Enhanced Direct Least Square Fitting of Ellipses

Abstract

This paper presents a robust and direct algorithm for the least-square fitting of ellipses to scattered data. The proposed algorithm makes use of well-known techniques that improve the robustness of the direct least-square fitting with a modest increase of the computational burden. Furthermore, by trivial modifications of the constrained minimization problem the algorithm may be converted to perform the specific fitting of other types of conics such as hyperbola. The method is simple and accurate and can be implemented with fixed time of computation. These characteristics coupled to its robustness and specificity makes the algorithm well-suited for applications requiring real-time machine vision.

Methods for Ellipse Detection from Edge Maps of Real Images

“…This method is invariant to affine transformation and is computationally efficient. While Fitzgibbon (Fitzgibbon et al, 1999) is arguably the most popular method used in the image processing community, some further work in this direction has been done (Harker et al, 2008;Maini, 2006;O'Leary et al, 2005). We also note the family of work (Ahn and Rauh, 1999;Ahn et al, 2002;Ahn et al, 2001) which uses geometric properties within the least squares method.…”

Real-Time Least-Square Fitting of Ellipses Applied to the RobotCub Platform

“…There are many techniques for ellipse detection. Most of thew work in real-time (even if depending on the image size) [7], [8].…”

“…In this paper we implemented for the first time in a real context the Enhance Direct Fitting of Ellipses (EDFE) technique [8] for the least-square fitting of ellipses, previously developed by our group. We implemented this as a continuation of a work started as a pure mathematical context in our team by Maini et Al [8].…”

“…We implemented this as a continuation of a work started as a pure mathematical context in our team by Maini et Al [8].…”

“…It is worth note we are not interested in the absolute error of each procedure (yet evaluated for each method in [4], [7], and [8]); nonetheless we are interested in verifying the systems' execution dissimilarities under the same situation. Moreover, we are not interested in analyzing these dissimilarities in terms of mathematical performance, as done by the authors in [4], [7], and [8], but their usage in practical applications and scenarios instead, such as finding the position of a target object within the 3D surrounding space. We used the simulation of a state of art robotics platform, the RobotCub, in order to test it at best before doing this with the real platform.…”