#include <itkStandardGradientDescentOptimizer.h>

Detailed Description

This class implements a gradient descent optimizer with a decaying gain.

If is a costfunction that has to be minimised, the following iterative algorithm is used to find the optimal parameters :

$x(k+1) = x(k) - a(k) dC/dx$

The gain at each iteration is defined by:

$a(k) = a / (A + k + 1)^\alpha$

.

It is very suitable to be used in combination with a stochastic estimate of the gradient . For example, in image registration problems it is often advantageous to compute the metric derivative ( ) on a new set of randomly selected image samples in each iteration. You may set the parameter NewSamplesEveryIteration to "true" to achieve this effect. For more information on this strategy, you may have a look at:

S. Klein, M. Staring, J.P.W. Pluim, "Comparison of gradient approximation techniques for optimisation of mutual information in nonrigid registration", in: SPIE Medical Imaging: Image Processing, Editor(s): J.M. Fitzpatrick, J.M. Reinhardt, SPIE press, 2005, vol. 5747, Proceedings of SPIE, pp. 192-203.

Or:

S. Klein, M. Staring, J.P.W. Pluim, "Evaluation of Optimization Methods for Nonrigid Medical Image Registration using Mutual Information and B-Splines" IEEE Transactions on Image Processing, 2007, nr. 16(12), December.

This class also serves as a base class for other GradientDescent type algorithms, like the AcceleratedGradientDescentOptimizer.

See also: StandardGradientDescent, AcceleratedGradientDescentOptimizer

Definition at line 65 of file itkStandardGradientDescentOptimizer.h.

Inheritance diagram for itk::StandardGradientDescentOptimizer:

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef StandardGradientDescentOptimizer	Self

typedef Superclass::StopConditionType	StopConditionType

typedef GradientDescentOptimizer2	Superclass

Public Types inherited from itk::GradientDescentOptimizer2
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScaledCostFunctionPointer	ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionType	ScaledCostFunctionType

typedef Superclass::ScalesType	ScalesType

typedef GradientDescentOptimizer2	Self

enum	StopConditionType { MaximumNumberOfIterations , MetricError , MinimumStepSize }

typedef ScaledSingleValuedNonLinearOptimizer	Superclass

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

typedef Superclass::CostFunctionType	CostFunctionType

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::MeasureType	MeasureType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef ScaledCostFunctionType::Pointer	ScaledCostFunctionPointer

typedef ScaledSingleValuedCostFunction	ScaledCostFunctionType

typedef NonLinearOptimizer::ScalesType	ScalesType

typedef ScaledSingleValuedNonLinearOptimizer	Self

typedef SingleValuedNonLinearOptimizer	Superclass

Public Member Functions
void	AdvanceOneStep (void) override

virtual const char *	GetClassName () const

virtual double	GetCurrentTime () const

virtual double	GetInitialTime () const

virtual double	GetParam_a () const

virtual double	GetParam_A () const

virtual double	GetParam_alpha () const

virtual void	ResetCurrentTimeToInitialTime (void)

virtual void	SetInitialTime (double _arg)

virtual void	SetParam_a (double _arg)

virtual void	SetParam_A (double _arg)

virtual void	SetParam_alpha (double _arg)

void	StartOptimization (void) override

Public Member Functions inherited from itk::GradientDescentOptimizer2
virtual void	AdvanceOneStep (void)

virtual const char *	GetClassName () const

virtual unsigned int	GetCurrentIteration () const

virtual const DerivativeType &	GetGradient ()

virtual const double &	GetLearningRate ()

virtual const unsigned long &	GetNumberOfIterations ()

virtual const DerivativeType &	GetSearchDirection ()

virtual const StopConditionType &	GetStopCondition ()

virtual const double &	GetValue ()

virtual void	MetricErrorResponse (ExceptionObject &err)

virtual void	ResumeOptimization (void)

virtual void	SetLearningRate (double _arg)

virtual void	SetNumberOfIterations (unsigned long _arg)

virtual void	SetUseOpenMP (bool _arg)

void	StartOptimization (void) override

virtual void	StopOptimization (void)

Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual const char *	GetClassName () const

const ParametersType &	GetCurrentPosition (void) const override

virtual bool	GetMaximize () const

virtual const ScaledCostFunctionType *	GetScaledCostFunction ()

virtual const ParametersType &	GetScaledCurrentPosition ()

bool	GetUseScales (void) const

virtual void	InitializeScales (void)

virtual void	MaximizeOff ()

virtual void	MaximizeOn ()

void	SetCostFunction (CostFunctionType *costFunction) override

virtual void	SetMaximize (bool _arg)

virtual void	SetUseScales (bool arg)

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::GradientDescentOptimizer2
static Pointer	New ()

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

Protected Member Functions
virtual double	Compute_a (double k) const

	StandardGradientDescentOptimizer ()

virtual void	UpdateCurrentTime (void)

	~StandardGradientDescentOptimizer () override

Protected Member Functions inherited from itk::GradientDescentOptimizer2
	GradientDescentOptimizer2 ()

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

	~GradientDescentOptimizer2 () override

Protected Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual void	GetScaledDerivative (const ParametersType &parameters, DerivativeType &derivative) const

virtual MeasureType	GetScaledValue (const ParametersType &parameters) const

virtual void	GetScaledValueAndDerivative (const ParametersType &parameters, MeasureType &value, DerivativeType &derivative) const

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

	ScaledSingleValuedNonLinearOptimizer ()

void	SetCurrentPosition (const ParametersType &param) override

virtual void	SetScaledCurrentPosition (const ParametersType &parameters)

	~ScaledSingleValuedNonLinearOptimizer () override

Protected Attributes
double	m_CurrentTime

bool	m_UseConstantStep

Protected Attributes inherited from itk::GradientDescentOptimizer2
unsigned long	m_CurrentIteration

DerivativeType	m_Gradient

double	m_LearningRate

unsigned long	m_NumberOfIterations

DerivativeType	m_SearchDirection

bool	m_Stop

StopConditionType	m_StopCondition

double	m_Value

Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer	m_ScaledCostFunction

ParametersType	m_ScaledCurrentPosition

Private Member Functions
void	operator= (const Self &)

	StandardGradientDescentOptimizer (const Self &)

Private Attributes
double	m_InitialTime

double	m_Param_a

double	m_Param_A

double	m_Param_alpha

Member Typedef Documentation

◆ ConstPointer

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

Definition at line 75 of file itkStandardGradientDescentOptimizer.h.

◆ CostFunctionType

typedef Superclass::CostFunctionType itk::StandardGradientDescentOptimizer::CostFunctionType

Definition at line 87 of file itkStandardGradientDescentOptimizer.h.

◆ DerivativeType

typedef Superclass::DerivativeType itk::StandardGradientDescentOptimizer::DerivativeType

Definition at line 86 of file itkStandardGradientDescentOptimizer.h.

◆ MeasureType

typedef Superclass::MeasureType itk::StandardGradientDescentOptimizer::MeasureType

Typedefs inherited from the superclass.

Definition at line 84 of file itkStandardGradientDescentOptimizer.h.

◆ ParametersType

typedef Superclass::ParametersType itk::StandardGradientDescentOptimizer::ParametersType

Definition at line 85 of file itkStandardGradientDescentOptimizer.h.

◆ Pointer

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

Definition at line 74 of file itkStandardGradientDescentOptimizer.h.

◆ ScaledCostFunctionPointer

typedef Superclass::ScaledCostFunctionPointer itk::StandardGradientDescentOptimizer::ScaledCostFunctionPointer

Definition at line 90 of file itkStandardGradientDescentOptimizer.h.

◆ ScaledCostFunctionType

typedef Superclass::ScaledCostFunctionType itk::StandardGradientDescentOptimizer::ScaledCostFunctionType

Definition at line 89 of file itkStandardGradientDescentOptimizer.h.

◆ ScalesType

typedef Superclass::ScalesType itk::StandardGradientDescentOptimizer::ScalesType

Definition at line 88 of file itkStandardGradientDescentOptimizer.h.

◆ Self

typedef StandardGradientDescentOptimizer itk::StandardGradientDescentOptimizer::Self

Standard ITK.

Definition at line 71 of file itkStandardGradientDescentOptimizer.h.

◆ StopConditionType

typedef Superclass::StopConditionType itk::StandardGradientDescentOptimizer::StopConditionType

Definition at line 91 of file itkStandardGradientDescentOptimizer.h.

◆ Superclass

typedef GradientDescentOptimizer2 itk::StandardGradientDescentOptimizer::Superclass

Definition at line 72 of file itkStandardGradientDescentOptimizer.h.

Constructor & Destructor Documentation

◆ StandardGradientDescentOptimizer() [1/2]

itk::StandardGradientDescentOptimizer::StandardGradientDescentOptimizer ( )

protected

◆ ~StandardGradientDescentOptimizer()

itk::StandardGradientDescentOptimizer::~StandardGradientDescentOptimizer ( )

inlineoverrideprotected

Definition at line 136 of file itkStandardGradientDescentOptimizer.h.

◆ StandardGradientDescentOptimizer() [2/2]

itk::StandardGradientDescentOptimizer::StandardGradientDescentOptimizer ( const Self & )

private

Member Function Documentation

◆ AdvanceOneStep()

void itk::StandardGradientDescentOptimizer::AdvanceOneStep ( void )

overridevirtual

Sets a new LearningRate before calling the Superclass' implementation, and updates the current time.

Reimplemented from itk::GradientDescentOptimizer2.

◆ Compute_a()

virtual double itk::StandardGradientDescentOptimizer::Compute_a ( double k ) const

protectedvirtual

Function to compute the parameter at time/iteration k.

◆ GetClassName()

virtual const char * itk::StandardGradientDescentOptimizer::GetClassName ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::GradientDescentOptimizer2.

Reimplemented in elastix::AdaGrad< TElastix >, itk::AdaptiveStepsizeOptimizer, elastix::AdaptiveStochasticGradientDescent< TElastix >, itk::AdaptiveStochasticGradientDescentOptimizer, elastix::PreconditionedStochasticGradientDescent< TElastix >, itk::PreconditionedASGDOptimizer, and elastix::StandardGradientDescent< TElastix >.

◆ GetCurrentTime()

virtual double itk::StandardGradientDescentOptimizer::GetCurrentTime ( ) const

virtual

Get the current time. This equals the CurrentIteration in this base class but may be different in inheriting classes, such as the AccelerateGradientDescent

◆ GetInitialTime()

virtual double itk::StandardGradientDescentOptimizer::GetInitialTime ( ) const

virtual

◆ GetParam_a()

virtual double itk::StandardGradientDescentOptimizer::GetParam_a ( ) const

virtual

◆ GetParam_A()

virtual double itk::StandardGradientDescentOptimizer::GetParam_A ( ) const

virtual

◆ GetParam_alpha()

virtual double itk::StandardGradientDescentOptimizer::GetParam_alpha ( ) const

virtual

◆ New()

static Pointer itk::StandardGradientDescentOptimizer::New ( )

static

Method for creation through the object factory.

◆ operator=()

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

private

◆ ResetCurrentTimeToInitialTime()

virtual void itk::StandardGradientDescentOptimizer::ResetCurrentTimeToInitialTime ( void )

inlinevirtual

Set the current time to the initial time. This can be useful to 'reset' the optimisation, for example if you changed the cost function while optimisation. Be careful with this function.

Definition at line 127 of file itkStandardGradientDescentOptimizer.h.

