Least squares ellipsoid specific fitting

Li, Qingde; Griffiths, J.G.

Abstract

In this paper, a sufficient condition for a quadric surface to be an ellipsoid has been developed and a closed-form solution for ellipsoid fitting is developed based on this constraint, which is a best fit to the given data amongst those ellipsoids whose short radii are at least half of their major radii, in the sense of algebraic distance. A simple search procedure is proposed to pursuit the 'best' ellipsoid when data cannot be well described by this type of ellipsoid. The proposed fitting algorithm is quick, stable and insensitive to small errors in the data.

Citation

Li, Q., & Griffiths, J. (2004). Least squares ellipsoid specific fitting. In Geometric Modeling and Processing, 2004. Proceedings (335 - 340). https://doi.org/10.1109/gmap.2004.1290055

• Conference Name: Geometric Modeling and Processing, 2004.
• Conference Location: Beijing, China
• Start Date: Apr 13, 2004
• End Date: Apr 15, 2004
• Acceptance Date: Dec 31, 2004
• Online Publication Date: Sep 27, 2004
• Publication Date: Dec 31, 2004
• Journal: Proceedings - Geometric Modeling and Processing 2004
• Publisher: Institute of Electrical and Electronics Engineers
• Pages: 335 - 340
• Book Title: Geometric Modeling and Processing, 2004. Proceedings
• ISBN: 0769520782
• DOI: https://doi.org/10.1109/gmap.2004.1290055
• Keywords: Least squares methods; Ellipsoids; Surface fitting; Sufficient conditions; Scattering; Geometry; Nonlinear equations; Computer science; Pattern recognition; Machine vision
• Public URL: https://hull-repository.worktribe.com/output/423867
• Publisher URL: https://ieeexplore.ieee.org/document/1290055