1 / 9

Ellipse Fitting: Image Point Adjustment for Best Fit

Explore fitting ellipses in images using a Euclidean distance approach. Learn the equations, computations, and optimizations involved in finding the best-fitting ellipse for a set of image points.

mauricioy
Download Presentation

Ellipse Fitting: Image Point Adjustment for Best Fit

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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.

More Related