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Minimum area ellipse - quadratic optimisation? [message #47561]

Thu, 16 February 2006 06:19

Olivia
Messages: 16
Registered: February 2006

Junior Member

Dear All,

My aim is to fit an ellipse with a known center onto a distribution of
points, where all points have to be inside or on the ellipse, and the
ellipse chosen is of the minimum area.

I thought a brute force and not very clever way of doing this would be
to calculate the area taking each set of 3 points to solve the 3
remaining unknowns, (a, b, and orientation angle), in the ellipse
equation, and finding which one had the smallest area. But this
wouldn't work obviously as there would be no condition that all the
other points have to be inside the ellipse. I have read up on quadratic
optimization but have to admit I do not really understand the maths.

I posted on this topic before, but it is important that my ellipse
fitting method does not rely on convex hulls. I wrote a program which
does fit ellipses to the point distributions, but not the ellipses with
the minimum area.

I am sure the problem can't be as hard as I am finding it, and I am
feeling right now like drawing the 600 or so ellipses my program needs
myself! Any suggestions really would be very helpful. Thanks,

Olivia

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[Message index]

		Minimum area ellipse - quadratic optimisation? By: Olivia on Thu, 16 February 2006 06:19
		Re: Minimum area ellipse - quadratic optimisation? By: greg michael on Tue, 21 February 2006 07:56
		Re: Minimum area ellipse - quadratic optimisation? By: Paolo Grigis on Mon, 20 February 2006 09:41
		Re: Minimum area ellipse - quadratic optimisation? By: Olivia on Mon, 20 February 2006 08:48

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