#include <itkQuasiNewtonOptimizerv4.h>

Inheritance diagram for itk::QuasiNewtonOptimizerv4:

Collaboration diagram for itk::QuasiNewtonOptimizerv4:

Detailed Description

Implement a Quasi-Newton optimizer with BFGS Hessian estimation.

Second order approximation of the cost function is usually more efficient since it estimates the descent or ascent direction more precisely. However, computation of Hessian is usually expensive or unavailable. Alternatively Quasi-Newton methods can estimate a Hessian from the gradients in previous steps. Here a specific Quasi-Newton method, BFGS, is used to compute the Quasi-Newton steps.

The Quasi-Newton method doesn't produce a valid step sometimes, ex. when the metric function is not a convex locally. In this scenario, the gradient step is used after being scaled properly.

A helper member object, m_ScalesEstimator may be set to estimate parameter scales and step scales. A step scale measures the magnitude of a step and is used for learning rate computation.

When m_ScalesEstimator is set, SetMaximumNewtonStepSizeInPhysicalUnits() may be called to set the maximum step size. If it is not called, m_MaximumNewtonStepSizeInPhysicalUnits defaults to lambda * OptimizerParameterScalesEstimator::EstimateMaximumStepSize(), where lambda is in [1,5].

When m_ScalesEstimator is not set, the parameter scales and learning rates defaults to ones, or can be set by users manually.

Definition at line 60 of file itkQuasiNewtonOptimizerv4.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef std::vector< HessianType >	HessianArrayType

typedef itk::Array2D < InternalComputationValueType >	HessianType

typedef Superclass::InternalComputationValueType	InternalComputationValueType

typedef SmartPointer< Self >	Pointer

typedef QuasiNewtonOptimizerv4	Self

typedef GradientDescentOptimizerv4	Superclass

Public Types inherited from itk::GradientDescentOptimizerv4
typedef SmartPointer< const Self >	ConstPointer

typedef itk::Function::WindowConvergenceMonitoringFunction < double >	ConvergenceMonitoringType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::InternalComputationValueType	InternalComputationValueType

typedef Superclass::MeasureType	MeasureType

typedef SmartPointer< Self >	Pointer

typedef GradientDescentOptimizerv4	Self

typedef GradientDescentOptimizerBasev4	Superclass

Public Types inherited from itk::GradientDescentOptimizerBasev4
typedef SmartPointer< const Self >	ConstPointer

typedef MetricType::DerivativeType	DerivativeType

typedef Superclass::InternalComputationValueType	InternalComputationValueType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::MetricType	MetricType

typedef MetricType::Pointer	MetricTypePointer

typedef SmartPointer< Self >	Pointer

typedef GradientDescentOptimizerBasev4	Self

typedef std::ostringstream	StopConditionDescriptionType

typedef std::string	StopConditionReturnStringType

enum	StopConditionType { MAXIMUM_NUMBER_OF_ITERATIONS, COSTFUNCTION_ERROR, UPDATE_PARAMETERS_ERROR, STEP_TOO_SMALL, QUASI_NEWTON_STEP_ERROR, CONVERGENCE_CHECKER_PASSED, OTHER_ERROR }

typedef ObjectToObjectOptimizerBase	Superclass

Public Types inherited from itk::ObjectToObjectOptimizerBase
typedef SmartPointer< const Self >	ConstPointer

typedef MetricType::InternalComputationValueType	InternalComputationValueType

typedef MetricType::MeasureType	MeasureType

typedef ObjectToObjectMetricBase	MetricType

typedef MetricType::Pointer	MetricTypePointer

typedef MetricType::NumberOfParametersType	NumberOfParametersType

typedef OptimizerParameters < double >	ParametersType

typedef SmartPointer< Self >	Pointer

typedef OptimizerParameters < double >	ScalesType

typedef ObjectToObjectOptimizerBase	Self

typedef Object	Superclass

Public Types inherited from itk::Object
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef Object	Self

typedef LightObject	Superclass

Public Types inherited from itk::LightObject
typedef SmartPointer< const Self >	ConstPointer

typedef SmartPointer< Self >	Pointer

typedef LightObject	Self

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

virtual const char *	GetNameOfClass () const

virtual const DerivativeType &	GetNewtonStep ()

virtual void	SetMaximumIterationsWithoutProgress (SizeValueType _arg)

virtual void	SetMaximumNewtonStepSizeInPhysicalUnits (InternalComputationValueType _arg)

virtual void	StartOptimization (bool doOnlyInitialization=false)

