ITK  4.4.0 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<class 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

typedef SmartPointer< const SelfConstPointer

typedef VariableSizeMatrix
< double >
CovarianceMatrixType

typedef MeasurementVectorRealType MeanVectorType

typedef itk::NumericTraits
< MeasurementVectorType >
::RealType
MeasurementVectorRealType

typedef
Superclass::MeasurementVectorSizeType
MeasurementVectorSizeType

typedef TVector MeasurementVectorType

typedef Superclass::Pointer MembershipFunctionPointer

typedef SmartPointer< SelfPointer

typedef
MahalanobisDistanceMembershipFunction
Self

typedef MembershipFunctionBase
< TVector >
Superclass

Public Types inherited from itk::Statistics::MembershipFunctionBase< TVector >
typedef SmartPointer< const SelfConstPointer

typedef unsigned int MeasurementVectorSizeType

typedef TVector MeasurementVectorType

typedef SmartPointer< SelfPointer

typedef MembershipFunctionBase Self

typedef FunctionBase< TVector,
double >
Superclass

Public Types inherited from itk::FunctionBase< TVector, double >
typedef SmartPointer< const SelfConstPointer

typedef TVector InputType

typedef double OutputType

typedef SmartPointer< SelfPointer

typedef FunctionBase Self

typedef Object Superclass

Public Types inherited from itk::Object
typedef SmartPointer< const SelfConstPointer

typedef SmartPointer< SelfPointer

typedef Object Self

typedef LightObject Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const SelfConstPointer

typedef SmartPointer< SelfPointer

typedef LightObject Self

## Public Member Functions

double Evaluate (const MeasurementVectorType &measurement) const

virtual const
CovarianceMatrixType
GetCovariance ()

virtual const MeanVectorTypeGetMean ()

virtual LightObject::Pointer InternalClone () const

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)

## Protected Member Functions

MahalanobisDistanceMembershipFunction (void)

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

virtual ~MahalanobisDistanceMembershipFunction (void)

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

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

virtual ~MembershipFunctionBase (void)

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

~FunctionBase ()

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

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

virtual void SetTimeStamp (const TimeStamp &time)

virtual ~Object ()

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 (void) const

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 flag)

Protected Types inherited from itk::LightObject
typedef int InternalReferenceCountType

Protected Attributes inherited from itk::LightObject
InternalReferenceCountType m_ReferenceCount

SimpleFastMutexLock m_ReferenceCountLock

## Member Typedef Documentation

template<class TVector >
 typedef SmartPointer< const Self > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::ConstPointer

Definition at line 70 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >
 typedef VariableSizeMatrix< double > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::CovarianceMatrixType

Type of the covariance matrix

Definition at line 92 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

Definition at line 89 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >
 typedef itk::NumericTraits< MeasurementVectorType >::RealType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::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.

template<class TVector >
 typedef Superclass::MeasurementVectorSizeType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorSizeType

Typedef to represent the length of measurement vectors

Definition at line 84 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >
 typedef TVector itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeasurementVectorType

Typedef alias for the measurement vectors

Definition at line 81 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

SmartPointer class for superclass

Definition at line 74 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >
 typedef SmartPointer< Self > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Pointer

Definition at line 69 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

Standard class typedefs

Definition at line 67 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >
 typedef MembershipFunctionBase< TVector > itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Superclass

Definition at line 68 of file itkMahalanobisDistanceMembershipFunction.h.

## Constructor & Destructor Documentation

template<class TVector >
 itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MahalanobisDistanceMembershipFunction ( void )
protected
template<class TVector >
 virtual itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::~MahalanobisDistanceMembershipFunction ( void )
inlineprotectedvirtual

Definition at line 125 of file itkMahalanobisDistanceMembershipFunction.h.

## Member Function Documentation

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

Strandard macros

Reimplemented from itk::Object.

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

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

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

template<class TVector >
 virtual const MeanVectorType& itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::GetMean ( )
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<class TVector >
 virtual const char* itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::GetNameOfClass ( ) const
virtual

Strandard macros

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

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

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

Strandard macros

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

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<class 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<class 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<class TVector >
 CovarianceMatrixType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::m_Covariance
private

Definition at line 130 of file itkMahalanobisDistanceMembershipFunction.h.

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

Definition at line 134 of file itkMahalanobisDistanceMembershipFunction.h.

template<class 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: