MahalanobisDistanceMembershipFunction models class membership using Mahalanobis distance. More...

#include <itkMahalanobisDistanceMembershipFunction.h>

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

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

Public Types
typedef SmartPointer< const Self >	ConstPointer
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< Self >	Pointer
typedef MahalanobisDistanceMembershipFunction	Self
typedef MembershipFunctionBase < TVector >	Superclass
Public Member Functions
MembershipFunctionPointer	Clone () const
double	Evaluate (const MeasurementVectorType &measurement) const
virtual const CovarianceMatrixType &	GetCovariance ()
virtual const MeanVectorType &	GetMean ()
void	SetCovariance (const CovarianceMatrixType &cov)
void	SetMean (const MeanVectorType &mean)
Protected Member Functions
	MahalanobisDistanceMembershipFunction (void)
void	PrintSelf (std::ostream &os, Indent indent) const
virtual	~MahalanobisDistanceMembershipFunction (void)
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 ()

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 guarenteed 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.

Member Typedef Documentation

template<class TVector >

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

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

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 >

typedef MeasurementVectorRealType itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MeanVectorType

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

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

Definition at line 84 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

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

Typedef alias for the measurement vectors

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

Definition at line 81 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef Superclass::Pointer itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::MembershipFunctionPointer

SmartPointer class for superclass

Definition at line 74 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

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

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

Definition at line 69 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

typedef MahalanobisDistanceMembershipFunction itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Self

Standard class typedefs

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

Definition at line 67 of file itkMahalanobisDistanceMembershipFunction.h.

template<class TVector >

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

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

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 ) [inline, protected, virtual]

Definition at line 125 of file itkMahalanobisDistanceMembershipFunction.h.

Member Function Documentation

template<class TVector >

MembershipFunctionPointer itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::Clone ( ) 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.

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

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.

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

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 >

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

Strandard macros

Reimplemented from itk::Object.

template<class TVector >

void itk::Statistics::MahalanobisDistanceMembershipFunction< TVector >::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const `[protected, virtual]`

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::Statistics::MembershipFunctionBase< TVector >.

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.