Reconstruction of an ellipse from its raster image
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2015-04-14
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Academic Publications, Ltd
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Abstract
Motivated by practical application, we investigate the ways how to obtain a description of an ellipse whose circumscribed rectangle is known exactly and whose coordinates of touching points are known up to a certain inaccuracy. We show the sufficient condition for determination of such an ellipse, derive the implicit and parametric equations and show a proposal of the solution by the modification of the standard regression method.
MotivovanĂ˝ praktickĂ˝mi aplikacemi, zkoumáme zpĹŻsoby, jak zĂskat popis elipsy, jejĂĹľ ohraniÄŤenĂ˝ obdĂ©lnĂk je známy, a jejĂĹľ souĹ™adnice dotyku bodĹŻ jsou známy s urÄŤitou pĹ™esnosti. Formulujeme dostateÄŤnĂ© podmĂnky pro stanovenĂ takovĂ© elipsy, odvozenĂ implicitnĂ a parametrickĂ© rovnice a ukazujeme návrh Ĺ™ešenĂ modifikacĂ standardnĂho regrese.
MotivovanĂ˝ praktickĂ˝mi aplikacemi, zkoumáme zpĹŻsoby, jak zĂskat popis elipsy, jejĂĹľ ohraniÄŤenĂ˝ obdĂ©lnĂk je známy, a jejĂĹľ souĹ™adnice dotyku bodĹŻ jsou známy s urÄŤitou pĹ™esnosti. Formulujeme dostateÄŤnĂ© podmĂnky pro stanovenĂ takovĂ© elipsy, odvozenĂ implicitnĂ a parametrickĂ© rovnice a ukazujeme návrh Ĺ™ešenĂ modifikacĂ standardnĂho regrese.
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International Journal of Pure and Applied Mathematics. 2015, vol. 2015 (101), issue 2, p. 141-155.
http://www.ijpam.eu/contents/2015-101-2/3/index.html
http://www.ijpam.eu/contents/2015-101-2/3/index.html
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en