ITK: itk::Statistics::GaussianDistribution Class Reference

typedef SmartPointer<const Self> itk::Statistics::GaussianDistribution::ConstPointer

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 61 of file itkGaussianDistribution.h.

typedef Array< double > itk::Statistics::ProbabilityDistribution::ParametersType [inherited]

Type of the parameter vector.

Definition at line 78 of file itkProbabilityDistribution.h.

typedef SmartPointer<Self> itk::Statistics::GaussianDistribution::Pointer

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 60 of file itkGaussianDistribution.h.

typedef GaussianDistribution itk::Statistics::GaussianDistribution::Self

Standard class typedefs

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 58 of file itkGaussianDistribution.h.

typedef ProbabilityDistribution itk::Statistics::GaussianDistribution::Superclass

Reimplemented from itk::Statistics::ProbabilityDistribution.

Definition at line 59 of file itkGaussianDistribution.h.

itk::Statistics::GaussianDistribution::GaussianDistribution ( void ) [protected]

virtual itk::Statistics::GaussianDistribution::~GaussianDistribution ( void ) [inline, protected, virtual]

Definition at line 228 of file itkGaussianDistribution.h.

unsigned long itk::Object::AddObserver	(	const EventObject &	event,
		Command *
	)			const `[inherited]`

unsigned long itk::Object::AddObserver	(	const EventObject &	event,
		Command *
	)			`[inherited]`

Allow people to add/remove/invoke observers (callbacks) to any ITK object. This is an implementation of the subject/observer design pattern. An observer is added by specifying an event to respond to and an itk::Command to execute. It returns an unsigned long tag which can be used later to remove the event or retrieve the command. The memory for the Command becomes the responsibility of this object, so don't pass the same instance of a command to two different objects

static void itk::LightObject::BreakOnError ( ) [static, inherited]

This method is called when itkExceptionMacro executes. It allows the debugger to break on error.

static double itk::Statistics::GaussianDistribution::CDF	(	double	x,
		double	mean,
		double	variance
	)			`[static]`

Static method to evaluate the cumulative distribution function (cdf) of a Gaussian. The parameters of the distribution are passed as separate values. The static method provides optimized access without requiring an instance of the class.

static double itk::Statistics::GaussianDistribution::CDF	(	double	x,
		const ParametersType &
	)			`[static]`

Static method to evaluate the cumulative distribution function (cdf) of a Gaussian. The parameters of the distribution are passed as a parameter vector. The ordering of the parameters is (mean, variance). The static method provides optimized access without requiring an instance of the class.

static double itk::Statistics::GaussianDistribution::CDF ( double x ) [static]

Static method to evaluate the cumulative distribution function (cdf) of a standardized (mean zero, unit variance) Gaussian. The static method provides optimized access without requiring an instance of the class. Accuracy is approximately 10^-8.

virtual LightObject::Pointer itk::Object::CreateAnother ( ) const [virtual, inherited]

Create an object from an instance, potentially deferring to a factory. This method allows you to create an instance of an object that is exactly the same type as the referring object. This is useful in cases where an object has been cast back to a base class.

Reimplemented from itk::LightObject.

virtual void itk::Object::DebugOff ( ) const [virtual, inherited]

Turn debugging output off.

virtual void itk::Object::DebugOn ( ) const [virtual, inherited]

Turn debugging output on.

virtual void itk::LightObject::Delete ( ) [virtual, inherited]

Delete an itk object. This method should always be used to delete an object when the new operator was used to create it. Using the C delete method will not work with reference counting.

virtual double itk::Statistics::GaussianDistribution::EvaluateCDF	(	double	x,
		double	mean,
		double	variance
	)			const `[virtual]`

Evaluate the cumulative distribution function (cdf). The parameters of the distribution are passed as separate parameters.

virtual double itk::Statistics::GaussianDistribution::EvaluateCDF	(	double	x,
		const ParametersType &
	)			const `[virtual]`

Evaluate the cumulative distribution function (cdf). The parameters for the distribution are passed as a parameters vector. The ordering of the parameters is (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluateCDF ( double x ) const [virtual]

Evaluate the cumulative distribution function (cdf). The parameters of the distribution are assigned via SetParameters().