◆ SetInitialTime()

virtual void itk::StandardGradientDescentOptimizer::SetInitialTime ( double _arg )

virtual

Set/Get the initial time. Should be >=0. This function is superfluous, since Param_A does effectively the same. However, in inheriting classes, like the AcceleratedGradientDescent the initial time may have a different function than Param_A. Default: 0.0

◆ SetParam_a()

virtual void itk::StandardGradientDescentOptimizer::SetParam_a ( double _arg )

virtual

Set/Get a.

◆ SetParam_A()

virtual void itk::StandardGradientDescentOptimizer::SetParam_A ( double _arg )

virtual

Set/Get A.

◆ SetParam_alpha()

virtual void itk::StandardGradientDescentOptimizer::SetParam_alpha ( double _arg )

virtual

Set/Get alpha.

◆ StartOptimization()

void itk::StandardGradientDescentOptimizer::StartOptimization ( void )

override

Set current time to 0 and call superclass' implementation.

◆ UpdateCurrentTime()

virtual void itk::StandardGradientDescentOptimizer::UpdateCurrentTime ( void )

protectedvirtual

Function to update the current time This function just increments the CurrentTime by 1. Inheriting functions may implement something smarter, for example, dependent on the progress

Reimplemented in itk::AdaptiveStepsizeOptimizer, itk::AdaptiveStochasticGradientDescentOptimizer, and itk::PreconditionedASGDOptimizer.

Field Documentation

◆ m_CurrentTime

double itk::StandardGradientDescentOptimizer::m_CurrentTime

protected

The current time, which serves as input for Compute_a

Definition at line 148 of file itkStandardGradientDescentOptimizer.h.

◆ m_InitialTime

double itk::StandardGradientDescentOptimizer::m_InitialTime

private

Settings

Definition at line 164 of file itkStandardGradientDescentOptimizer.h.

◆ m_Param_a

double itk::StandardGradientDescentOptimizer::m_Param_a

private

Parameters, as described by Spall.

Definition at line 159 of file itkStandardGradientDescentOptimizer.h.

◆ m_Param_A

double itk::StandardGradientDescentOptimizer::m_Param_A

private

Definition at line 160 of file itkStandardGradientDescentOptimizer.h.

◆ m_Param_alpha

double itk::StandardGradientDescentOptimizer::m_Param_alpha

private

Definition at line 161 of file itkStandardGradientDescentOptimizer.h.

◆ m_UseConstantStep

bool itk::StandardGradientDescentOptimizer::m_UseConstantStep

protected

Constant step size or others, different value of k.

Definition at line 151 of file itkStandardGradientDescentOptimizer.h.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Member Functions

Private Attributes

Member Typedef Documentation

◆ ConstPointer

◆ CostFunctionType

◆ DerivativeType

◆ MeasureType

◆ ParametersType

◆ Pointer

◆ ScaledCostFunctionPointer

◆ ScaledCostFunctionType

◆ ScalesType

◆ Self

◆ StopConditionType

◆ Superclass

Constructor & Destructor Documentation

◆ StandardGradientDescentOptimizer() [1/2]

◆ ~StandardGradientDescentOptimizer()

◆ StandardGradientDescentOptimizer() [2/2]

Member Function Documentation

◆ AdvanceOneStep()

◆ Compute_a()

◆ GetClassName()

◆ GetCurrentTime()

◆ GetInitialTime()

◆ GetParam_a()

◆ GetParam_A()

◆ GetParam_alpha()

◆ New()

◆ operator=()

◆ ResetCurrentTimeToInitialTime()

◆ SetInitialTime()

◆ SetParam_a()

◆ SetParam_A()

◆ SetParam_alpha()

◆ StartOptimization()

◆ UpdateCurrentTime()

Field Documentation

◆ m_CurrentTime

◆ m_InitialTime

◆ m_Param_a

◆ m_Param_A

◆ m_Param_alpha

◆ m_UseConstantStep