The minimum barrier distance
Identifieur interne : 001701 ( Main/Exploration ); précédent : 001700; suivant : 001702The minimum barrier distance
Auteurs : Robin Strand [Suède] ; Krzysztof Chris Ciesielski [États-Unis] ; Filip Malmberg [Suède] ; Punam K. Saha [États-Unis]Source :
- Computer vision and image understanding : (Print) [ 1077-3142 ] ; 2013.
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- Pascal (Inist)
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Abstract
In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions fA, whose domain D is a compact subsets of the Euclidean space n. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in n, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of fA along the path. We present several important properties of MBD, including the theorems: on the equivalence between the MBD ρA and its alternative definition A; and on the convergence of their digital versions, ρA and A, to the continuous MBD ρA = A as we increase a precision of sampling. This last result provides an estimation of the discrepancy between the value of ρA and of its approximation A. An efficient computational solution for the approximation A of *ρA is presented. We experimentally investigate the robustness of MBD to noise and blur, as well as its stability with respect to the change of a position of points within the same object (or its background). These experiments are used to compare MBD with other distance functions: fuzzy distance, geodesic distance, and max-arc distance. A favorable outcome for MBD of this comparison suggests that the proposed minimum barrier distance is potentially useful in different imaging tasks, such as image segmentation.
Affiliations:
- Suède, États-Unis
- East Middle Sweden, Iowa, Svealand
- Iowa City, Uppsala
- Université d'Uppsala, Université de l'Iowa
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Saha</name><affiliation wicri:level="4"><inist:fA14 i1="04"><s1>Department of Electrical and Computer Engineering, The University of Iowa</s1><s2>Iowa City, IA 52242</s2><s3>USA</s3><sZ>4 aut.</sZ></inist:fA14><country>États-Unis</country><placeName><settlement type="city">Iowa City</settlement><region type="state">Iowa</region></placeName><orgName type="university">Université de l'Iowa</orgName></affiliation><affiliation wicri:level="4"><inist:fA14 i1="05"><s1>Department of Radiology, The University of Iowa</s1><s2>Iowa City, IA 52242</s2><s3>USA</s3><sZ>4 aut.</sZ></inist:fA14><country>États-Unis</country><placeName><settlement type="city">Iowa City</settlement><region type="state">Iowa</region></placeName><orgName type="university">Université de l'Iowa</orgName></affiliation></author></analytic><series><title level="j" type="main">Computer vision and image understanding : (Print)</title><title level="j" type="abbreviated">Comput. vis. image underst. : (Print)</title><idno type="ISSN">1077-3142</idno><imprint><date when="2013">2013</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Computer vision and image understanding : (Print)</title><title level="j" type="abbreviated">Comput. vis. image underst. : (Print)</title><idno type="ISSN">1077-3142</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Computer vision</term><term>Discrete geometry</term><term>Equivalence theorem</term><term>Euclidean space</term><term>Fuzzy logic</term><term>Geodesic</term><term>Image processing</term><term>Image segmentation</term><term>Imaging</term><term>Minimal distance</term><term>Mobile computing</term><term>Pervasive computing</term><term>Real function</term><term>Robustness</term><term>Sampling</term><term>Stability</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Vision ordinateur</term><term>Informatique diffuse</term><term>Formation image</term><term>Traitement image</term><term>Distance minimale</term><term>Théorème équivalence</term><term>Géodésique</term><term>Géométrie discrète</term><term>Fonction réelle</term><term>Espace euclidien</term><term>Echantillonnage</term><term>Robustesse</term><term>Stabilité</term><term>Logique floue</term><term>.</term><term>Informatique mobile</term><term>Segmentation image</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">In this paper we introduce a minimum barrier distance, MBD, defined for the (graphs of) real-valued bounded functions f<sub>A</sub>, whose domain D is a compact subsets of the Euclidean space <sup>n</sup>. The formulation of MBD is presented in the continuous setting, where D is a simply connected region in <sup>n</sup>, as well as in the case where D is a digital scene. The MBD is defined as the minimal value of the barrier strength of a path between the points, which constitutes the length of the smallest interval containing all values of f<sub>A</sub> along the path. We present several important properties of MBD, including the theorems: on the equivalence between the MBD ρ<sub>A</sub> and its alternative definition <sub>A</sub>; and on the convergence of their digital versions, ρ<sub>A</sub> and <sub>A</sub>, to the continuous MBD ρ<sub>A</sub> = <sub>A</sub> as we increase a precision of sampling. This last result provides an estimation of the discrepancy between the value of ρ<sub>A</sub> and of its approximation <sub>A</sub>. An efficient computational solution for the approximation <sub>A</sub> of *ρ<sub>A</sub> is presented. We experimentally investigate the robustness of MBD to noise and blur, as well as its stability with respect to the change of a position of points within the same object (or its background). These experiments are used to compare MBD with other distance functions: fuzzy distance, geodesic distance, and max-arc distance. A favorable outcome for MBD of this comparison suggests that the proposed minimum barrier distance is potentially useful in different imaging tasks, such as image segmentation.</div></front></TEI><affiliations><list><country><li>Suède</li><li>États-Unis</li></country><region><li>East Middle Sweden</li><li>Iowa</li><li>Svealand</li></region><settlement><li>Iowa City</li><li>Uppsala</li></settlement><orgName><li>Université d'Uppsala</li><li>Université de l'Iowa</li></orgName></list><tree><country name="Suède"><region name="Svealand"><name sortKey="Strand, Robin" sort="Strand, Robin" uniqKey="Strand R" first="Robin" last="Strand">Robin Strand</name></region><name sortKey="Malmberg, Filip" sort="Malmberg, Filip" uniqKey="Malmberg F" first="Filip" last="Malmberg">Filip Malmberg</name></country><country name="États-Unis"><noRegion><name sortKey="Ciesielski, Krzysztof Chris" sort="Ciesielski, Krzysztof Chris" uniqKey="Ciesielski K" first="Krzysztof Chris" last="Ciesielski">Krzysztof Chris Ciesielski</name></noRegion><name sortKey="Ciesielski, Krzysztof Chris" sort="Ciesielski, Krzysztof Chris" uniqKey="Ciesielski K" first="Krzysztof Chris" last="Ciesielski">Krzysztof Chris Ciesielski</name><name sortKey="Saha, Punam K" sort="Saha, Punam K" uniqKey="Saha P" first="Punam K." last="Saha">Punam K. Saha</name><name sortKey="Saha, Punam K" sort="Saha, Punam K" uniqKey="Saha P" first="Punam K." last="Saha">Punam K. Saha</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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