Module imagingbook.common

Package imagingbook.common.geometry.fitting.ellipse.algebraic

Class EllipseFitFitzgibbonOriginal

java.lang.Object

imagingbook.common.geometry.fitting.ellipse.algebraic.EllipseFitFitzgibbonOriginal

All Implemented Interfaces:

EllipseFitAlgebraic

public class EllipseFitFitzgibbonOriginal
extends Object
implements EllipseFitAlgebraic

Algebraic ellipse fit based on Fitzgibbon's original method [1], as described in [2] (WITHOUT the additional numerical improvements). Based on generalized symmetric eigenproblem solution. See [3, Sec. 11.2.1] for a detailed description. Note: This implementation does not use data centering nor accepts a specific reference point. With exactly 5 input points (generally sufficient for ellipse fitting) the scatter matrix X is singular and thus the Cholesky decomposition used by the GeneralizedSymmetricEigenDecomposition cannot be applied. Thus at least 6 distinct input points are required (i.e., no duplicate points are allowed).

[1] A. W. Fitzgibbon, M. Pilu, and R. B. Fisher. Direct least- squares fitting of ellipses. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(5), 476-480 (1999).
[2] R. Halíř and J. Flusser. Numerically stable direct least squares fitting of ellipses. In "Proceedings of the 6th International Conference in Central Europe on Computer Graphics and Visualization (WSCG’98)", pp. 125-132, Plzeň, CZ (February 1998).
[3] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

Version:

2022/11/17

Nested Class Summary

Nested classes/interfaces inherited from interface imagingbook.common.geometry.fitting.ellipse.algebraic.EllipseFitAlgebraic

EllipseFitAlgebraic.FitType

Constructor Summary

Constructors

Constructor	Description
EllipseFitFitzgibbonOriginal(Pnt2d[] points)

Method Summary

Modifier and Type	Method	Description
double[]	getParameters()	Returns a vector of algebraic ellipse parameters: (a,b,c,d,e,f), representing the ellipse by a x^2 + b x y + c y^2 + d x + e y + f = 0.

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface imagingbook.common.geometry.fitting.ellipse.algebraic.EllipseFitAlgebraic

getDataOffsetCorrectionMatrix, getEllipse, isEllipse

Constructor Details

EllipseFitFitzgibbonOriginal

public EllipseFitFitzgibbonOriginal(Pnt2d[] points)

Method Details

getParameters

public double[] getParameters()

Description copied from interface: EllipseFitAlgebraic

Returns a vector of algebraic ellipse parameters: (a,b,c,d,e,f), representing the ellipse by a x^2 + b x y + c y^2 + d x + e y + f = 0.

Specified by:

getParameters in interface EllipseFitAlgebraic

Returns:

the ellipse parameters