<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04735268</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-17T02:07:48+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">An Alternative Definition for Digital Convexity</title>
            <author role="aut">
              <persName>
                <forename type="first">Jacques-Olivier</forename>
                <surname>Lachaud</surname>
              </persName>
              <email type="md5">2a431ce2102b83463b6748470681324e</email>
              <email type="domain">univ-savoie.fr</email>
              <idno type="idhal" notation="string">jacques-olivier-lachaud</idno>
              <idno type="idhal" notation="numeric">1177322</idno>
              <idno type="halauthorid" notation="string">119506-1177322</idno>
              <idno type="ORCID">https://orcid.org/0000-0003-4236-2133</idno>
              <affiliation ref="#struct-79"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Jacques-Olivier</forename>
                <surname>Lachaud</surname>
              </persName>
              <email type="md5">2a431ce2102b83463b6748470681324e</email>
              <email type="domain">univ-savoie.fr</email>
            </editor>
            <funder ref="#projanr-41912"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2024-10-15 09:22:05</date>
              <date type="whenModified">2024-10-17 03:26:27</date>
              <date type="whenReleased">2024-10-16 07:52:53</date>
              <date type="whenProduced">2022-04-11</date>
              <date type="whenEndEmbargoed">2024-10-15</date>
              <ref type="file" target="https://hal.science/hal-04735268v1/document">
                <date notBefore="2024-10-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04735268v1/file/article-full.pdf" id="file-4735268-4124004">
                <date notBefore="2024-10-15"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="39326">
                <persName>
                  <forename>Jacques-Olivier</forename>
                  <surname>Lachaud</surname>
                </persName>
                <email type="md5">2a431ce2102b83463b6748470681324e</email>
                <email type="domain">univ-savoie.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04735268</idno>
            <idno type="halUri">https://hal.science/hal-04735268</idno>
            <idno type="halBibtex">lachaud:hal-04735268</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Mathematical Imaging and Vision&lt;/i&gt;, 2022, 64 (7), pp.718-735. &lt;a target="_blank" href="https://dx.doi.org/10.1007/s10851-022-01076-0"&gt;&amp;#x27E8;10.1007/s10851-022-01076-0&amp;#x27E9;&lt;/a&gt;</idno>
            <idno type="halRef">Journal of Mathematical Imaging and Vision, 2022, 64 (7), pp.718-735. &amp;#x27E8;10.1007/s10851-022-01076-0&amp;#x27E9;</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-4735268-4124004"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-SAVOIE">Université Savoie Mont Blanc</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="LAMA" corresp="UNIV-SAVOIE">Laboratoire de mathématiques de l'Université de Savoie Mont Blanc</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="LAMA-EQUIPE-LIMD" corresp="LAMA">LIMD</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">An Alternative Definition for Digital Convexity</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Jacques-Olivier</forename>
                    <surname>Lachaud</surname>
                  </persName>
                  <email type="md5">2a431ce2102b83463b6748470681324e</email>
                  <email type="domain">univ-savoie.fr</email>
                  <idno type="idhal" notation="string">jacques-olivier-lachaud</idno>
                  <idno type="idhal" notation="numeric">1177322</idno>
                  <idno type="halauthorid" notation="string">119506-1177322</idno>
                  <idno type="ORCID">https://orcid.org/0000-0003-4236-2133</idno>
                  <affiliation ref="#struct-79"/>
                </author>
              </analytic>
              <monogr>
                <idno type="localRef">LIMD</idno>
                <idno type="halJournalId" status="VALID">15761</idno>
                <idno type="issn">0924-9907</idno>
                <idno type="eissn">1573-7683</idno>
                <title level="j">Journal of Mathematical Imaging and Vision</title>
                <imprint>
                  <publisher>Springer Verlag</publisher>
                  <biblScope unit="volume">64</biblScope>
                  <biblScope unit="issue">7</biblScope>
                  <biblScope unit="pp">718-735</biblScope>
                  <date type="datePub">2022-04-11</date>
                </imprint>
              </monogr>
              <idno type="doi">10.1007/s10851-022-01076-0</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">Digital geometry</term>
                <term xml:lang="en">Digital convexity</term>
                <term xml:lang="en">Simple connectedness</term>
                <term xml:lang="en">Arithmetic planes</term>
                <term xml:lang="en">Tangential cover</term>
                <term xml:lang="en">Digital surface reconstruction</term>
                <term xml:lang="en">Digital geometry ¨Digital convexity ¨Simple connectedness Ärithmetic planes ¨Tangential cover ¨Digital surface reconstruction. Mathematics Subject Classification (2020) 68U05 ¨52-08 ¨52C05 52C07</term>
              </keywords>
              <classCode scheme="acm" n="I.3.5">I.: Computing Methodologies/I.3: COMPUTER GRAPHICS/I.3.5: Computational Geometry and Object Modeling</classCode>
              <classCode scheme="https://dl.acm.org/ccs" n="ACM2012.F.5.1"/>
              <classCode scheme="halDomain" n="info">Computer Science [cs]</classCode>
              <classCode scheme="halDomain" n="info.info-cg">Computer Science [cs]/Computational Geometry [cs.CG]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>This paper proposes full convexity as an alternative definition of digital convexity, which is valid in arbitrary dimension. It solves many problems related to its usual definitions, like possible non-connectedness or non-simple connectedness, while encompassing its desirable features. Fully convex sets are digitally convex, but are also connected and simply connected. They have a morphological characterization, which induces a simple convexity test algorithm. Arithmetic planes are fully convex too. Full convexity implies local full convexity, hence it enables local shape analysis, with an unambiguous definition of convex, concave and planar points. As a kind of relative full convexity, we propose a natural definition of tangent subsets to a digital set. It gives rise to the tangential cover in 2D, and to consistent extensions in arbitrary dimension. Finally, we present two applications of tangency: the first one is a simple algorithm for building a polygonal mesh from a set of digital points, with reversibility property, the second one is the definition and computation of shortest paths within digital sets.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-79" status="VALID">
          <idno type="RNSR">200111810M</idno>
          <orgName>Laboratoire de Mathématiques</orgName>
          <orgName type="acronym">LAMA</orgName>
          <date type="start">1999-01-01</date>
          <desc>
            <address>
              <addrLine>Université Savoie Mont Blanc, Campus Scientifique, Bâtiment Le Chablais  73376 Le Bourget du Lac, France</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lama.univ-savoie.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-432896" type="direct"/>
            <relation name="UMR5127 / EP2067" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-432896" status="VALID">
          <idno type="ROR">https://ror.org/04gqg1a07</idno>
          <orgName>Université Savoie Mont Blanc</orgName>
          <orgName type="acronym">USMB [Université de Savoie] [Université de Chambéry]</orgName>
          <date type="start">1979-10-01</date>
          <desc>
            <address>
              <addrLine>27, rue Marcoz - 73000 Chambéry</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-smb.fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-41912" status="VALID">
          <idno type="anr">ANR-15-CE40-0006</idno>
          <idno type="program">Défi de tous les savoirs</idno>
          <orgName>CoMeDiC</orgName>
          <desc>Métriques convergentes pour le calcul digital</desc>
          <date type="start">2015</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>