imagingbook.pub.fd

Class FourierDescriptor

java.lang.Object

imagingbook.pub.fd.FourierDescriptor

All Implemented Interfaces:

Cloneable

Direct Known Subclasses:

FourierDescriptorFromPolygon, FourierDescriptorUniform

public abstract class FourierDescriptor
extends Object
implements Cloneable

This is the abstract super-class for Fourier descriptors. It cannot be instantiated.

Version:

2015/08/13

Field Summary

Fields

Modifier and Type	Field and Description
protected Complex[]	g
protected Complex[]	G
protected double	reconstructionScale

Constructor Summary

Constructors

Constructor and Description
FourierDescriptor()

Method Summary

Modifier and Type	Method and Description
FourierDescriptor	clone()
double	distanceComplex(FourierDescriptor fd2)
double	distanceComplex(FourierDescriptor fd2, int Mp)
double	distanceMagnitude(FourierDescriptor fd2)
double	distanceMagnitude(FourierDescriptor fd2, int Mp)
Complex	getCoefficient(int m)
int	getCoefficientIndex(int m)
Complex[]	getCoefficients()
Complex	getEllipsePoint(Complex G1, Complex G2, int m, double t) Get the reconstructed point for two DFT coefficients G1, G2 at a given position t.
int	getMaxCoefficientPairs()
double	getMaxDftMagnitude()
int	getMaxDftMagnitudeIndex()
int	getMaxNegHarmonic()
int	getMaxPosHarmonic()
Complex[]	getReconstruction(int N) Calculates a reconstruction from the full DFT spectrum with N samples.
Complex[]	getReconstruction(int N, int Mp) Calculate a reconstruction from the partial DFT spectrum with N sample points and using Mp coefficient pairs.
Complex	getReconstructionPoint(double t) Reconstructs a single spatial point from the complete FD at the fractional path position t in [0,1].
Complex	getReconstructionPoint(double t, int Mp)
double	getReconstructionScale()
Complex[]	getSamples()
double	getStartPointPhase(int Mp) Calculates the 'canonical' start point.
protected static Complex[]	makeComplex(Point2D[] points)
Path2D	makeEllipse(Complex G1, Complex G2, int m, double xOffset, double yOffset)
Path2D	makeFourierPairsReconstruction() Reconstructs the shape using all FD pairs.
Path2D	makeFourierPairsReconstruction(int Mp) Reconstructs the shape obtained from FD-pairs 0,...,Mp as a polygon (path).
FourierDescriptor[]	makeInvariant()
FourierDescriptor[]	makeInvariant(int Mp)
double	makeRotationInvariant()
double	makeScaleInvariant() Normalizes this descriptor destructively to the L2 norm of G, keeps G_0 untouched.
FourierDescriptor[]	makeStartPointInvariant()
void	makeTranslationInvariant() Sets the zero (DC) coefficient to zero.
void	rotate(double phi) For testing: apply shape rotation to this FourierDescriptor (phi in radians)
void	setCoefficient(int m, Complex z)
void	setCoefficient(int m, double a, double b)
int	size()
FourierDescriptor	truncate(int Mp) Truncates this Fourier descriptor to the Mp lowest-frequency coefficients.

Methods inherited from class java.lang.Object

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

Field Detail

g

protected Complex[] g

G

protected Complex[] G

reconstructionScale

protected double reconstructionScale

Constructor Detail

FourierDescriptor

public FourierDescriptor()

Method Detail

getReconstructionScale

public double getReconstructionScale()

truncate

public FourierDescriptor truncate(int Mp)

Truncates this Fourier descriptor to the Mp lowest-frequency coefficients. For example, the original Fourier descriptor with 10 coefficients a,b,...,j

 m    = 0 1 2 3 4 5 6 7 8 9
 G[m] = a b c d e f g h i j
 

becomes (with P = 3)

 m    = 0 1 2 3 4 5 6
 G[m] = a b c d h i j
 

Parameters:

Mp - number of coefficients to remain

Returns:

a new (truncated) instance of FourierDescriptor

clone

public FourierDescriptor clone()

