Minimum volume ellipsoid

Abstract

The minimum volume ellipsoid (MVE) estimator is based on the smallest volume ellipsoid that covers h of the n observations. It is an affine equivariant, highbreakdown robust estimator of multivariate location and scatter. The MVE can be computed by a resampling algorithm. Its low bias makes the MVE very useful for outlier detection in multivariate data, often through the use of MVE-based robust distances. We review the basic MVE definition as well as some useful extensions such as the one-step reweighted MVE. We discuss the main properties of the MVE including its breakdown value, affine equivariance, and efficiency. We discuss the basic resampling algorithm to calculate the MVE and illustrate its use on two examples. An overview of applications is given, as well as some related classes of robust estimators of multivariate location and scatter. 

Kidney Detection and Segmentation in Contrast-Enhanced Ultrasound 3D Images

“…Furthermore, they do not explicitly use the fact that only one ellipsoid is present in the image. On the other hand, statistical approaches like robust Minimum Volume Ellipsoid (MVE) estimators [12] are better suited but require prior knowledge on the proportion of outliers (here the noise, artifacts or neighboring structures), which may vary from one image to another and is thus not available. We therefore propose an original variational framework, that is robust and fast, to estimate the best ellipsoid in an image I : Ω ⊂ R 3 → R + .…”

Kidney detection and real-time segmentation in 3D contrast-enhanced ultrasound images

“…However their extension to 3D, though possible, are usually computationally expensive mainly because of the number of parameters to estimate (9 for a 3D ellipsoid). On the other hand, statistical approaches like robust Minimum Volume Ellipsoid (MVE) estimators [6] are better suited but require prior knowledge on the proportion of outliers (here the noise and artifacts), which may vary from one image to another and is thus not available.…”

On the use of minimum volume ellipsoids and symplectic capacities for studying classical uncertainties for joint position–momentum measurements

“…See for instance [7,9] for a proof of the first formula (26). The second formula follows from the first in view of the equality (22). The first formula (26) shows that the symplectic capacity of M is the area of the intersection of that ellipsoid with the x 1 , p 1 plane once it has been put in normal form (24).…”