Biedl et al.[1] first posed the problem of finding the center of a circle, starting from a point on the boundary, using a limited number of operations. We solve an open problem, presented in their work: finding the center of an ellipse. We present new algorithms for finding the center of the ellipse and provide results of experiments showing how these algorithms perform under the introduction o...

Due to their simplicity and ease of handling quadrarcs have been used to provide a piecewise circular approximation to ellipses for many hundreds of years. Like biarcs there are many possible criteria for choosing joint positions between the arcs. This paper provides an algebraic formulation of 10 of these quadrarc constructions. For a range of ellipse eccentricities these quadrarcs are assesse...

In this paper, we propose an arc-search corrector-predictor interior-point method for solving $P_*(kappa)$-linear complementarity problems. The proposed algorithm searches the optimizers along an ellipse that is an approximation of the central path. The algorithm generates a sequence of iterates in the wide neighborhood of central path introduced by Ai and Zhang. The algorithm does not de...

The development of unmanned crane is an important issue of Factory Automation in steel industry. This paper focus on unmanned crane for picking up coils on a trailer although positions and diameters of coils is not fixed. In order to pick up those coils, unmanned crane should know exact 3D coil position. Therefore, in order to find out exact 3D coil’s centers, this paper propose the system that...

This work presents a new efficient method for fitting ellipses to scattered data. Previous algorithms either fitted general conics or were computationally expensive. By minimizing the algebraic distance subject to the constraint 4 2 1 the new method incorporates the ellipticity constraint into the normalization factor. The new method combines several advantages: (i) It is ellipse-specific so th...

If E is any ellipse inscribed in a convex quadrilateral, D – , then we prove that Area (E) Area(D – ) π 4 , and equality holds if and only if D – is a parallelogram and E is tangent to the sides of D – at the midpoints. We also prove that the foci of the unique ellipse of maximal area inscribed in a parallelogram, D – , lie on the orthogonal least squares line for the vertices of D – . This doe...

The study of the mass center (CM) motion of the left ventricle (LV) area in echocardiographic videos is presented. CM of any phase of the cardiac cycle is inside an ellipse. An area of the ellipse is not more than 2% of the area of LV in systole. The criterion to identify correct and incorrect forms of contours are proposed for automatic contouring of LV in the frames of a video sequence.

This paper studies numerical schemes for fitting an ellipse to points in an image. First, the problem is posed as maximum likelihood, and the relationship to the KCR lower bound is stated. Then, the algorithms of FNS, HEIV, renormalization, and Gauss-Newton iterations are described. Using simulated and real image data, their convergence properties are compared, and their dependence on the shape...

Harker and O’Leary’s [3] recently proposed a new distance measure for conics. This paper compares its accuracy and effectiveness against several other error of fits (EOFs) for ellipses using: 1/ visualisations of the distortions with respect to the Euclidean distance; 2/ a set of evaluation measures specifically designed for assessing ellipse EOFs [7, 8]; 3/ the accuracy of LMedS ellipse fittin...