Public Member Functions inherited from itk::GradientDescentOptimizerv4
virtual void	EstimateLearningRate ()

virtual const InternalComputationValueType &	GetConvergenceValue ()

virtual const InternalComputationValueType &	GetLearningRate ()

virtual const InternalComputationValueType &	GetMaximumStepSizeInPhysicalUnits ()

virtual void	ResumeOptimization ()

virtual void	SetConvergenceWindowSize (SizeValueType _arg)

virtual void	SetLearningRate (InternalComputationValueType _arg)

virtual void	SetMaximumStepSizeInPhysicalUnits (InternalComputationValueType _arg)

virtual void	SetMinimumConvergenceValue (InternalComputationValueType _arg)

virtual void	SetScalesEstimator (OptimizerParameterScalesEstimator *_arg)

virtual void	StopOptimization (void)

virtual void	SetDoEstimateScales (bool _arg)

virtual const bool &	GetDoEstimateScales ()

virtual void	DoEstimateScalesOn ()

virtual void	DoEstimateScalesOff ()

virtual void	SetDoEstimateLearningRateAtEachIteration (bool _arg)

virtual const bool &	GetDoEstimateLearningRateAtEachIteration ()

virtual void	DoEstimateLearningRateAtEachIterationOn ()

virtual void	DoEstimateLearningRateAtEachIterationOff ()

virtual void	SetDoEstimateLearningRateOnce (bool _arg)

virtual const bool &	GetDoEstimateLearningRateOnce ()

virtual void	DoEstimateLearningRateOnceOn ()

virtual void	DoEstimateLearningRateOnceOff ()

virtual void	SetReturnBestParametersAndValue (bool _arg)

virtual const bool &	GetReturnBestParametersAndValue ()

virtual void	ReturnBestParametersAndValueOn ()

virtual void	ReturnBestParametersAndValueOff ()

Public Member Functions inherited from itk::GradientDescentOptimizerBasev4
virtual SizeValueType	GetCurrentIteration () const

virtual const DerivativeType &	GetGradient ()

virtual const SizeValueType &	GetNumberOfIterations ()

virtual const StopConditionType &	GetStopCondition ()

virtual const StopConditionReturnStringType	GetStopConditionDescription () const

virtual void	SetNumberOfIterations (SizeValueType _arg)

virtual void	ModifyGradientByScales ()

virtual void	ModifyGradientByLearningRate ()

Public Member Functions inherited from itk::ObjectToObjectOptimizerBase
virtual const MeasureType &	GetCurrentMetricValue ()

const ParametersType &	GetCurrentPosition ()

virtual const ThreadIdType &	GetNumberOfThreads ()

virtual const ScalesType &	GetScales ()

virtual const bool &	GetScalesAreIdentity ()

const MeasureType &	GetValue ()

virtual const ScalesType &	GetWeights ()

virtual const bool &	GetWeightsAreIdentity ()

virtual void	SetNumberOfThreads (ThreadIdType number)

virtual void	SetScales (ScalesType _arg)

virtual void	SetWeights (ScalesType _arg)

virtual void	SetMetric (MetricType *_arg)

virtual MetricType *	GetModifiableMetric ()

virtual const MetricType *	GetMetric () const

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

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary (void)

const MetaDataDictionary &	GetMetaDataDictionary (void) const

virtual ModifiedTimeType	GetMTime () const

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

virtual void	Register () const

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

virtual void	SetReferenceCount (int)

virtual void	UnRegister () 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

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::GradientDescentOptimizerv4
static Pointer	New ()

Protected Member Functions
virtual void	AdvanceOneStep (void)

void	CombineGradientNewtonStep (void)

virtual bool	ComputeHessianAndStepWithBFGS (IndexValueType location)

virtual void	EstimateNewtonStep ()

virtual void	EstimateNewtonStepOverSubRange (const IndexRangeType &subrange)

void	ModifyCombinedNewtonStep ()

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

	QuasiNewtonOptimizerv4 ()

virtual void	ResetNewtonStep (IndexValueType location)

virtual	~QuasiNewtonOptimizerv4 ()

