#include <itkMahalanobisDistanceMembershipFunction.h>

Inheritance diagram for itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >:

Collaboration diagram for itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >:

Detailed Description

template<class TVector>
class itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >

MahalanobisDistanceMembershipFunction models class membership using Mahalanobis distance.

MahalanobisDistanceMembershipFunction is a subclass of MembershipFunctionBase that models class membership (or likelihood) using the Mahalanobis distance. The mean and covariance structure of the Mahalanobis distance are established using the methods SetMean() and SetCovariance(). The mean is a vector-type that is the same vector-type as the measurement vector but guaranteed to have a real element type. For instance, if the measurement type is an Vector<int,3>, then the mean is Vector<double,3>. If the measurement type is a VariableLengthVector<float>, then the mean is VariableLengthVector<double>. In contrast to this behavior, the covariance is always a VariableSizeMatrix<double>.

Note that this membership function does not return a probability density function in contrast to the GaussianMembershipFunction.

Note, as is the case in other packages (MATLAB, R), the value returned by this membership function is the squared distance.

If the covariance is singular or nearly singular, the membership function behaves somewhat like (the opposite of) an impulse located at the mean. In this case, we specify the covariance to be a diagonal matrix with large values along the diagonal. This membership function, therefore, will return large but differentiable values everywhere and decay to zero sharply near the mean.

Definition at line 62 of file itkMahalanobisDistanceMembershipFunction.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef VariableSizeMatrix < double >	CovarianceMatrixType

typedef MeasurementVectorRealType	MeanVectorType

typedef itk::NumericTraits < MeasurementVectorType > ::RealType	MeasurementVectorRealType

typedef Superclass::MeasurementVectorSizeType	MeasurementVectorSizeType

typedef TVector	MeasurementVectorType

typedef Superclass::Pointer	MembershipFunctionPointer

typedef SmartPointer< Self >	Pointer

typedef MahalanobisDistanceMembershipFunction	Self

typedef MembershipFunctionBase < TVector >	Superclass

Public Types inherited from itk::Statistics::MembershipFunctionBase< TVector >
typedef SmartPointer< const Self >	ConstPointer

typedef unsigned int	MeasurementVectorSizeType

typedef TVector	MeasurementVectorType

typedef SmartPointer< Self >	Pointer

typedef MembershipFunctionBase	Self

typedef FunctionBase< TVector, double >	Superclass

Public Types inherited from itk::FunctionBase< TVector, double >
typedef SmartPointer< const Self >	ConstPointer

typedef TVector	InputType

typedef double	OutputType

typedef SmartPointer< Self >	Pointer

typedef FunctionBase	Self

typedef Object	Superclass

Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
double	Evaluate (const MeasurementVectorType &measurement) const

virtual const CovarianceMatrixType &	GetCovariance ()

virtual const MeanVectorType &	GetMean ()

virtual LightObject::Pointer	InternalClone () const

void	SetCovariance (const CovarianceMatrixType &cov)

void	SetMean (const MeanVectorType &mean)

Public Member Functions inherited from itk::Statistics::MembershipFunctionBase< TVector >
virtual MeasurementVectorSizeType	GetMeasurementVectorSize () const

virtual void	SetMeasurementVectorSize (MeasurementVectorSizeType s)

Protected Member Functions
	MahalanobisDistanceMembershipFunction (void)

void	PrintSelf (std::ostream &os, Indent indent) const

virtual	~MahalanobisDistanceMembershipFunction (void)

Protected Member Functions inherited from itk::Statistics::MembershipFunctionBase< TVector >
	MembershipFunctionBase ()

void	PrintSelf (std::ostream &os, Indent indent) const

virtual	~MembershipFunctionBase (void)

Protected Member Functions inherited from itk::FunctionBase< TVector, double >
	FunctionBase ()

	~FunctionBase ()

Protected Member Functions inherited from itk::Object
	Object ()

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &time)

virtual	~Object ()

