ITK  5.4.0
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itk::Statistics::GaussianMembershipFunction< TMeasurementVector > Class Template Reference

#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 CovarianceMatrixTypeGetCovariance () const
 
virtual const CovarianceMatrixTypeGetInverseCovariance () const
 
virtual const MeanVectorTypeGetMean () 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
 
 itkOverrideGetNameOfClassMacro (MembershipFunctionBase)
 
virtual void SetMeasurementVectorSize (MeasurementVectorSizeType s)
 
- Public Member Functions inherited from itk::FunctionBase< TMeasurementVector, double >
 itkOverrideGetNameOfClassMacro (FunctionBase)
 
- 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
 
CommandGetCommand (unsigned long tag)
 
bool GetDebug () const
 
MetaDataDictionaryGetMetaDataDictionary ()
 
const MetaDataDictionaryGetMetaDataDictionary () const
 
virtual ModifiedTimeType GetMTime () const
 
virtual const TimeStampGetTimeStamp () const
 
bool HasObserver (const EventObject &event) const
 
void InvokeEvent (const EventObject &)
 
void InvokeEvent (const EventObject &) const
 
 itkOverrideGetNameOfClassMacro (Object)
 
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
 
 itkVirtualGetNameOfClassMacro (LightObject)
 
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 {}
 
 itkOverrideGetNameOfClassMacro (GaussianMembershipFunction)
 
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 TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::ConstPointer = SmartPointer<const Self>

Definition at line 65 of file itkGaussianMembershipFunction.h.

◆ CovarianceMatrixType

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::CovarianceMatrixType = VariableSizeMatrix<double>

Type of the covariance matrix

Definition at line 87 of file itkGaussianMembershipFunction.h.

◆ MeanVectorType

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::MeanVectorType = MeasurementVectorRealType

Definition at line 84 of file itkGaussianMembershipFunction.h.

◆ MeasurementVectorRealType

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::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 83 of file itkGaussianMembershipFunction.h.

◆ MeasurementVectorType

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::MeasurementVectorType = TMeasurementVector

Typedef alias for the measurement vectors

Definition at line 76 of file itkGaussianMembershipFunction.h.

◆ MembershipFunctionPointer

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::MembershipFunctionPointer = typename Superclass::Pointer

SmartPointer class for superclass

Definition at line 73 of file itkGaussianMembershipFunction.h.

◆ Pointer

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::Pointer = SmartPointer<Self>

Definition at line 64 of file itkGaussianMembershipFunction.h.

◆ Self

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::Self = GaussianMembershipFunction

Standard class type aliases

Definition at line 62 of file itkGaussianMembershipFunction.h.

◆ Superclass

template<typename TMeasurementVector >
using itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::Superclass = MembershipFunctionBase<TMeasurementVector>

Definition at line 63 of file itkGaussianMembershipFunction.h.

Constructor & Destructor Documentation

◆ GaussianMembershipFunction()

template<typename TMeasurementVector >
itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::GaussianMembershipFunction ( )
protected

◆ ~GaussianMembershipFunction()

template<typename TMeasurementVector >
itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::~GaussianMembershipFunction ( )
overrideprotecteddefault

Member Function Documentation

◆ Evaluate()

template<typename TMeasurementVector >
double itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::Evaluate ( const MeasurementVectorType measurement) const
overridevirtual

Evaluate the probability density of a measurement vector.

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

◆ GetCovariance()

template<typename TMeasurementVector >
virtual const CovarianceMatrixType& itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::GetCovariance ( ) const
virtual

◆ GetInverseCovariance()

template<typename TMeasurementVector >
virtual const CovarianceMatrixType& itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::GetInverseCovariance ( ) const
virtual

◆ GetMean()

template<typename TMeasurementVector >
virtual const MeanVectorType& itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::GetMean ( ) const
virtual

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

◆ InternalClone()

template<typename TMeasurementVector >
LightObject::Pointer itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::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.

◆ itkOverrideGetNameOfClassMacro()

template<typename TMeasurementVector >
itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::itkOverrideGetNameOfClassMacro ( GaussianMembershipFunction< TMeasurementVector >  )

Standard macros

◆ New()

template<typename TMeasurementVector >
static Pointer itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::New ( )
static

Standard macros

◆ PrintSelf()

template<typename TMeasurementVector >
void itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::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 TMeasurementVector >
void itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::SetCovariance ( const CovarianceMatrixType cov)

Set the covariance matrix. Covariance matrix is a VariableSizeMatrix of doubles. The inverse of the covariance matrix and the normalization term for the multivariate Gaussian are calculated whenever the covariance matrix is changed.

◆ SetMean()

template<typename TMeasurementVector >
void itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::SetMean ( const MeanVectorType mean)

Set the mean of the Gaussian distribution. Mean is a vector type similar to the measurement type but with a real element type.

Member Data Documentation

◆ m_Covariance

template<typename TMeasurementVector >
CovarianceMatrixType itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::m_Covariance {}
private

Definition at line 131 of file itkGaussianMembershipFunction.h.

◆ m_CovarianceNonsingular

template<typename TMeasurementVector >
bool itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::m_CovarianceNonsingular {}
private

Boolean to cache whether the covariance is singular or nearly singular

Definition at line 142 of file itkGaussianMembershipFunction.h.

◆ m_InverseCovariance

template<typename TMeasurementVector >
CovarianceMatrixType itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::m_InverseCovariance {}
private

Definition at line 135 of file itkGaussianMembershipFunction.h.

◆ m_Mean

template<typename TMeasurementVector >
MeanVectorType itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::m_Mean {}
private

Definition at line 130 of file itkGaussianMembershipFunction.h.

◆ m_PreFactor

template<typename TMeasurementVector >
double itk::Statistics::GaussianMembershipFunction< TMeasurementVector >::m_PreFactor {}
private

Definition at line 139 of file itkGaussianMembershipFunction.h.


The documentation for this class was generated from the following file: