#include <itkQuasiNewtonOptimizerv4.h>

Inheritance diagram for itk::QuasiNewtonOptimizerv4:

Collaboration diagram for itk::QuasiNewtonOptimizerv4:

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 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 ()
Static Public Member Functions
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 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
Private Member Functions
void	operator= (const Self &)
	QuasiNewtonOptimizerv4 (const Self &)
Private Attributes
QuasiNewtonOptimizerv4EstimateNewtonStepThreader::Pointer	m_EstimateNewtonStepThreader
Friends
class	QuasiNewtonOptimizerv4EstimateNewtonStepThreader

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.

Member Typedef Documentation

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

Reimplemented from itk::GradientDescentOptimizerv4.

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

Internal computation type, for maintaining a desired precision

Reimplemented from itk::GradientDescentOptimizerv4.

Definition at line 74 of file itkQuasiNewtonOptimizerv4.h.

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

Reimplemented from itk::GradientDescentOptimizerv4.

Definition at line 67 of file itkQuasiNewtonOptimizerv4.h.

typedef QuasiNewtonOptimizerv4 itk::QuasiNewtonOptimizerv4::Self

Standard class typedefs.

Reimplemented from itk::GradientDescentOptimizerv4.

Definition at line 65 of file itkQuasiNewtonOptimizerv4.h.

typedef GradientDescentOptimizerv4 itk::QuasiNewtonOptimizerv4::Superclass

Reimplemented from itk::GradientDescentOptimizerv4.

Definition at line 66 of file itkQuasiNewtonOptimizerv4.h.

Constructor & Destructor Documentation

itk::QuasiNewtonOptimizerv4::QuasiNewtonOptimizerv4 ( ) [protected]

virtual itk::QuasiNewtonOptimizerv4::~QuasiNewtonOptimizerv4 ( ) [protected, virtual]

itk::QuasiNewtonOptimizerv4::QuasiNewtonOptimizerv4 ( const Self & ) [private]

Member Function Documentation

virtual void itk::QuasiNewtonOptimizerv4::AdvanceOneStep ( void ) [protected, virtual]

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 ) [protected, virtual]

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 ( ) [protected, virtual]

Estimate a Newton step

virtual void itk::QuasiNewtonOptimizerv4::EstimateNewtonStepOverSubRange ( const IndexRangeType & subrange ) [protected, virtual]

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.

Reimplemented from itk::GradientDescentOptimizerv4.

void itk::QuasiNewtonOptimizerv4::operator= ( const Self & ) [private]

Mutex lock to protect modification to the reference count

Reimplemented from itk::GradientDescentOptimizerv4.

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

virtual void itk::QuasiNewtonOptimizerv4::ResetNewtonStep ( IndexValueType location ) [protected, virtual]

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 ( ) [virtual]

Start and run the optimization

Reimplemented from itk::GradientDescentOptimizerv4.