics</topic><topic>Shape</topic><topic>Skeleton</topic><topic>Three dimensional</topic><topic>Topology</topic><topic>Transduction; acoustical devices for the generation and reproduction of sound</topic><topic>X-ray imaging</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Couprie, M.</creatorcontrib><creatorcontrib>Bertrand, G.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998-Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>Pascal-Francis</collection><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>ANTE: Abstracts in New Technology & Engineering</collection><collection>Engineering Research Database</collection><collection>MEDLINE - Academic</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>IEEE transactions on pattern analysis and machine intelligence</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Couprie, M.</au><au>Bertrand, G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces</atitle><jtitle>IEEE transactions on pattern analysis and machine intelligence</jtitle><stitle>TPAMI</stitle><addtitle>IEEE Trans Pattern Anal Mach Intell</addtitle><date>2009-04-01</date><risdate>2009</risdate><volume>31</volume><issue>4</issue><spage>637</spage><epage>648</epage><pages>637-648</pages><issn>0162-8828</issn><eissn>1939-3539</eissn><coden>ITPIDJ</coden><abstract>A point of a discrete object is called simple if it can be deleted from this object without altering topology. 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| subjects | Acoustics Algorithms Animation Applied sciences Artificial intelligence Biomedical imaging Collapse Computation and Language Computer Science Computer science control theory systems Digital Exact sciences and technology Fundamental areas of phenomenology (including applications) Image analysis Image Processing and Computer Vision Image retrieval Image segmentation Image sequence analysis Intelligence Magnetic resonance imaging Pattern analysis Pattern Recognition Pattern recognition. Digital image processing. Computational geometry Physics Shape Skeleton Three dimensional Topology Transduction acoustical devices for the generation and reproduction of sound X-ray imaging |
| title | New Characterizations of Simple Points in 2D, 3D, and 4D Discrete Spaces |
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