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluateInverseCDF	(	double	p,
		double	mean,
		double	variance
	)			const `[virtual]`

Evaluate the inverse cumulative distribution function (inverse cdf). Parameter p must be between 0.0 and 1.0. The parameters of the distribution are passed as separate parameters.

virtual double itk::Statistics::GaussianDistribution::EvaluateInverseCDF	(	double	p,
		const ParametersType &
	)			const `[virtual]`

Evaluate the inverse cumulative distribution function (inverse cdf). Parameter p must be between 0.0 and 1.0. The parameters for the distribution are passed as a parameters vector. The ordering of the parameters is (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluateInverseCDF ( double p ) const [virtual]

Evaluate the inverse cumulative distribution function (inverse cdf). Parameter p must be between 0.0 and 1.0. The parameters of the distribution are assigned via SetParameters().

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluatePDF	(	double	x,
		double	mean,
		double	variance
	)			const `[virtual]`

Evaluate the probability density function (pdf). The parameters of the distribution are passed as separate parameters.

virtual double itk::Statistics::GaussianDistribution::EvaluatePDF	(	double	x,
		const ParametersType &
	)			const `[virtual]`

Evaluate the probability density function (pdf). The parameters for the distribution are passed as a parameters vector. The ordering of the parameters is (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

virtual double itk::Statistics::GaussianDistribution::EvaluatePDF ( double x ) const [virtual]

Evaluate the probability density function (pdf). The parameters of the distribution are assigned via SetParameters().

Implements itk::Statistics::ProbabilityDistribution.

Command* itk::Object::GetCommand ( unsigned long tag ) [inherited]

Get the command associated with the given tag. NOTE: This returns a pointer to a Command, but it is safe to asign this to a Command::Pointer. Since Command inherits from LightObject, at this point in the code, only a pointer or a reference to the Command can be used.

bool itk::Object::GetDebug ( ) const [inherited]

Get the value of the debug flag.

static bool itk::Object::GetGlobalWarningDisplay ( ) [static, inherited]

virtual double itk::Statistics::GaussianDistribution::GetMean ( ) const [virtual]

Get the mean of the Gaussian distribution. Defaults to 0.0. The mean is stored in position 0 of the parameters vector.

Implements itk::Statistics::ProbabilityDistribution.

const MetaDataDictionary& itk::Object::GetMetaDataDictionary ( void ) const [inherited]

Returns:: A constant reference to this objects MetaDataDictionary.

MetaDataDictionary& itk::Object::GetMetaDataDictionary ( void ) [inherited]

Returns:: A reference to this objects MetaDataDictionary.

Warning:: This reference may be changed.

virtual unsigned long itk::Object::GetMTime ( ) const [virtual, inherited]

Return this objects modified time.

Referenced by itk::SpatialObject< ::itk::GetMeshDimension< TMesh >::PointDimension >::GetObjectMTime().

virtual const char* itk::Statistics::GaussianDistribution::GetNameOfClass ( ) const [virtual]

Strandard macros

Reimplemented from itk::Statistics::ProbabilityDistribution.

virtual unsigned long itk::Statistics::GaussianDistribution::GetNumberOfParameters ( void ) const [inline, virtual]

Return the number of parameters. For a univariate Gaussian, this is 2 (mean, variance).

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 71 of file itkGaussianDistribution.h.

virtual const ParametersType& itk::Statistics::ProbabilityDistribution::GetParameters ( ) [virtual, inherited]

Get the parameters of the distribution. See concrete subclasses for the order of parameters. Subclasses may provide convenience methods for setting parameters, i.e. SetDegreesOfFreedom(), etc.

virtual int itk::LightObject::GetReferenceCount ( ) const [inline, virtual, inherited]

Gets the reference count on this object.

Definition at line 98 of file itkLightObject.h.

virtual double itk::Statistics::GaussianDistribution::GetVariance ( ) const [virtual]

Get the variance of the Gaussian distribution. Defaults to 1.0. The variance is stored in position 1 of the parameters vector.

Implements itk::Statistics::ProbabilityDistribution.

static void itk::Object::GlobalWarningDisplayOff ( ) [inline, static, inherited]

Definition at line 100 of file itkObject.h.