Protected Member Functions inherited from itk::GradientDescentOptimizerv4
	GradientDescentOptimizerv4 ()

virtual	~GradientDescentOptimizerv4 ()

virtual void	ModifyGradientByScalesOverSubRange (const IndexRangeType &subrange)

virtual void	ModifyGradientByLearningRateOverSubRange (const IndexRangeType &subrange)

Protected Member Functions inherited from itk::GradientDescentOptimizerBasev4
	GradientDescentOptimizerBasev4 ()

virtual	~GradientDescentOptimizerBasev4 ()

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

virtual	~ObjectToObjectOptimizerBase ()

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
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

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

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

virtual	~LightObject ()

Protected Attributes
SizeValueType	m_BestIteration

ParametersType	m_BestPosition

MeasureType	m_BestValue

ParametersType	m_CurrentPosition

HessianArrayType	m_HessianArray

SizeValueType	m_MaximumIterationsWithoutProgress

InternalComputationValueType	m_MaximumNewtonStepSizeInPhysicalUnits

DerivativeType	m_NewtonStep

std::vector< bool >	m_NewtonStepValidFlags

std::string	m_NewtonStepWarning

ParametersType	m_OptimalStep

DerivativeType	m_PreviousGradient

ParametersType	m_PreviousPosition

MeasureType	m_PreviousValue

Protected Attributes inherited from itk::GradientDescentOptimizerv4
ParametersType	m_BestParameters

ConvergenceMonitoringType::Pointer	m_ConvergenceMonitoring

InternalComputationValueType	m_ConvergenceValue

SizeValueType	m_ConvergenceWindowSize

MeasureType	m_CurrentBestValue

InternalComputationValueType	m_LearningRate

InternalComputationValueType	m_MaximumStepSizeInPhysicalUnits

InternalComputationValueType	m_MinimumConvergenceValue

bool	m_ReturnBestParametersAndValue

OptimizerParameterScalesEstimator::Pointer	m_ScalesEstimator

Protected Attributes inherited from itk::GradientDescentOptimizerBasev4
SizeValueType	m_CurrentIteration

DerivativeType	m_Gradient

GradientDescentOptimizerBasev4ModifyGradientByLearningRateThreader::Pointer	m_ModifyGradientByLearningRateThreader

GradientDescentOptimizerBasev4ModifyGradientByScalesThreader::Pointer	m_ModifyGradientByScalesThreader

SizeValueType	m_NumberOfIterations

bool	m_Stop

StopConditionType	m_StopCondition

StopConditionDescriptionType	m_StopConditionDescription

Protected Attributes inherited from itk::ObjectToObjectOptimizerBase
MeasureType	m_CurrentMetricValue

MetricTypePointer	m_Metric

ThreadIdType	m_NumberOfThreads

ScalesType	m_Scales

bool	m_ScalesAreIdentity

ScalesType	m_Weights

bool	m_WeightsAreIdentity

Private Member Functions
void	operator= (const Self &)

	QuasiNewtonOptimizerv4 (const Self &)

Private Attributes
QuasiNewtonOptimizerv4EstimateNewtonStepThreader::Pointer	m_EstimateNewtonStepThreader

Friends
class	QuasiNewtonOptimizerv4EstimateNewtonStepThreader

Additional Inherited Members
Protected Types inherited from itk::GradientDescentOptimizerBasev4
typedef GradientDescentOptimizerBasev4ModifyGradientByScalesThreader::IndexRangeType	IndexRangeType

Member Typedef Documentation

typedef SmartPointer< const Self > itk::QuasiNewtonOptimizerv4::ConstPointer

Definition at line 68 of file itkQuasiNewtonOptimizerv4.h.

typedef std::vector<HessianType> itk::QuasiNewtonOptimizerv4::HessianArrayType

Type for an array of Hessian matrix for local support

Definition at line 82 of file itkQuasiNewtonOptimizerv4.h.

typedef itk::Array2D<InternalComputationValueType> itk::QuasiNewtonOptimizerv4::HessianType

Type for Hessian matrix in the Quasi-Newton method

Definition at line 79 of file itkQuasiNewtonOptimizerv4.h.

typedef Superclass::InternalComputationValueType itk::QuasiNewtonOptimizerv4::InternalComputationValueType

Definition at line 74 of file itkQuasiNewtonOptimizerv4.h.

typedef SmartPointer< Self > itk::QuasiNewtonOptimizerv4::Pointer

Definition at line 67 of file itkQuasiNewtonOptimizerv4.h.

typedef QuasiNewtonOptimizerv4 itk::QuasiNewtonOptimizerv4::Self

Standard class typedefs.

