Ray optics and phase ellipse Optics are developed as tools for designing charged particle beam guidance systems. Specific examples of basic optical systems and of phase ellipse matching are presented as illustrations of these mathematical techniques. Presented at the Conference on Charged Particle Optics Giessen, West Germany September 8-12, 1980 also submitted to Nuclear Instruments and Method...

The most frequently observed focal conic domains (FCD's) in lamellar phases are those based on confocal paris of ellipse and hyperbola. Experimentally, the eccentricity of the ellipse takes a broad range of values 0</=e<1. We present an analytical expression for the curvature energy of a FCD that is valid in the entire range 0</=e<1. Generally, the curvature energy of an isolated FCD reaches a ...

We propose a new approach for detecting ellipses. The approach is based on the geometrical property that five points on an ellipse can determine the parameters of the ellipse, and the symmetry of ellipses is used to obtain these points. Using symmetry, we classify the edge points in an input image into several subimages. Ellipses with different symmetric axes will lie in different subimages. In...

We study the external tritangent Apollonius (or Voronoi) circle to three ellipses. This problem arises when one wishes to compute the Apollonius (or Voronoi) diagram of a set of ellipses, but is also of independent interest in enumerative geometry. This paper is restricted to non-intersecting ellipses, but the extension to arbitrary ellipses is possible. We propose an efficient representation o...

We propose a two-step method for detecting human heads with their orientations. In the first step, the method employs an ellipse as the contour model of human-head appearances to deal with wide variety of appearances. Our method then evaluates the ellipse to detect possible human heads. In the second step, on the other hand, our method focuses on features inside the ellipse, such as eyes, the m...

Abstract: Real-Time tracking of elliptical objects, e.g. a ball, is a well studied field. However, the question between a monocular and binocular approach for 3D objects localization is still an open issue. In this work we implemented a real-time algorithm for 3D ball localization and tracking from 2D image ellipse fitting with calibrated cameras. We will exploit both approaches, together with ...

People attending teleconference meetings usually follow specific trajectories corresponding to their intentions. In most situations the meeting video content can by sufficiently characterized by capturing the head trajectories. The tracking of the head is done using a particle filter built on cues such as color, gradient and shape. The head is represented by an ellipse with fuzzy color histogra...

We propose a two-step method for detecting human heads and estimating face orientations under the dynamic environment. In the first step, the method employs an ellipse as the contour model of humanhead appearances to deal with wide variety of appearances. Our method then evaluates the ellipse to detect possible human heads. In the second step, on the other hand, our method focuses on features, ...

This work presents a quasi-three dimensional scattering model to predict the polarization properties of an indoor radio channel. The proposed model considers not only the effect of the polarization of fields scattered by scatterers but also extends the ellipse model to a quasi-three dimensional model. In the model, all scatterers are considered as a patch scatterer and distribution properties o...

Ellipse detection is a very important problem in the field of pattern recognition and computer vision. The existing algorithms often use a bottom-up strategy to combine edge points or elliptical arcs into ellipses, hence limit their robustness. In this paper, we propose a fast and robust ellipse detection algorithm which can accurately detect ellipses in the images. The main idea of the propose...