#include <itkGaussianMembershipFunction.h>

Detailed Description

template<typename TMeasurementVector>
class itk::Statistics::GaussianMembershipFunction< TMeasurementVector >

GaussianMembershipFunction models class membership through a multivariate Gaussian function.

GaussianMembershipFunction is a subclass of MembershipFunctionBase that models class membership (or likelihood) using a multivariate Gaussian function. The mean and covariance structure of the Gaussian 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>.

If the covariance is singular or nearly singular, the membership function behaves somewhat like 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 small but differentiable values everywhere and increase sharply near the mean.

Examples: Examples/Statistics/BayesianPluginClassifier.cxx, and Examples/Statistics/GaussianMembershipFunction.cxx.

Definition at line 56 of file itkGaussianMembershipFunction.h.

Inheritance diagram for itk::Statistics::GaussianMembershipFunction< TMeasurementVector >:

Collaboration diagram for itk::Statistics::GaussianMembershipFunction< TMeasurementVector >:

Public Types
using	ConstPointer = SmartPointer< const Self >

using	CovarianceMatrixType = VariableSizeMatrix< double >

using	MeanVectorType = MeasurementVectorRealType

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

using	MeasurementVectorType = TMeasurementVector

using	MembershipFunctionPointer = typename Superclass::Pointer

using	Pointer = SmartPointer< Self >

using	Self = GaussianMembershipFunction

using	Superclass = MembershipFunctionBase< TMeasurementVector >

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

using	MeasurementVectorSizeType = unsigned int

using	MeasurementVectorType = TMeasurementVector

using	Pointer = SmartPointer< Self >

using	Self = MembershipFunctionBase

using	Superclass = FunctionBase< TMeasurementVector, double >

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

using	InputType = TMeasurementVector

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 CovarianceMatrixType &	GetInverseCovariance () 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< TMeasurementVector >
virtual MeasurementVectorSizeType	GetMeasurementVectorSize () const

const char *	GetNameOfClass () const override

virtual void	SetMeasurementVectorSize (MeasurementVectorSizeType s)

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

unsigned long	AddObserver (const EventObject &event, Command *) 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

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)

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 void	Delete ()

virtual int	GetReferenceCount () const

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

Protected Member Functions
	GaussianMembershipFunction ()

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

	~GaussianMembershipFunction () override=default

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

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

	~MembershipFunctionBase () override=default

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

	~FunctionBase () override=default

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

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

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

	~Object () override

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 {}

double	m_PreFactor {}

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 {}