References itk::Object::SetGlobalWarningDisplay().

static void itk::Object::GlobalWarningDisplayOn ( ) [inline, static, inherited]

Definition at line 98 of file itkObject.h.

References itk::Object::SetGlobalWarningDisplay().

virtual bool itk::Statistics::GaussianDistribution::HasMean ( ) const [inline, virtual]

Does this distribution have a mean?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 126 of file itkGaussianDistribution.h.

bool itk::Object::HasObserver ( const EventObject & event ) const [inherited]

Return true if an observer is registered for this event.

virtual bool itk::Statistics::GaussianDistribution::HasVariance ( ) const [inline, virtual]

Does this distribution have a variance?

Implements itk::Statistics::ProbabilityDistribution.

Definition at line 138 of file itkGaussianDistribution.h.

static double itk::Statistics::GaussianDistribution::InverseCDF	(	double	p,
		double	mean,
		double	variance
	)			`[static]`

Static method to evaluate the inverse cumulative distribution function of a Gaussian. The parameters of the distribution are passed as separate values. The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0

static double itk::Statistics::GaussianDistribution::InverseCDF	(	double	p,
		const ParametersType &
	)			`[static]`

Static method to evaluate the inverse cumulative distribution function of a Gaussian. The parameters of the distribution are passed as a parameter vector. The ordering of the parameters is (mean, variance). The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0

static double itk::Statistics::GaussianDistribution::InverseCDF ( double p ) [static]

Static method to evaluate the inverse cumulative distribution function of a standardized (mean zero, unit variance) Gaussian. The static method provides optimized access without requiring an instance of the class. Parameter p must be between 0.0 and 1.0.

THis implementation was provided by Robert W. Cox from the Biophysics Research Institute at the Medical College of Wisconsin. This function is based off of a rational polynomial approximation to the inverse Gaussian CDF which can be found in M. Abramowitz and I.A. Stegun. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. John Wiley & Sons. New York. Equation 26.2.23. pg. 933. 1972.

Since the initial approximation only provides an estimate within 4.5 E-4 of the true value, 3 Newton-Raphson interations are used to refine the approximation. Accuracy is approximately 10^-8.

Let, Q(x) = (1/sqrt(2*pi)) Int_{x}^{infinity} e^{-t^2/2} dt = 0.5 * erfc(x/sqrt(2))

Given p, this function computes x such that Q(x) = p, for 0 < p < 1

Note that the Gaussian CDF is defined as P(x) = (1/sqrt(2*pi)) Int_{-infinity}{x} e^{-t^2/2} dt = 1 - Q(x)

This function has been modified to compute the inverse of P(x) instead of Q(x).

void itk::Object::InvokeEvent ( const EventObject & ) const [inherited]

Call Execute on all the Commands observing this event id. The actions triggered by this call doesn't modify this object.

void itk::Object::InvokeEvent ( const EventObject & ) [inherited]

Call Execute on all the Commands observing this event id.

virtual void itk::Object::Modified ( ) const [virtual, inherited]

Update the modification time for this object. Many filters rely on the modification time to determine if they need to recompute their data.

Referenced by itk::NarrowBandImageFilterBase< TInputImage, itk::Image< TOutputPixelType,::itk::GetImageDimension< TInputImage >::ImageDimension > >::InsertNarrowBandNode(), itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetCenter(), itk::HistogramAlgorithmBase< TInputHistogram >::SetInputHistogram(), itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetMatrix(), itk::NarrowBandImageFilterBase< TInputImage, itk::Image< TOutputPixelType,::itk::GetImageDimension< TInputImage >::ImageDimension > >::SetNarrowBand(), itk::NarrowBandImageFilterBase< TInputImage, itk::Image< TOutputPixelType,::itk::GetImageDimension< TInputImage >::ImageDimension > >::SetNarrowBandInnerRadius(), itk::NarrowBandImageFilterBase< TInputImage, itk::Image< TOutputPixelType,::itk::GetImageDimension< TInputImage >::ImageDimension > >::SetNarrowBandTotalRadius(), itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetOffset(), itk::ThresholdLabelerImageFilter< TInputImage, TOutputImage >::SetRealThresholds(), itk::CollidingFrontsImageFilter< TInputImage, TOutputImage >::SetSeedPoints1(), itk::CollidingFrontsImageFilter< TInputImage, TOutputImage >::SetSeedPoints2(), itk::NonUniformBSpline< TDimension >::SetSplineOrder(), itk::ThresholdLabelerImageFilter< TInputImage, TOutputImage >::SetThresholds(), itk::Statistics::GoodnessOfFitFunctionBase< TInputHistogram >::SetTotalObservedScale(), and itk::MatrixOffsetTransformBase< TScalarType, 3, 3 >::SetTranslation().