Protected Member Functions inherited from itk::LightObject
	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Private Attributes
CovarianceMatrixType	m_Covariance

bool	m_CovarianceNonsingular

CovarianceMatrixType	m_InverseCovariance

MeanVectorType	m_Mean

virtual const char *	GetNameOfClass () const

virtual ::itk::LightObject::Pointer	CreateAnother (void) const

static Pointer	New ()

Additional Inherited Members
Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool flag)

Protected Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

Protected Attributes inherited from itk::LightObject
InternalReferenceCountType	m_ReferenceCount

SimpleFastMutexLock	m_ReferenceCountLock

Member Typedef Documentation

template<class TVector >

typedef SmartPointer< const Self > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::ConstPointer

Definition at line 70 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef VariableSizeMatrix< double > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::CovarianceMatrixType

Type of the covariance matrix

Definition at line 92 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef MeasurementVectorRealType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeanVectorType

Definition at line 89 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef itk::NumericTraits< MeasurementVectorType >::RealType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorRealType

Type of the mean vector. RealType on a vector-type is the same vector-type but with a real element type.

Definition at line 88 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef Superclass::MeasurementVectorSizeType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorSizeType

Typedef to represent the length of measurement vectors

Definition at line 84 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef TVector itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorType

Typedef alias for the measurement vectors

Definition at line 81 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef Superclass::Pointer itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MembershipFunctionPointer

SmartPointer class for superclass

Definition at line 74 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef SmartPointer< Self > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Pointer

Definition at line 69 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef MahalanobisDistanceMembershipFunction itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Self

Standard class typedefs

Definition at line 67 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef MembershipFunctionBase< TVector > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Superclass

Definition at line 68 of file itkMahalanobisDistanceMembershipFunction.h.

Constructor & Destructor Documentation

template<class TVector >

itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MahalanobisDistanceMembershipFunction ( void )

protected

template<class TVector >

virtual itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::~MahalanobisDistanceMembershipFunction ( void )

inlineprotectedvirtual

Definition at line 125 of file itkMahalanobisDistanceMembershipFunction.h.

Member Function Documentation

template<class TVector >

virtual::itk::LightObject::Pointer itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::CreateAnother ( void ) const

virtual

Strandard macros

Reimplemented from itk::Object.

template<class TVector >

double itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Evaluate ( const MeasurementVectorType & measurement ) const

virtual

Evaluate the Mahalanobis distance of a measurement using the prescribed mean and covariance. Note that the Mahalanobis distance is not a probability density. The square of the distance is returned.

Implements itk::Statistics::MembershipFunctionBase< TVector >.

template<class TVector >

virtual const CovarianceMatrixType& itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::GetCovariance ( )

virtual

Get the covariance matrix. Covariance matrix is a VariableSizeMatrix of doubles.

template<class TVector >

virtual const MeanVectorType& itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::GetMean ( )

virtual

Get the mean of the Mahalanobis distance. Mean is a vector type similar to the measurement type but with a real element type.

template<class TVector >

virtual const char* itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::GetNameOfClass ( ) const

virtual

Strandard macros

Reimplemented from itk::Statistics::MembershipFunctionBase< TVector >.

template<class TVector >

virtual LightObject::Pointer itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::InternalClone ( ) const

virtual

Method to clone a membership function, i.e. create a new instance of the same type of membership function and configure its ivars to match.

Reimplemented from itk::LightObject.

template<class TVector >

static Pointer itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::New ( )

static

Strandard macros

template<class TVector >

void itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

protectedvirtual

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::Object.

template<class TVector >

void itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::SetCovariance ( const CovarianceMatrixType & cov )

Set the covariance matrix. Covariance matrix is a VariableSizeMatrix of doubles. The inverse of the covariance matrix is calculated whenever the covaraince matrix is changed.

template<class TVector >

void itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::SetMean ( const MeanVectorType & mean )

Set the mean used in the Mahalanobis distance. Mean is a vector type similar to the measurement type but with a real element type.