An Improved Riemannian Metric Approximation for Graph Cuts
Identifieur interne : 002762 ( Main/Exploration ); précédent : 002761; suivant : 002763An Improved Riemannian Metric Approximation for Graph Cuts
Auteurs : Ond Ej Dan K [République tchèque] ; Pavel Matula [République tchèque]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Boykov and Kolmogorov showed that it is possible to find globally minimal contours and surfaces via graph cuts by embedding an appropriate metric approximation into the graph edge weights and derived the requisite formulas for Euclidean and Riemannian metrics [3]. In [9] we have proposed an improved Euclidean metric approximation that is invariant under (horizontal and vertical) mirroring, applicable to grids with anisotropic resolution and with a smaller approximation error. In this paper, we extend our method to general Riemannian metrics that are essential for graph cut based image segmentation or stereo matching. It is achieved by the introduction of a transformation reducing the Riemannian case to the Euclidean one and adjusting the formulas from [9] to be able to cope with non-orthogonal grids. We demonstrate that the proposed method yields smaller approximation errors than the previous approaches both in theory and practice.
Url:
DOI: 10.1007/978-3-642-19867-0_6
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 002565
- to stream Istex, to step Curation: 002533
- to stream Istex, to step Checkpoint: 000662
- to stream Main, to step Merge: 002804
- to stream Main, to step Curation: 002762
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">An Improved Riemannian Metric Approximation for Graph Cuts</title><author><name sortKey="Dan K, Ond Ej" sort="Dan K, Ond Ej" uniqKey="Dan K O" first="Ond Ej" last="Dan K">Ond Ej Dan K</name></author><author><name sortKey="Matula, Pavel" sort="Matula, Pavel" uniqKey="Matula P" first="Pavel" last="Matula">Pavel Matula</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:A024DCF6FCA721CA5E3811E9C7DE82EC1A6EFA51</idno><date when="2011" year="2011">2011</date><idno type="doi">10.1007/978-3-642-19867-0_6</idno><idno type="url">https://api.istex.fr/ark:/67375/HCB-QRL16VZM-L/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">002565</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">002565</idno><idno type="wicri:Area/Istex/Curation">002533</idno><idno type="wicri:Area/Istex/Checkpoint">000662</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000662</idno><idno type="wicri:doubleKey">0302-9743:2011:Dan K O:an:improved:riemannian</idno><idno type="wicri:Area/Main/Merge">002804</idno><idno type="wicri:Area/Main/Curation">002762</idno><idno type="wicri:Area/Main/Exploration">002762</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">An Improved Riemannian Metric Approximation for Graph Cuts</title><author><name sortKey="Dan K, Ond Ej" sort="Dan K, Ond Ej" uniqKey="Dan K O" first="Ond Ej" last="Dan K">Ond Ej Dan K</name><affiliation wicri:level="3"><country xml:lang="fr">République tchèque</country><wicri:regionArea>Centre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, Brno</wicri:regionArea><placeName><settlement type="city">Brno</settlement><region>Moravie</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">République tchèque</country></affiliation></author><author><name sortKey="Matula, Pavel" sort="Matula, Pavel" uniqKey="Matula P" first="Pavel" last="Matula">Pavel Matula</name><affiliation wicri:level="3"><country xml:lang="fr">République tchèque</country><wicri:regionArea>Centre for Biomedical Image Analysis, Faculty of Informatics, Masaryk University, Brno</wicri:regionArea><placeName><settlement type="city">Brno</settlement><region>Moravie</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">République tchèque</country></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno 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: Boykov and Kolmogorov showed that it is possible to find globally minimal contours and surfaces via graph cuts by embedding an appropriate metric approximation into the graph edge weights and derived the requisite formulas for Euclidean and Riemannian metrics [3]. In [9] we have proposed an improved Euclidean metric approximation that is invariant under (horizontal and vertical) mirroring, applicable to grids with anisotropic resolution and with a smaller approximation error. In this paper, we extend our method to general Riemannian metrics that are essential for graph cut based image segmentation or stereo matching. It is achieved by the introduction of a transformation reducing the Riemannian case to the Euclidean one and adjusting the formulas from [9] to be able to cope with non-orthogonal grids. We demonstrate that the proposed method yields smaller approximation errors than the previous approaches both in theory and practice.</div></front></TEI><affiliations><list><country><li>République tchèque</li></country><region><li>Moravie</li></region><settlement><li>Brno</li></settlement></list><tree><country name="République tchèque"><region name="Moravie"><name sortKey="Dan K, Ond Ej" sort="Dan K, Ond Ej" uniqKey="Dan K O" first="Ond Ej" last="Dan K">Ond Ej Dan K</name></region><name sortKey="Dan K, Ond Ej" sort="Dan K, Ond Ej" uniqKey="Dan K O" first="Ond Ej" last="Dan K">Ond Ej Dan K</name><name sortKey="Matula, Pavel" sort="Matula, Pavel" uniqKey="Matula P" first="Pavel" last="Matula">Pavel Matula</name><name sortKey="Matula, Pavel" sort="Matula, Pavel" uniqKey="Matula P" first="Pavel" last="Matula">Pavel Matula</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002762 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 002762 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Lorraine
|area= InforLorV4
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:A024DCF6FCA721CA5E3811E9C7DE82EC1A6EFA51
|texte= An Improved Riemannian Metric Approximation for Graph Cuts
}}
| This area was generated with Dilib version V0.6.33. |  |