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...

The Grad–Shafranov plasma equilibrium equation was originally solved analytically in toroidal geometry, which fitted the geometric shape of first Tokamaks. poloidal surface Tokamak has evolved over years from a circular to D-shaped ellipse. natural geometry that describes such is prolate elliptical one, i.e., cap-cyclide coordinate system. When written this can be terms general Heun function. I...

An ellipse rotating in the image plane can produce several different percepts. The two-dimensional (2D) percepts are either a rotating rigid ellipse or a constantly deforming non-rigid ellipse. The 3D percept is a rotating rigid circular disk that is tilted relative to the image plane. Stimuli that generate 3D percepts based on purely 2D rotational motion are known as stereokinetic stimuli. We ...