Overrides:

clone in class Object

getMaxNegHarmonic

public int getMaxNegHarmonic()

getMaxPosHarmonic

public int getMaxPosHarmonic()

getMaxCoefficientPairs

public int getMaxCoefficientPairs()

makeComplex

protected static Complex[] makeComplex(Point2D[] points)

getSamples

public Complex[] getSamples()

getCoefficients

public Complex[] getCoefficients()

size

public int size()

getCoefficientIndex

public int getCoefficientIndex(int m)

getCoefficient

public Complex getCoefficient(int m)

setCoefficient

public void setCoefficient(int m,
                           Complex z)

setCoefficient

public void setCoefficient(int m,
                           double a,
                           double b)

getReconstruction

public Complex[] getReconstruction(int N)

Calculates a reconstruction from the full DFT spectrum with N samples.

Parameters:

N - number of samples

Returns:

reconstructed contour points

getReconstruction

public Complex[] getReconstruction(int N,
                                   int Mp)

Calculate a reconstruction from the partial DFT spectrum with N sample points and using Mp coefficient pairs.

Parameters:

N - number of samples

Mp - number of coefficient pairs

Returns:

reconstructed contour points

getReconstructionPoint

public Complex getReconstructionPoint(double t)

Reconstructs a single spatial point from the complete FD at the fractional path position t in [0,1].

Parameters:

t - path position

Returns:

single contour point

getReconstructionPoint

public Complex getReconstructionPoint(double t,
                                      int Mp)

makeEllipse

public Path2D makeEllipse(Complex G1,
                          Complex G2,
                          int m,
                          double xOffset,
                          double yOffset)

getEllipsePoint

public Complex getEllipsePoint(Complex G1,
                               Complex G2,
                               int m,
                               double t)

Get the reconstructed point for two DFT coefficients G1, G2 at a given position t.

Parameters:

G1 - first coefficient

G2 - second coefficient

m - frequency number

t - contour position

Returns:

reconstructed point

makeFourierPairsReconstruction

public Path2D makeFourierPairsReconstruction()

Reconstructs the shape using all FD pairs.

Returns:

reconstructed shape

makeFourierPairsReconstruction

public Path2D makeFourierPairsReconstruction(int Mp)

Reconstructs the shape obtained from FD-pairs 0,...,Mp as a polygon (path).

Parameters:

Mp - number of Fourier coefficient pairs

Returns:

reconstructed shape

getMaxDftMagnitudeIndex

public int getMaxDftMagnitudeIndex()

getMaxDftMagnitude

public double getMaxDftMagnitude()

makeInvariant

public FourierDescriptor[] makeInvariant()

makeInvariant

public FourierDescriptor[] makeInvariant(int Mp)

makeStartPointInvariant

public FourierDescriptor[] makeStartPointInvariant()

makeTranslationInvariant

public void makeTranslationInvariant()

Sets the zero (DC) coefficient to zero.

makeScaleInvariant

public double makeScaleInvariant()

Normalizes this descriptor destructively to the L2 norm of G, keeps G_0 untouched.

Returns:

the scale factor used for normalization

makeRotationInvariant

public double makeRotationInvariant()

rotate

public void rotate(double phi)

For testing: apply shape rotation to this FourierDescriptor (phi in radians)

Parameters:

phi - rotation angle

getStartPointPhase

public double getStartPointPhase(int Mp)

Calculates the 'canonical' start point. This version uses (a) a coarse search for a global maximum of fp() and subsequently (b) a numerical optimization using Brent's method (implemented with Apache Commons Math).

Parameters:

Mp - number of Fourier coefficient pairs

Returns:

start point phase

distanceComplex

public double distanceComplex(FourierDescriptor fd2)

distanceComplex

public double distanceComplex(FourierDescriptor fd2,
                              int Mp)

distanceMagnitude

public double distanceMagnitude(FourierDescriptor fd2)

distanceMagnitude

public double distanceMagnitude(FourierDescriptor fd2,
                                int Mp)