Module imagingbook.common

Package imagingbook.common.geometry.fitting.circle.algebraic

Class CircleFitKasaB

java.lang.Object

imagingbook.common.geometry.fitting.circle.algebraic.CircleFitKasaB

All Implemented Interfaces:

CircleFitAlgebraic

public class CircleFitKasaB
extends Object
implements CircleFitAlgebraic

This is an implementation of the modified Kåsa [1] circle fitting algorithm described in [2, Sec. 5.1]. A description of the concrete algorithm can be found in [3, Alg. 11.1]. See CircleFitKasaA for the original version.

Compared to the original Kåsa algorithm, this variant also solves a 3x3 linear system but uses a slightly different setup of the scatter matrix (using only powers of 2 instead of 3). A numerical solver is used for this purpose. The algorithm is fast but shares the same numerical instabilities and bias when sample points are taken from a small circle segment. It fails when matrix M becomes singular. Fits to exactly 3 (non-collinear) points are handled properly. Data centering is used to improve numerical stability (alternatively, a reference point can be specified).

[1] I. Kåsa. "A circle fitting procedure and its error analysis", IEEE Transactions on Instrumentation and Measurement 25(1), 8–14 (1976).
[2] N. Chernov. "Circular and Linear Regression: Fitting Circles and Lines by Least Squares". Monographs on Statistics and Applied Probability. Taylor & Francis (2011).
[3] W. Burger, M.J. Burge, Digital Image Processing – An Algorithmic Introduction, 3rd ed, Springer (2022).

See Also:

• CircleFitKasaA
• CircleFitKasaC

Nested Class Summary

Nested classes/interfaces inherited from interface imagingbook.common.geometry.fitting.circle.algebraic.CircleFitAlgebraic

CircleFitAlgebraic.FitType

Constructor Summary

Constructors

Constructor	Description
CircleFitKasaB(Pnt2d[] points)	Constructor.
CircleFitKasaB(Pnt2d[] points, Pnt2d xref)	Constructor.

Method Summary

Modifier and Type	Method	Description
double[]	getParameters()	Returns parameters (A, B, C, D) of the AlgebraicCircle or null if the fit was unsuccessful.

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.circle.algebraic.CircleFitAlgebraic

getAlgebraicCircle, getGeometricCircle, normalizeP

Constructor Details

CircleFitKasaB

public CircleFitKasaB(Pnt2d[] points)

Constructor. The centroid of the sample points is used as the reference point.

Parameters:

points - sample points

CircleFitKasaB

public CircleFitKasaB(Pnt2d[] points,
 Pnt2d xref)

Constructor. The centroid of the sample points is used as the reference point for data centering if null is passed for xref.

Parameters:

points - sample points

xref - reference point or null

Method Details

getParameters

public double[] getParameters()

Description copied from interface: CircleFitAlgebraic

Returns parameters (A, B, C, D) of the AlgebraicCircle or null if the fit was unsuccessful. Parameters are not normalized.

Specified by:

getParameters in interface CircleFitAlgebraic

Returns:

the algebraic circle parameters or null