ITK  5.0.0 Insight Segmentation and Registration Toolkit
itk::Statistics::MahalanobisDistanceMembershipFunction< TVector > Class Template Reference

`#include <itkMahalanobisDistanceMembershipFunction.h>`

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

## 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 62 of file itkMahalanobisDistanceMembershipFunction.h.

## Public Types

using ConstPointer = SmartPointer< const Self >

using CovarianceMatrixType = VariableSizeMatrix< double >

using MeanVectorType = MeasurementVectorRealType

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

using MeasurementVectorSizeType = typename Superclass::MeasurementVectorSizeType

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 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< TVector >
virtual MeasurementVectorSizeType GetMeasurementVectorSize () const

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

virtual void DebugOff () const

virtual void DebugOn () const

CommandGetCommand (unsigned long tag)

bool GetDebug () const

virtual ModifiedTimeType GetMTime () const

virtual const TimeStampGetTimeStamp () 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 noexceptoverride

virtual void SetObjectName (std::string _arg)

virtual const std::string & GetObjectName () const

Public Member Functions inherited from itk::LightObject
virtual void Delete ()

virtual int GetReferenceCount () const

itkCloneMacro (Self)

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

## 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

virtual void SetTimeStamp (const TimeStamp &time)

~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

virtual const char * GetNameOfClass () const

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

static Pointer New ()

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)

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

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

Definition at line 70 of file itkMahalanobisDistanceMembershipFunction.h.

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

Type of the covariance matrix

Definition at line 92 of file itkMahalanobisDistanceMembershipFunction.h.

template<typename TVector >

Definition at line 89 of file itkMahalanobisDistanceMembershipFunction.h.

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.

template<typename TVector >
 using itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorSizeType = typename Superclass::MeasurementVectorSizeType

Typedef to represent the length of measurement vectors

Definition at line 84 of file itkMahalanobisDistanceMembershipFunction.h.

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

Typedef alias for the measurement vectors

Definition at line 81 of file itkMahalanobisDistanceMembershipFunction.h.

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

SmartPointer class for superclass

Definition at line 78 of file itkMahalanobisDistanceMembershipFunction.h.

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

Definition at line 69 of file itkMahalanobisDistanceMembershipFunction.h.

template<typename TVector >

Standard class type aliases

Definition at line 67 of file itkMahalanobisDistanceMembershipFunction.h.

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

Definition at line 68 of file itkMahalanobisDistanceMembershipFunction.h.

## Constructor & Destructor Documentation

template<typename TVector >
 itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MahalanobisDistanceMembershipFunction ( )
protected
template<typename TVector >
 itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::~MahalanobisDistanceMembershipFunction ( )
overrideprotecteddefault

## Member Function Documentation

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

Strandard macros

Reimplemented from itk::Object.

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.

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

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

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.

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

Strandard macros

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

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.

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

Strandard macros

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.

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 covaraince matrix is changed.

template<typename 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.

## Member Data Documentation

template<typename TVector >
 CovarianceMatrixType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::m_Covariance
private

Definition at line 130 of file itkMahalanobisDistanceMembershipFunction.h.

template<typename TVector >
 bool itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::m_CovarianceNonsingular
private

Boolean to cache whether the covarinace is singular or nearly singular

Definition at line 137 of file itkMahalanobisDistanceMembershipFunction.h.

template<typename TVector >
 CovarianceMatrixType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::m_InverseCovariance
private

Definition at line 134 of file itkMahalanobisDistanceMembershipFunction.h.

template<typename TVector >
 MeanVectorType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::m_Mean
private

Definition at line 129 of file itkMahalanobisDistanceMembershipFunction.h.

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