47,932 research outputs found
Hyperaccurate Ellipse Fitting without Iterations
This paper presents a new method for fitting an ellipse to a point sequence extracted from images. It is widely known that the best fit is obtained by maximum likelihood. However, it requires iterations, which may not converge in the presence of large noise. Our approach is algebraic distance minimization; no iterations are required. Exploiting the fact that the solution depends on the way the scale is normalized, we analyze the accuracy to high order error terms with the scale normalization weight unspecified and determine it so that the bias is zero up to the second order. We demonstrate by experiments that our method is superior to the Taubin method, also algebraic
and known to be highly accurate
Direct Least-Squares Ellipse Fitting
Many biological and astronomical forms can be best represented by ellipses. While some more complex curves might represent the shape more accurately, ellipses have the advantage that they are easily parameterised and define the location, orientation and dimensions of the data more clearly. In this paper, we present a method of direct least-squares ellipse fitting by solving a generalised eigensystem. This is more efficient and more accurate than many alternative approaches to the ellipse-fitting problem such as fuzzy c-shells clustering and Hough transforms. This method was developed for human body modelling as part of a larger project to design a marker-free gait analysis system which is being undertaken at the National Rehabilitation Hospital, Dublin
New Confocal Hyperbola-based Ellipse Fitting with Applications to Estimating Parameters of Mechanical Pipes from Point Clouds
This manuscript presents a new method for fitting ellipses to two-dimensional
data using the confocal hyperbola approximation to the geometric distance of
points to ellipses. The proposed method was evaluated and compared to
established methods on simulated and real-world datasets. First, it was
revealed that the confocal hyperbola distance considerably outperforms other
distance approximations such as algebraic and Sampson. Next, the proposed
ellipse fitting method was compared with five reliable and established methods
proposed by Halir, Taubin, Kanatani, Ahn and Szpak. The performance of each
method as a function of rotation, aspect ratio, noise, and arc-length were
examined. It was observed that the proposed ellipse fitting method achieved
almost identical results (and in some cases better) than the gold standard
geometric method of Ahn and outperformed the remaining methods in all
simulation experiments. Finally, the proposed method outperformed the
considered ellipse fitting methods in estimating the geometric parameters of
cylindrical mechanical pipes from point clouds. The results of the experiments
show that the confocal hyperbola is an excellent approximation to the true
geometric distance and produces reliable and accurate ellipse fitting in
practical settings
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