1. Closed embeddings into Lipscomb's universal spaceUroš Milutinović, 2007, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: matematika, topologija, dimenzija pokrivanja, posplošena krivulja Sierpińskega, univerzalni prostor, Lipscombov univerzalni prostor, vložitev, razširitev, poln metrični prostor, zaprta vložitev, mathematics, topology, covering dimension, embedding, closed embedding, generalized Sierpiński curve, universal space, Lipscomb universal space, complete metric space, extension
Objavljeno: 10.07.2015; Ogledov: 615; Prenosov: 18
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2. Automated landmark points detection by using a mixture of approachesBožidar Potočnik, 2015, izvirni znanstveni članek Opis: This paper deals with the automated detection of a closed curvećs dominant points. We treat a curve as a 1-D function of the arc length. The problem of detecting dominant points is translated into seeking the extrema of the corresponding 1-D function. Three approaches for automated dominant points detection are presented: (1) an approach based on fitting polynomial, (2) an approach using 1-D computer registration and (3) an innovative approach based on a multi-resolution scheme, zero-crossing and hierarchical clustering. Afterwards, two methods are introduced based on the linearly and non-linearly mixing the results from the three approaches. We then mix the results in a mean-square error sense by using the linear and non-linear fittings, respectively. We experimentally demonstrate the problem of detecting 21 landmarks on 38 vole-teeth that by mixing, the detection accuracy is improved by up to 41.47 % with respect to the results for individual approaches, as applied within the mixture.
Ključne besede: closed curve, dominant point, landmark, automated detection, mixing model fitting, vole-tooth
Objavljeno: 10.07.2015; Ogledov: 760; Prenosov: 16
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3. Closed embeddings into Lipscomb's universal spaceIvan Ivanšić, Uroš Milutinović, 2006 Opis: Naj bo ▫${mathcal{J}}(tau)$▫ Lipscombov enodimenzionalni prostor in ▫$L_n(tau) = {x in {mathcal{J}}(tau)^{n+1}|$▫ vsaj ena koordinata od ▫{sl x}▫ je iracionalna ▫$} subseteq {mathcal{J}}(tau)^{n+1}$▫ Lipscombov ▫$n$▫-dimenzionalni univerzalni prostor s težo ▫$tau ge aleph_0$▫. V tem članku dokazujemo, da če je ▫$X$▫ poln metrizabilni prostor in velja ▫$dim X le n$▫, ▫$wX le tau$▫, tedaj obstaja zaprta vložitev prostora ▫$X$▫ v ▫$L_n(tau)$▫. Še več, vsako zvezno funkcijo ▫$f: X to {mathcal{J}}(tau)^{n+1}$▫ lahko poljubno natančno aproksimiramo z zaprto vložitvijo ▫$psi: X to L_n(tau)$▫. Razen tega sta dokazani relativna verzija in punktirana verzija. V primeru separabilnosti je dokazan analogni rezultat, v katerem je klasična trikotna krivulja Sierpińskega (ki je homeomorfna ▫${mathcal{J}}(3)$▫) nadomestila ▫${mathcal{J}(aleph_0)}$▫.
Ključne besede: matematika, topologija, dimenzija pokrivanja, posplošena krivulja Sierpińskega, univerzalni prostor, Lipscombov univerzalni prostor, vložitev, razširitev, poln metrični prostor, zaprta vložitev, mathematics, topology, covering dimension, embedding, closed embedding, generalized Sierpiński curve, universal space, Lipscomb universal space, complete metric space, extension
Objavljeno: 10.07.2015; Ogledov: 568; Prenosov: 68
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