@MISC{Moshtagh_minimumvolume, author = {Nima Moshtagh}, title = {MINIMUM VOLUME ENCLOSING ELLIPSOIDS}, year = {} }

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Abstract

Abstract. Two different methods for computing the covering ellipses of a set of points are presented. The first method finds the optimal ellipsoids with the minimum volume. The second method uses the first and second moments of the data points to compute the parameters of an ellipsoid that covers most of the points. A MATLAB software is written to verify the results. 1.

... In section 2 we formulate it as an optimization problem and minimize the volume of the covering ellipse. Sections 2, 3 and 4 are based on two papers [2] and [3] that make improvements to the work of =-=[1]-=- who first introduced an algorithm for finding the minimum volume ellipsoids. In section 6, we use the first and second moments of the data points to find an approximate ellipsoid that encloses as man...

... colored box. We approach the problem in two ways. In section 2 we formulate it as an optimization problem and minimize the volume of the covering ellipse. Sections 2, 3 and 4 are based on two papers =-=[2]-=- and [3] that make improvements to the work of [1] who first introduced an algorithm for finding the minimum volume ellipsoids. In section 6, we use the first and second moments of the data points to ...

... box. We approach the problem in two ways. In section 2 we formulate it as an optimization problem and minimize the volume of the covering ellipse. Sections 2, 3 and 4 are based on two papers [2] and =-=[3]-=- that make improvements to the work of [1] who first introduced an algorithm for finding the minimum volume ellipsoids. In section 6, we use the first and second moments of the data points to find an ...

...n section 6, we use the first and second moments of the data points to find an approximate ellipsoid that encloses as many pixels as possible. This part of the paper is based on the work presented in =-=[4]-=-. 1s2 NIMA MOSHTAGH NIMA@GRASP.UPENN.EDU 50 100 150 200 50 100 150 200 250 300 (a) Original Image Figure 1. The colored boxes. 50 100 150 200 50 100 150 200 250 300 (b) Color Detection output 2. Minim...