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Numerically Stable Direct Least Squares Fitting Of Ellipses
, 1998
"... This paper presents a numerically stable noniterative algorithm for fitting an ellipse to a set of data points. The approach is based on a least squares minimization and it guarantees an ellipsespecific solution even for scattered or noisy data. The optimal solution is computed directly, no iter ..."
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Cited by 79 (0 self)
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This paper presents a numerically stable noniterative algorithm for fitting an ellipse to a set of data points. The approach is based on a least squares minimization and it guarantees an ellipsespecific solution even for scattered or noisy data. The optimal solution is computed directly, no iterations are required. This leads to a simple, stable and robust fitting method which can be easily implemented. The proposed algorithm has no computational ambiguity and it is able to fit more than 100,000 points in a second. Keywords: ellipses, fitting, least squares, eigenvectors INTRODUCTION One of basic tasks in pattern recognition and computer vision is a fitting of geometric primitives to a set of points (see [Duda73] for a summary). The use of primitive models allows reduction and simplification of data and, consequently, faster and simpler processing. A very important primitive is an ellipse, which, being a perspective projection of a circle, is exploited in many applications of ...
Unbiased Estimation of Ellipses by Bootstrapping
 IEEE PAMI
, 1996
"... A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being ind ..."
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Cited by 17 (2 self)
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A general method for eliminating the bias of nonlinear estimators using bootstrap is presented. Instead of the traditional mean bias we consider the definition of bias based on the median. The method is applied to the problem of fitting ellipse segments to noisy data. No assumption beyond being independent identically distributed (i.i.d.) is made about the error distribution and experiments with both synthetic and real data prove the effectiveness of the technique. Index terms: implicit models, curve fitting, bootstrap, lowlevel processing. 1 Conic Fitting Image formation is a perspective projection of the 3D visual environment. Features extracted from a 2D image can be useful only if they preserve some of the geometric properties of the 3D object they correspond to. Collinearity and conicity are such properties, and therefore line and conic segments are widely used as geometric primitives in computer vision. Let f(u; `) = 0 be the implicit model of a geometric primitive in the ima...
Determination of the method of construction of 1650 B.C. wall paintings
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2006
"... Abstract—In this paper, a methodology of general applicability is presented for answering the question if an artist used a number of archetypes to draw a painting or if he drew it freehand. In fact, the contour line parts of the drawn objects that potentially correspond to archetypes are initially s ..."
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Cited by 3 (2 self)
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Abstract—In this paper, a methodology of general applicability is presented for answering the question if an artist used a number of archetypes to draw a painting or if he drew it freehand. In fact, the contour line parts of the drawn objects that potentially correspond to archetypes are initially spotted. Subsequently, the exact form of these archetypes and their appearance throughout the painting is determined. Themethodhasbeenapplied to celebratedThera LateBronzeAgewall paintingswith full success. It has beendemonstrated that the artist or group of artists has used seven geometrical archetypes and seven corresponding wellconstructed stencils (four hyperbolae, two ellipses, and one Archimedes ’ spiral) to draw the wall painting “Gathering of Crocus ” in 1650 B.C. Thismethod of drawing seems to be unique in the history of arts and of great importance for archaeology, and the history of mathematics and sciences, as well. Index Terms—Image line pattern analysis, archaeological image edge analysis, archaeological object reconstruction, curve fitting, statistical pattern matching. Ç 1
A Bilinear Approach to the Parameter Estimation of a general Heteroscedastic Linear System with Application to Conic Fitting
"... A bilinear approach to the parameter estimation of a general heteroscedastic linear system, with application to conic fitting ..."
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Cited by 2 (1 self)
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A bilinear approach to the parameter estimation of a general heteroscedastic linear system, with application to conic fitting
Robust BiasCorrected Least Squares Fitting Of Ellipses
, 2000
"... This paper presents a robust and accurate technique for an estimation of the bestt ellipse going through the given set of points. The approach is based on a least squares minimization of algebraic distances of the points with a correction of the statistical bias caused during the computation. An ..."
