2015
DOI: 10.1590/s1982-21702015000200019
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Least Squares Fitting of Ellipsoid Using Orthogonal Distances

Abstract: In this paper, we present techniques for ellipsoid fitting which are based on minimizing the sum of the squares of the geometric distances between the data and the ellipsoid. The literature often uses "orthogonal fitting" in place of "geometric fitting" or "best-fit". For many different purposes, the best-fit ellipsoid fitting to a set of points is required. The problem offitting ellipsoid is encounteredfrequently intheimage processing, face recognition, computer games, geodesy etc. Today, increasing GPS and sa… Show more

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Cited by 31 publications
(13 citation statements)
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“…Since a hyperboloid can be degenerated into other kinds of elliptic quadrics, such as an elliptic paraboloid. Therefore a proper constraint must be added Bektas [15]. …”
Section: Algebraic Direct Hyperboloid Fitting Methodsmentioning
confidence: 99%
See 1 more Smart Citation
“…Since a hyperboloid can be degenerated into other kinds of elliptic quadrics, such as an elliptic paraboloid. Therefore a proper constraint must be added Bektas [15]. …”
Section: Algebraic Direct Hyperboloid Fitting Methodsmentioning
confidence: 99%
“…The geometric (shortest,orthogonal) distance is defined to be the distance between a data point and its closest point on the hyperboloid. For detailed information on this subject refer to Bektas [15]. The following link can be used for the shortest distance and projection …”
Section: Orthogonal (Geometric) Hyperboloid Fitting Methodsmentioning
confidence: 99%
“…An adjustment of the ellipsoid is carried out using Least Square Adjustment (Bektas 2015). The norm L2 is used.…”
Section: Ellipsoid Fittingmentioning
confidence: 99%
“…Здесь рассматривается проблема подгонки эллипсоида для произвольного множества точек, имеющая фундаментальное значение во многих областях прикладной науки: в астрономии, геоде-зии, цифровой обработке изображений, в робототехнике, в метрологии и др. [7].…”
Section: Introductionunclassified
“…Здесь рассматривается проблема подгонки эллипсоида для произвольного множества точек, имеющая фундаментальное значение во многих областях прикладной науки: в астрономии, геоде-зии, цифровой обработке изображений, в робототехнике, в метрологии и др. [7].В структурных моделях X предполагается случайной величиной с некоторым законом распределения с неизвестными параметрами [4]. Такая постановка более характерна для ситуа-ций, когда происходит наблюдение за естественным состоянием некоторого случайного процес-са, и не вполне соответствует условиям активного эксперимента.…”
unclassified