static Pointer itk::Statistics::GaussianDistribution::New ( ) [static]

Method for creation through the object factory.

Reimplemented from itk::Object.

static double itk::Statistics::GaussianDistribution::PDF	(	double	x,
		double	mean,
		double	variance
	)			`[static]`

Static method to evaluate the probability density function (pdf) of a Gaussian. The parameters of the distribution are passed as separate values. The static method provides optimized access without requiring an instance of the class.

static double itk::Statistics::GaussianDistribution::PDF	(	double	x,
		const ParametersType &
	)			`[static]`

Static method to evaluate the probability density function (pdf) of a Gaussian. The parameters of the distribution are passed as a parameter vector. The ordering of the parameters is (mean, variance). The static method provides optimized access without requiring an instance of the class.

static double itk::Statistics::GaussianDistribution::PDF ( double x ) [static]

Static method to evaluate the probability density function (pdf) of a standardized (mean zero, unit variance) Gaussian. The static method provides optimized access without requiring an instance of the class.

void itk::LightObject::Print	(	std::ostream &	os,
		Indent	indent = `0`
	)			const `[inherited]`

Cause the object to print itself out.

Referenced by itk::WeakPointer< itk::ProcessObject >::Print().

virtual void itk::LightObject::PrintHeader	(	std::ostream &	os,
		Indent	indent
	)			const `[protected, virtual, inherited]`

bool itk::Object::PrintObservers	(	std::ostream &	os,
		Indent	indent
	)			const `[protected, inherited]`

void itk::Statistics::GaussianDistribution::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::ProbabilityDistribution.

virtual void itk::LightObject::PrintTrailer	(	std::ostream &	os,
		Indent	indent
	)			const `[protected, virtual, inherited]`

virtual void itk::Object::Register ( ) const [virtual, inherited]

Increase the reference count (mark as used by another object).

Reimplemented from itk::LightObject.

void itk::Object::RemoveAllObservers ( ) [inherited]

Remove all observers .

void itk::Object::RemoveObserver ( unsigned long tag ) [inherited]

Remove the observer with this tag value.

void itk::Object::SetDebug ( bool debugFlag ) const [inherited]

Set the value of the debug flag. A non-zero value turns debugging on.

static void itk::Object::SetGlobalWarningDisplay ( bool flag ) [static, inherited]

This is a global flag that controls whether any debug, warning or error messages are displayed.

Referenced by itk::Object::GlobalWarningDisplayOff(), and itk::Object::GlobalWarningDisplayOn().

virtual void itk::Statistics::GaussianDistribution::SetMean ( double ) [virtual]

Set the mean of the Gaussian distribution. Defaults to 0.0. The mean is stored in position 0 of the parameters vector.

void itk::Object::SetMetaDataDictionary ( const MetaDataDictionary & rhs ) [inherited]

Returns:: Set the MetaDataDictionary

virtual void itk::Statistics::ProbabilityDistribution::SetParameters ( const ParametersType & params ) [inline, virtual, inherited]

Set the parameters of the distribution. See concrete subclasses for the order of the parameters. Subclasses may provide convenience methods for setting parameters, i.e. SetDegreesOfFreedom(), etc.

Definition at line 96 of file itkProbabilityDistribution.h.

virtual void itk::Object::SetReferenceCount ( int ) [virtual, inherited]

Sets the reference count (use with care)

Reimplemented from itk::LightObject.

virtual void itk::Statistics::GaussianDistribution::SetVariance ( double ) [virtual]

Set the variance of the Gaussian distribution. Defaults to 1.0. The variance is stored in position 1 of the parameters vector.

virtual void itk::Object::UnRegister ( ) const [virtual, inherited]

Decrease the reference count (release by another object).