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Cited by 2 (0 self)
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This paper presents a robust and accurate technique for an estimation of the bestt ellipse going through the given set of points. The approach is based on a least squares minimization of algebraic distances of the points with a correction of the statistical bias caused during the computation. An accurate ellipsespecic solution is guaranteed even for scattered or noisy data with outliers. Although the nal algorithm is iterative, it typically converges in a fraction of time needed for a true orthogonal tting based on Eucleidan distances of points. Keywords: ellipses, least squares, robust tting, Mestimators, statistical bias, renormalization 1
A Novel Bayesian Method for Fitting Parametric and NonParametric Models to Noisy Data
, 1999
"... We o#er a simple paradigm for #tting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classic MSE algorithms. This is done by considering each point on the model as a possible sourcefor each data point. ..."
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Cited by 1 (0 self)
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We o#er a simple paradigm for #tting models, parametric and nonparametric, to noisy data, which resolves some of the problems associated with classic MSE algorithms. This is done by considering each point on the model as a possible sourcefor each data point.
AN INTERACTIVE SOFTWARE FOR CURVE FITTING
"... An interactive and user friendly software in Visual Basic is presented for obtaining suitable coefficients in curve fitting operations. A general conjugate gradient optimization algorithm (GCGGSAP) is implemented for fitting curves to existing data. The user supplies up to 100 pairs of data in the ..."
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Cited by 1 (1 self)
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An interactive and user friendly software in Visual Basic is presented for obtaining suitable coefficients in curve fitting operations. A general conjugate gradient optimization algorithm (GCGGSAP) is implemented for fitting curves to existing data. The user supplies up to 100 pairs of data in the form of a worksheet. The program determines values of parameters of a function such that deviations from the given data are minimized. Sum of the squares of the differences is postulated as an optimization criterion, which is assigned as a multivariant objective function to be minimized. To start the curve fitting process, the user selects one of a number of available models or their combinations. CurveFit is able to make intuitive identifications, and it is able to determine the best fit for a given set of data, utilizing builtin optimization criteria. The output from the software includes the input data, the corresponding set of calculated values, and the differences between the two sets. Data sets and plots can be printed directly from within CurveFit, or alternatively, they can be exported to Excel for
APPROVED FOR PUBLIC RELEASE
, 1996
"... This report details the work done on developing an autoscaling system for the LowLatitude Ionospheric Sounding Program (LLISP). The report firstly describes the performance of a number of different filtering routines for automatic cleaning of LLISP oblique ionograms. Secondly, it then presents tech ..."
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This report details the work done on developing an autoscaling system for the LowLatitude Ionospheric Sounding Program (LLISP). The report firstly describes the performance of a number of different filtering routines for automatic cleaning of LLISP oblique ionograms. Secondly, it then presents techniques developed to automatically extract a feature vector from a filtered ionogram. A third stage uses the feature vectors to identify the prominent modes and other important features of the ionograms, and to track these modes and features as they evolve across sequences of ionograms. This work will automate the task of identifying and tracking ionospheric propagation modes in ionograms. The resulting system will be used to process current LLISP data streams to extract large volumes of significant information: this will help the understanding of ionospheric processes and can be used as input to automatic frequency management systems for communications networks.
NUMERICALLY STABLE DIRECT LEAST SQUARES FITTING OF ELLIPSES
"... This paper presents a numerically stable noniterative algorithm for fitting an ellipse to a set of data points. The approach is based on a least squares minimization and it guarantees an ellipsespecific solution even for scattered or noisy data. The optimal solution is computed directly, no iterat ..."
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This paper presents a numerically stable noniterative algorithm for fitting an ellipse to a set of data points. The approach is based on a least squares minimization and it guarantees an ellipsespecific solution even for scattered or noisy data. The optimal solution is computed directly, no iterations are required. This leads to a simple, stable and robust fitting method which can be easily implemented. The proposed algorithm has no computational ambiguity and it is able to fit more than 100,000 points in a second.
4 MTIE ANO SUBTITLE Fitting Optimal Piecewise Linear FiJcjnJtions Using Genetic Algorithms
, 1997
"... 1 AGENCY USE ONLY,LDJV « o/an«; 2. REPORT DATE ..."