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Now the projection-type smoother used in conjunction with a 20% trimmed mean is recommended with the minimum volume ellipsoid method a close second.
The reliability and robustness of the normal estimation subroutine was compared against well-known normal estimation methods including the Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators, along with Maximum Likelihood Sample Consensus (MLESAC).
An illustration of the relationship between the DCP and the minimum volume ellipsoid is in Figure 6.
Jackson and Chen [8] compared Mahalanobis distances to minimum volume ellipsoid for identifying outliers for multivariate data.
Alameddine et al. [1] demonstrated a case study to analyze the effectiveness of the minimum covariance determinant MCD, the minimum volume ellipsoid MVE, and M-estimator.
In [20], the dark channel prior (DCP) method [9] was explained using a minimum volume ellipsoid which we will reproduce here for completeness.
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Graphical example of the relationship between the DCP and the minimum distance to three different minimum volume ellipsoids on the red-green plane.
For this LMI the next minimum-volume ellipsoid that contains the solution set is computed.
For each individual group of uncertainties, the minimum-volume ellipsoid problem is reformulated into a semi-definite programming (SDP) problem and thus can be efficiently solved to its global optimum.
Since John [18] initiated semi-infinite programming precisely to deduce important results about two such geometric problems: the problems of covering a compact body in finite dimensional spaces by the minimum-volume disk and the minimum-volume ellipsoid, many researchers have been investigated the theory, applications and methods for the semi-infinite programming (see, for example, [19 22]).
A new method, called kernel minimum volume covering ellipsoid (KMVCE) estimation, that finds an ellipsoid in a kernel-defined feature space is presented.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com