In this paper, we propose an unbiased minimum variance es-timator to estimate the parameters of an ellipse. The objective of the optimization is to compute a minimum variance estimator. The experimental results show the dramatic improvement over existed weighted least sum of squares approach especially when the ellipse is occluded.

Two methods for approximating the normal distance to an ellipse using a) its orthogonal hyperbolae, and b) Stirling’s oval are described. Analysis with a set of quantitative set of measures shows that the former provides an accurate approximation with little irregularities or biases. Its suitability is evaluated by comparing several approximations as error of fit functions and applying them to ...

We compare several On Surface Radiation Boundary Conditions in two dimensions, for solving the Helmholtz equation exterior to an ellipse. We also introduce a new boundary condition for an ellipse based on amodal expansion inMathieu functions. We compare the OSRC to a finite difference method. © 2009 Elsevier B.V. All rights reserved.

Our fully automatic method to compute the biparietal diameter (BPD) and occipitofrontal diameter (OFD) from fetal ultrasound images is based on fitting an ellipse modelling the head contour of the fetus to ultrasound images. This is achieved by minimizing a cost function with respect to the parameters of the ellipse using a global multiscale multistart Nelder-Mead algorithm.

Microlocal defect measures for Cauchy data of Dirichlet, resp. Neumann, eigenfunctions an ellipse $E$ are determined. We prove that, any invariant curve the billiard map on boundary phase space $B^\* E$ ellipse, there exists a sequence whose concentrates curve. use this result to give new proof that ellipses infinitesimally spectrally rigid among $C^\\infty$ domains with symmetries ellipse.

Given a finite set Σ of lines in the plane, we discuss necessary and sufficient conditions on when there is an ellipse E, with specified center (h, k) and angle of rotation α, which is tangent to each line in Σ. In all cases we assume that no three of the lines are parallel or have a common intersection point, else no such ellipse could exist. If such an ellipse exists, we say that (h, k) is α ...

UNLABELLED Unlike the motion of a continuous contour, the motion of a single dot is unambiguous and immune to the aperture problem. Here we exploit this fact to explore the conditions under which unambiguous local motion signals are used to drive global percepts of an ellipse undergoing rotation. In previous work, we have shown that a thin, high aspect ratio ellipse will appear to rotate faster...