Orthogonal distance from an ellipsoid

Bektaş, Sebahattin

doi:10.1590/s1982-21702014000400053

Cited by 24 publications

(11 citation statements)

References 4 publications

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“…The quantity (target function) to be minimized Bektas [12]. To overcome the problems with the algebraic distances, it is natural to replace them by the orthogonal distances which are invariant to transformations in Euclidean space and which do not exhibit the high curvature bias.…”

Section: Orthogonal (Geometric) Hyperboloid Fitting Methodsmentioning

confidence: 99%

“…Throughout this paper, we assume that these conditions are satisfied. For the solution of the fitting problem, the linear or linearized relationship, written between the given data points and unknown parameters (one equation per data points), consists of equations, including unknown parameters Bektas [13].…”

Section: Fitting Hyperboloid To Noisy Datamentioning

confidence: 99%

“…Ligas [8] claims his method turns out to be more accurate, faster and applicable than Feltens method. Bektas [12] is a little more advanced than the Ligas [10]. A recent work on the subject gives us useful information on this topic (the orthogonal distance to Hyperboloid) for detailed information on this subject refer to Bektas [13].…”

Section: Introductionmentioning

confidence: 99%

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Design of Hyperboloid Structures

Bektaş¹

2017

MOJCE

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In this paper, we present the design of hyperboloid structures and techniques for hyperboloid fitting which are based on minimizing the sum of the squares of the geometric distances between the noisy data and the hyperboloid. The literature often uses "orthogonal fitting" in place of "best fitting". For many different purposes, the best-fit hyperboloid fitting to a set of points is required. Algebraic fitting methods solve the linear least squares (LS) problem, and are relatively straightforward and fast. Fitting orthogonal hyperboloid is a difficult issue. Usually, it is impossible to reach a solution with classic LS algorithms. Because they are often faced with the problem of convergence. Therefore, it is necessary to use special algorithms e.g. nonlinear least square algorithms. We propose to use geometric fitting as opposed to algebraic fitting. Hyperboloid has a complex geometry as well as hyperboloid structures have always been interested. The two main reasons, apart from aesthetic considerations, are strength and efficiency.

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Section: Orthogonal (Geometric) Hyperboloid Fitting Methodsmentioning

confidence: 99%

Section: Fitting Hyperboloid To Noisy Datamentioning

confidence: 99%

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Design of Hyperboloid Structures

Bektaş¹

2017

MOJCE

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“…The orthogonal distances, are therefore, calculated for every point of the model using the equations presented by Bektas (2014). Table 1 shows the results for patient one.…”

Section: Distances From the Ellipsoidmentioning

confidence: 99%

Analysis of Repeatability on Videogrammetry for Infants’ Cranial Deformation

García¹,

Lerma²,

Mateu³

et al. 2017

Proceedings - 1st Congress in Geomatics Engineering - CIGeo

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Abstract:Cranial deformation affects a large number of infants. The methodologies commonly employed to measure the deformation include, among others, calliper measurements and visual assessment for mild cases and radiological imaging for severe cases, where surgical intervention is considered. Visual assessment and calliper measurements usually lack the required level of accuracy to evaluate the deformation. Radiological imaging, including Computed Tomography (CT) and Magnetic Resonance Imaging (MRI), are costly and highly invasive. The use of smartphones to record videos that can be used for three-dimensional (3D) modelling of the head has emerged as a low-cost, noninvasive methodology to extract 3D information of the patient. To be able to analyse the deformation, a novel technique is employed: the obtained model is compared with an ideal head. In this study we have tested the repeatability of the process. For this purpose, several models of two patients have been obtained and the differences between them are evaluated. The results show that the differences in the ellipsoid semiaxis for the same patient are usually below 4 mm, although they increase up to 6.4 mm in some cases. The variability in the distances to the ideal head, which are the values used to evaluate deformity, reaches a maximum value of 2.7 mm. The errors obtained are comparable to those of classical measurement techniques and show the potential of the methodology in development.Keywords: Photogrammetry, Low-cost, Plagiocephaly, 3D modelling Resumen:La deformación craneal afecta a un elevado porcentaje de lactantes, a pesar de esto, no existen estándares para su medición. Existen diversas metodologías empleadas para el análisis de este tipo de deformación, que van desde el análisis visual o la medición con calibre en casos leves, a pruebas radiológicas en casos más graves, en los que se plantea la posibilidad de una intervención quirúrgica. El análisis visual y la medición con calibre a menudo carecen de la precisión requerida para evaluar la deformación, mientras que las pruebas radiológicas (Tomografía Axial Computarizada, TAC, o Resonancia Magnética, RM) son altamente invasivas y tienen un alto coste. Otras soluciones como la fotografía tridimensional (3D) incluyen complejos sistemas de varias cámaras, lo que también supone un coste elevado. La posibilidad de utilizar videos tomados con teléfonos inteligentes para la creación de modelos 3D craneales se ha convertido en una posibilidad para obtener información 3D del paciente de forma precisa y con un coste bajo. Para analizar la deformación se ha planteado una metodología que consiste en calcular las distancias entre el modelo generado y una forma craneal ideal. En este estudio se ha llevado a cabo el análisis de la repetibilidad del proceso de obtención del modelo y de la cabeza ideal ajustada, para ello se han obtenido varios modelos 3D de dos pacientes y se han evaluado las diferencias entre ellos. Los resultados muestran unas diferencias en los semiejes de los elipsoides de aproximadamen...

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“…Our aim to find the orthogonal distances from a shifted-oriented ellipsoid see Figure 2. For detailed information on this subject refer to Bektas (2014). [-0.0006 -0.0008 -0.0010 0.0005 -0.0005 0.0003 0.0092 0.0050 0.0278] The conical coefficients in the Least Absolute Values Method is, v=[ -0.0071 -0.0084 -0.0096 0.0047 -0.0040 0.0023 0.0880 0.0061 0.0271]…”

Section: Finding Orthogonal Distances From the Ellipsoidmentioning

confidence: 99%

Least Squares Fitting of Ellipsoid Using Orthogonal Distances

Bektaş

2015

Bol. Ciênc. Geod.

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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 satellite measurementsprecisionwill allow usto determine amore realistic Earth ellipsoid. Several studies have shown that the Earth, other planets, natural satellites, asteroids and comets can be modeled as triaxial ellipsoids Burša and Šima (1980), Iz et all (2011). Determining the reference ellipsoid for the Earth is an important ellipsoid fitting application, because all geodetic calculations are performed on the reference ellipsoid. Algebraic fitting methods solve the linear least squares (LS) problem, and are relatively straightforward and fast. Fitting orthogonal ellipsoid is a difficult issue. Usually, it is impossible to reach a solution with classic LS algorithms. Because they are often faced with the problem of convergence. Therefore, it is necessary to use special algorithms e.g. nonlinear least square algorithms. We propose to use geometric fitting as opposed to algebraic ﬁtting. This is computationally more intensive, but it provides scope for placing visually apparent constraints on ellipsoid parameter estimation and is free from curvature bias Ray and Srivastava (2008).

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Orthogonal distance from an ellipsoid

Cited by 24 publications

References 4 publications

Design of Hyperboloid Structures

Design of Hyperboloid Structures

Analysis of Repeatability on Videogrammetry for Infants’ Cranial Deformation

Least Squares Fitting of Ellipsoid Using Orthogonal Distances

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