ITK  5.4.0
Insight Toolkit
Public Types | Public Member Functions | Protected Member Functions | Private Attributes | List of all members
itk::Statistics::MahalanobisDistanceMembershipFunction< TVector > Class Template Reference

#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 CovarianceMatrixTypeGetCovariance () 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
 
 itkOverrideGetNameOfClassMacro (MembershipFunctionBase)
 
virtual void SetMeasurementVectorSize (MeasurementVectorSizeType s)
 
- Public Member Functions inherited from itk::FunctionBase< TVector, 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

 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 &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 {}
 
 itkOverrideGetNameOfClassMacro (MahalanobisDistanceMembershipFunction)
 
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

Type of the covariance matrix

Definition at line 92 of file itkMahalanobisDistanceMembershipFunction.h.

◆ MeanVectorType

Definition at line 89 of file itkMahalanobisDistanceMembershipFunction.h.

◆ 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.

◆ 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

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

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()

◆ ~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.

◆ 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.

◆ itkOverrideGetNameOfClassMacro()

template<typename TVector >
itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::itkOverrideGetNameOfClassMacro ( MahalanobisDistanceMembershipFunction< TVector >  )

Standard macros

◆ New()

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

Standard macros

◆ 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.

◆ SetMean()

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

◆ m_Covariance

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

Definition at line 135 of file itkMahalanobisDistanceMembershipFunction.h.

◆ m_CovarianceNonsingular

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

Boolean to cache whether the covariance is singular or nearly singular

Definition at line 142 of file itkMahalanobisDistanceMembershipFunction.h.

◆ m_InverseCovariance

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

Definition at line 139 of file itkMahalanobisDistanceMembershipFunction.h.

◆ m_Mean

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

Definition at line 134 of file itkMahalanobisDistanceMembershipFunction.h.


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