Definition at line 65 of file itkQuasiNewtonOptimizerv4.h.

typedef GradientDescentOptimizerv4 itk::QuasiNewtonOptimizerv4::Superclass

Definition at line 66 of file itkQuasiNewtonOptimizerv4.h.

Constructor & Destructor Documentation

itk::QuasiNewtonOptimizerv4::QuasiNewtonOptimizerv4 ( )

protected

virtual itk::QuasiNewtonOptimizerv4::~QuasiNewtonOptimizerv4 ( )

protectedvirtual

itk::QuasiNewtonOptimizerv4::QuasiNewtonOptimizerv4 ( const Self & )

private

Member Function Documentation

virtual void itk::QuasiNewtonOptimizerv4::AdvanceOneStep ( void )

protectedvirtual

Advance one step using the Quasi-Newton step. When the Newton step is invalid, the gradient step will be used.

Reimplemented from itk::GradientDescentOptimizerv4.

void itk::QuasiNewtonOptimizerv4::CombineGradientNewtonStep ( void )

protected

Combine a gradient step with a Newton step. The Newton step will be used when it is valid. Otherwise the gradient step will be used.

virtual bool itk::QuasiNewtonOptimizerv4::ComputeHessianAndStepWithBFGS ( IndexValueType location )

protectedvirtual

Estimate the next Hessian and step with BFGS method. The details of the method are described at http://en.wikipedia.org/wiki/BFGS_method .

virtual::itk::LightObject::Pointer itk::QuasiNewtonOptimizerv4::CreateAnother ( void ) const

virtual

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::GradientDescentOptimizerv4.

virtual void itk::QuasiNewtonOptimizerv4::EstimateNewtonStep ( )

protectedvirtual

Estimate a Newton step

virtual void itk::QuasiNewtonOptimizerv4::EstimateNewtonStepOverSubRange ( const IndexRangeType & subrange )

protectedvirtual

Estimate the quasi-newton step over a given index range.

virtual const char* itk::QuasiNewtonOptimizerv4::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::GradientDescentOptimizerv4.

virtual const DerivativeType& itk::QuasiNewtonOptimizerv4::GetNewtonStep ( )

virtual

Get the most recent Newton step.

void itk::QuasiNewtonOptimizerv4::ModifyCombinedNewtonStep ( )

protected

Estimate and apply the learning rate(s) for a combined Newton step. A combined Newton step uses the Newton step by default and the gradient step when the Newton step is not valid.

The learning rate is less than 1.0 and is restricted by m_MaximumNewtonStepSizeInPhysicalUnits.

static Pointer itk::QuasiNewtonOptimizerv4::New ( )

static

Method for creation through the object factory.

void itk::QuasiNewtonOptimizerv4::operator= ( const Self & )

private

virtual void itk::QuasiNewtonOptimizerv4::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::GradientDescentOptimizerv4.

virtual void itk::QuasiNewtonOptimizerv4::ResetNewtonStep ( IndexValueType location )

protectedvirtual

Reset the Hessian to identity matrix and the Newton step to zeros.

virtual void itk::QuasiNewtonOptimizerv4::SetMaximumIterationsWithoutProgress ( SizeValueType _arg )

virtual

Set the maximum tolerable number of iteration without any progress

virtual void itk::QuasiNewtonOptimizerv4::SetMaximumNewtonStepSizeInPhysicalUnits ( InternalComputationValueType _arg )

virtual

Set the maximum step size.

When SetScalesEstimator is called by user, the optimizer will compute learning rates as m_MaximumNewtonStepSizeInPhysicalUnits / m_ScalesEstimator->EstimateStepScale(newtonStep).

If SetMaximumNewtonStepSizeInPhysicalUnits is not called by user, m_MaximumNewtonStepSizeInPhysicalUnits defaults to lambda * m_ScalesEstimator->EstimateMaximumStepSize(),

where EstimateMaximumStepSize returns one voxel spacing and lambda may be in [1,5] according to our experience.

virtual void itk::QuasiNewtonOptimizerv4::StartOptimization ( bool doOnlyInitialization = false )

virtual

Start and run the optimization

Reimplemented from itk::GradientDescentOptimizerv4.