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Ellipse Fitting

Ellipse Fitting. COMP 4900C Winter 2008. Ellipses in Images. Perspective projection of circles form ellipses in the images. Equations of Ellipse. Let. Then. Given a set of N image points find the parameter vector such that the ellipse. fits best in the least square sense:.

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Ellipse Fitting

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  1. Ellipse Fitting COMP 4900C Winter 2008

  2. Ellipses in Images Perspective projection of circles form ellipses in the images.

  3. Equations of Ellipse Let Then

  4. Given a set of N image points find the parameter vector such that the ellipse fits best in the least square sense: Where is the distance from to the ellipse. Ellipse Fitting: Problem Statement

  5. is the point on the ellipse that is nearest to Euclidean Distance Fit is normal to the ellipse at

  6. Compute Distance Function Computing the distance function is a constrained optimization problem: subject to Using Lagrange multiplier, define: where Then the problem becomes: we have Set

  7. 1. First-order approximation at 2. Assume is close to , then Two Approximations

  8. Solve for Approximate Distance Function Substitute back

  9. Given a set of N image points find the parameter vector such that Ellipse Fitting with Euclidean Distance This problem can be solved by using a numerical nonlinear optimization system.

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