org.openimaj.math.geometry.shape.algorithm

Class GeneralisedProcrustesAnalysis

java.lang.Object

org.openimaj.math.geometry.shape.algorithm.GeneralisedProcrustesAnalysis

public class GeneralisedProcrustesAnalysis
extends Object

Implementation of shape alignment using Generalised Procrustes Analysis. The alignment process is iterative and stops after a given number of iterations or when the Procrustes Distance between the current mean and previous reference shape is less than a threshold (i.e. the rate of change is small). All shapes are aligned inplace. The reference shape is optionally normalised to a standardised scale and translated to the origin.

Author:

Jonathon Hare (jsh2@ecs.soton.ac.uk)

Constructor Summary

Constructors

Constructor and Description
GeneralisedProcrustesAnalysis(float threshold) Construct the GeneralisedProcrustesAnalysis with the given parameters.
GeneralisedProcrustesAnalysis(float threshold, int maxIters) Construct the GeneralisedProcrustesAnalysis with the given parameters.

Method Summary

Modifier and Type	Method and Description
PointList	align(List<PointList> shapes) Align the input shapes to the "mean" shape.
static PointList	alignPoints(List<PointList> inputShapes, float threshold, int maxIters) Align the input shapes to the "mean" shape using Generalised Procrustes Analysis.
protected static PointList	alignPointsAndAverage(List<PointList> shapes, PointList reference, double referenceScaling, Point2d referenceCog)

Methods inherited from class java.lang.Object

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

Constructor Detail

GeneralisedProcrustesAnalysis

public GeneralisedProcrustesAnalysis(float threshold,
                                     int maxIters)

Construct the GeneralisedProcrustesAnalysis with the given parameters. The alignment process is iterative and stops after a given number of iterations (last parameter) or when the Procrustes Distance between the current mean and previous reference shape is less than a threshold (i.e. the rate of change is small) (first parameter).

Parameters:

threshold - the threshold on the Procrustes Distance at which to stop iterating

maxIters - the maximum number of iterations.

GeneralisedProcrustesAnalysis

public GeneralisedProcrustesAnalysis(float threshold)

Construct the GeneralisedProcrustesAnalysis with the given parameters. The alignment process is iterative and stops after a default number of iterations (10) or when the Procrustes Distance between the current mean and previous reference shape is less than a threshold (i.e. the rate of change is small)

Parameters:

threshold - the threshold on the Procrustes Distance at which to stop iterating

Method Detail

align

public PointList align(List<PointList> shapes)

Align the input shapes to the "mean" shape. All shapes are aligned inplace. The mean shape is returned.

Parameters:

shapes - The shapes to align

Returns:

the mean shape.

alignPoints

public static PointList alignPoints(List<PointList> inputShapes,
                                    float threshold,
                                    int maxIters)

Align the input shapes to the "mean" shape using Generalised Procrustes Analysis. The alignment process is iterative and stops after a given number of iterations or when the Procrustes Distance between the current mean and previous reference shape is less than a threshold (i.e. the rate of change is small). All shapes are aligned inplace. The reference shape is initially normalised to a standardised scale and translated to the origin. The mean shape is returned.

Parameters:

inputShapes - The shapes to align

threshold - the threshold on the Procrustes Distance at which to stop iterating

maxIters - the maximum number of iterations.

Returns:

the mean shape

alignPointsAndAverage

protected static PointList alignPointsAndAverage(List<PointList> shapes,
                                                 PointList reference,
                                                 double referenceScaling,
                                                 Point2d referenceCog)