#include <itkMahalanobisDistanceMembershipFunction.h>

Detailed Description

template<typename 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 63 of file itkMahalanobisDistanceMembershipFunction.h.

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

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

Public Types
using	ConstPointer = SmartPointer< const Self >

using	CovarianceMatrixType = VariableSizeMatrix< double >

using	MeanVectorType = MeasurementVectorRealType

using	MeasurementVectorRealType = typename itk::NumericTraits< MeasurementVectorType >::RealType

using	MeasurementVectorType = TVector

using	MembershipFunctionPointer = typename Superclass::Pointer

using	Pointer = SmartPointer< Self >

using	Self = MahalanobisDistanceMembershipFunction

using	Superclass = MembershipFunctionBase< TVector >

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

using	MeasurementVectorSizeType = unsigned int

using	MeasurementVectorType = TVector

using	Pointer = SmartPointer< Self >

using	Self = MembershipFunctionBase

using	Superclass = FunctionBase< TVector, double >

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

using	InputType = TVector

using	OutputType = double

using	Pointer = SmartPointer< Self >

using	Self = FunctionBase

using	Superclass = Object

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

using	Pointer = SmartPointer< Self >

using	Self = Object

using	Superclass = LightObject

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

using	Pointer = SmartPointer< Self >

using	Self = LightObject

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

virtual const CovarianceMatrixType &	GetCovariance () const

virtual const MeanVectorType &	GetMean () const

LightObject::Pointer	InternalClone () const override

void	SetCovariance (const CovarianceMatrixType &cov)

void	SetMean (const MeanVectorType &mean)

Public Member Functions inherited from itk::Statistics::MembershipFunctionBase< TVector >
double	Evaluate (const MeasurementVectorType &x) const override=0

virtual MeasurementVectorSizeType	GetMeasurementVectorSize () const

const char *	GetNameOfClass () const override

virtual void	SetMeasurementVectorSize (MeasurementVectorSizeType s)

Public Member Functions inherited from itk::FunctionBase< TVector, double >
virtual OutputType	Evaluate (const InputType &input) const=0

const char *	GetNameOfClass () const override

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *cmd) const

unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const

LightObject::Pointer	CreateAnother () const override

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

const char *	GetNameOfClass () const override

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag) const

void	SetDebug (bool debugFlag) const

void	SetReferenceCount (int) override

void	UnRegister () const noexcept override

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

void	SetMetaDataDictionary (MetaDataDictionary &&rrhs)

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
Pointer	Clone () const

virtual Pointer	CreateAnother () const

virtual void	Delete ()

virtual const char *	GetNameOfClass () const

virtual int	GetReferenceCount () const

void	Print (std::ostream &os, Indent indent=0) const

virtual void	Register () const

virtual void	SetReferenceCount (int)

virtual void	UnRegister () const noexcept

Protected Member Functions
	MahalanobisDistanceMembershipFunction ()

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

	~MahalanobisDistanceMembershipFunction () override=default

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

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

	~MembershipFunctionBase () override=default

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

	~FunctionBase () override=default

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

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

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

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

	~Object () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

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

virtual void	PrintSelf (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 {}

const char *	GetNameOfClass () const override

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 val)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Protected Attributes inherited from itk::LightObject
std::atomic< int >	m_ReferenceCount {}

Member Typedef Documentation

◆ ConstPointer

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::ConstPointer = SmartPointer<const Self>

Definition at line 70 of file itkMahalanobisDistanceMembershipFunction.h.

◆ CovarianceMatrixType

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::CovarianceMatrixType = VariableSizeMatrix<double>

Type of the covariance matrix

Definition at line 92 of file itkMahalanobisDistanceMembershipFunction.h.

◆ MeanVectorType

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeanVectorType = MeasurementVectorRealType

Definition at line 89 of file itkMahalanobisDistanceMembershipFunction.h.

◆ MeasurementVectorRealType

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorRealType = typename itk::NumericTraits<MeasurementVectorType>::RealType

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.

◆ MeasurementVectorType

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorType = TVector

Typedef alias for the measurement vectors

Definition at line 81 of file itkMahalanobisDistanceMembershipFunction.h.

◆ MembershipFunctionPointer

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MembershipFunctionPointer = typename Superclass::Pointer

SmartPointer class for superclass

Definition at line 78 of file itkMahalanobisDistanceMembershipFunction.h.

◆ Pointer

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Pointer = SmartPointer<Self>

Definition at line 69 of file itkMahalanobisDistanceMembershipFunction.h.

◆ Self

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Self = MahalanobisDistanceMembershipFunction

Standard class type aliases

Definition at line 67 of file itkMahalanobisDistanceMembershipFunction.h.

◆ Superclass

template<typename TVector >

using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Superclass = MembershipFunctionBase<TVector>

Definition at line 68 of file itkMahalanobisDistanceMembershipFunction.h.

Constructor & Destructor Documentation

◆ MahalanobisDistanceMembershipFunction()

template<typename TVector >

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

protected

◆ ~MahalanobisDistanceMembershipFunction()

template<typename TVector >

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

overrideprotecteddefault

Member Function Documentation

◆ Evaluate()

template<typename TVector >

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

overridevirtual

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 >.

◆ GetCovariance()

template<typename TVector >

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

virtual

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

◆ GetMean()

template<typename TVector >

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

virtual

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

◆ GetNameOfClass()

template<typename TVector >

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

overridevirtual

See also: LightObject::GetNameOfClass()

Reimplemented from itk::Object.

◆ InternalClone()

template<typename TVector >

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

overridevirtual

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.

◆ New()

template<typename TVector >

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

static

See also: LightObject::GetNameOfClass()

◆ PrintSelf()

template<typename TVector >

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

overrideprotectedvirtual

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.

◆ SetCovariance()

template<typename 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 covariance matrix is changed.