Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered inf...

Corresponding to each convex (or more general) subset of n-dimensional Euclidean space, Rn, there is a unique ellipsoid with the following property. The moment of inertia of the ellipsoid and the moment of inertia of the convex set are the same about every 1-dimensional subspace of Rn. This ellipsoid is called the Legendre ellipsoid of the convex set. The Legendre ellipsoid is a well-known conc...

OBJECTIVE To assess the clinical feasibility and the accuracy of two pragmatic methods in comparison with a conventional computer based method of measurement of masses from CT. METHODS Nineteen CT scans of 11 patients with severe head injury, showing 34 traumatic lesions, were examined. The volume of every lesion was digitally measured, then a panel of three examiners independently repeated t...

The ellipsoid body, a doughnut-shaped part of the fly brain, is essential for visual working memory. Gaseous second messengers establish a functional ellipsoid body and act as a short-term aid in orientation behavior.

Sonographic images of the gallbladder enable satisfactory approximation of gallbladder volume using the sum-of-cylinders method. The sum-of-cylinder measurements, however, are moderately cumbersome and time consuming to perform. In this investigation, in vitro and in vivo testing was done to determine that a simple ellipsoid method applied to sonographic gallbladder images yields reasonable vol...

This paper applies a method known in the engineering literature as Effective Independence Distribution (EID) to an approximation of the minimum volume ellipsoid, a high breakdown robust estimator of multivariate location and scale. The calculation of the minimum volume ellipsoid is an extremely computationally intensive task. Previous methods for approximating the MVE have focused on bootstrap-...

PURPOSE To evaluate the patterns of tumor shape and to compare tumor volume derived from simple diameter-based ellipsoid measurement with that derived from tracing the entire tumor contour using region of interest (ROI)-based 3D volumetry with respect to the prediction outcome in cervical cancer patients treated with concurrent chemotherapy and radiotherapy. MATERIALS AND METHODS Magnetic res...

This bound is achieved by the maximum volume ellipsoid contained in K. Ellipsoids have also been critical to the design and analysis of efficient algorithms. The most notable example is the ellipsoid algorithm (1, 2) for linear (3) and convex optimization (4), which represents a frontier of polynomial-time solvability. For the basic problems of sampling and integration in high dimension, the in...