Reimplemented from itk::LightObject.

ParametersType itk::Statistics::ProbabilityDistribution::m_Parameters [protected, inherited]

Definition at line 158 of file itkProbabilityDistribution.h.

volatile int itk::LightObject::m_ReferenceCount [mutable, protected, inherited]

Number of uses of this object by other objects.

Definition at line 119 of file itkLightObject.h.

SimpleFastMutexLock itk::LightObject::m_ReferenceCountLock [mutable, protected, inherited]

Mutex lock to protect modification to the reference count

Definition at line 122 of file itkLightObject.h.

itk::Statistics::GaussianDistribution Class Reference

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation


Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef Array< double >	ParametersType
typedef SmartPointer< Self >	Pointer
typedef GaussianDistribution	Self
typedef ProbabilityDistribution	Superclass
Public Member Functions
virtual LightObject::Pointer	CreateAnother () const
virtual void	DebugOff () const
virtual void	DebugOn () const
virtual void	Delete ()
virtual double	EvaluateCDF (double x, double mean, double variance) const
virtual double	EvaluateCDF (double x, const ParametersType &) const
virtual double	EvaluateCDF (double x) const
virtual double	EvaluateInverseCDF (double p, double mean, double variance) const
virtual double	EvaluateInverseCDF (double p, const ParametersType &) const
virtual double	EvaluateInverseCDF (double p) const
virtual double	EvaluatePDF (double x, double mean, double variance) const
virtual double	EvaluatePDF (double x, const ParametersType &) const
virtual double	EvaluatePDF (double x) const
Command *	GetCommand (unsigned long tag)
bool	GetDebug () const
virtual double	GetMean () const
const MetaDataDictionary &	GetMetaDataDictionary (void) const
MetaDataDictionary &	GetMetaDataDictionary (void)
virtual unsigned long	GetMTime () const
virtual const char *	GetNameOfClass () const
virtual unsigned long	GetNumberOfParameters () const
virtual const ParametersType &	GetParameters ()
virtual int	GetReferenceCount () const
virtual double	GetVariance () const
virtual bool	HasMean () const
bool	HasObserver (const EventObject &event) const
virtual bool	HasVariance () const
void	InvokeEvent (const EventObject &) const
void	InvokeEvent (const EventObject &)
virtual void	Modified () const
void	Print (std::ostream &os, Indent indent=0) const
virtual void	Register () const
void	RemoveAllObservers ()
void	RemoveObserver (unsigned long tag)
void	SetDebug (bool debugFlag) const
virtual void	SetMean (double)
void	SetMetaDataDictionary (const MetaDataDictionary &rhs)
virtual void	SetReferenceCount (int)
virtual void	SetVariance (double)
virtual void	UnRegister () const

unsigned long	AddObserver (const EventObject &event, Command *) const
unsigned long	AddObserver (const EventObject &event, Command *)

virtual void	SetParameters (const ParametersType &params)
Static Public Member Functions
static void	BreakOnError ()
static double	CDF (double x, double mean, double variance)
static double	CDF (double x, const ParametersType &)
static double	CDF (double x)
static double	InverseCDF (double p, double mean, double variance)
static double	InverseCDF (double p, const ParametersType &)
static Pointer	New ()
static double	PDF (double x, double mean, double variance)
static double	PDF (double x, const ParametersType &)
static double	PDF (double x)

static bool	GetGlobalWarningDisplay ()
static void	GlobalWarningDisplayOff ()
static void	GlobalWarningDisplayOn ()
static void	SetGlobalWarningDisplay (bool flag)

static double	InverseCDF (double p)
Protected Member Functions
	GaussianDistribution (void)
bool	PrintObservers (std::ostream &os, Indent indent) const
void	PrintSelf (std::ostream &os, Indent indent) const
virtual	~GaussianDistribution (void)

virtual void	PrintHeader (std::ostream &os, Indent indent) const
virtual void	PrintTrailer (std::ostream &os, Indent indent) const
Protected Attributes
ParametersType	m_Parameters
volatile int	m_ReferenceCount
SimpleFastMutexLock	m_ReferenceCountLock