#include <itkStandardGradientDescentOptimizer.h>

Detailed Description

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

If $C(x)$ is a costfunction that has to be minimised, the following iterative algorithm is used to find the optimal parameters $x$ :

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

The gain $a(k)$ at each iteration $k$ 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 $dC/dx$ . For example, in image registration problems it is often advantageous to compute the metric derivative ( $dC/dx$ ) 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:

[legend]

Public Types
using	ConstPointer = SmartPointer<const Self>

using	Pointer = SmartPointer<Self>

using	ScaledCostFunctionPointer

using	ScaledCostFunctionType

using	ScalesType

using	Self = StandardGradientDescentOptimizer

enum	StopConditionType

using	Superclass = GradientDescentOptimizer2

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

using	Pointer = SmartPointer<Self>

using	ScaledCostFunctionPointer

using	ScaledCostFunctionType

using	ScalesType

using	Self = GradientDescentOptimizer2

enum	StopConditionType { MaximumNumberOfIterations , MetricError , MinimumStepSize }

using	Superclass = ScaledSingleValuedNonLinearOptimizer

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

using	Pointer = SmartPointer<Self>

using	ScaledCostFunctionPointer = ScaledCostFunctionType::Pointer

using	ScaledCostFunctionType = ScaledSingleValuedCostFunction

using	ScalesType = NonLinearOptimizer::ScalesType

using	Self = ScaledSingleValuedNonLinearOptimizer

using	Superclass = SingleValuedNonLinearOptimizer

Public Member Functions
void	AdvanceOneStep () 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

	ITK_DISALLOW_COPY_AND_MOVE (StandardGradientDescentOptimizer)

virtual void	ResetCurrentTimeToInitialTime ()

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 () override

Public Member Functions inherited from itk::GradientDescentOptimizer2
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 ()

	ITK_DISALLOW_COPY_AND_MOVE (GradientDescentOptimizer2)

virtual void	MetricErrorResponse (ExceptionObject &err)

virtual void	ResumeOptimization ()

virtual void	SetLearningRate (double _arg)

virtual void	SetNumberOfIterations (unsigned long _arg)

void	StartOptimization () override

virtual void	StopOptimization ()

Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
const ParametersType &	GetCurrentPosition () const override

virtual bool	GetMaximize () const

virtual const ScaledCostFunctionType *	GetScaledCostFunction ()

virtual const ParametersType &	GetScaledCurrentPosition ()

bool	GetUseScales () const

virtual void	InitializeScales ()

	ITK_DISALLOW_COPY_AND_MOVE (ScaledSingleValuedNonLinearOptimizer)

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 ()

	~StandardGradientDescentOptimizer () override=default

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

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

	~GradientDescentOptimizer2 () override=default

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=default

Protected Attributes
double	m_CurrentTime { 0.0 }

bool	m_UseConstantStep { false }

Protected Attributes inherited from itk::GradientDescentOptimizer2
DerivativeType	m_Gradient {}

DerivativeType	m_SearchDirection {}

StopConditionType	m_StopCondition { MaximumNumberOfIterations }

Protected Attributes inherited from itk::ScaledSingleValuedNonLinearOptimizer
ScaledCostFunctionPointer	m_ScaledCostFunction {}

ParametersType	m_ScaledCurrentPosition {}

Private Attributes
double	m_InitialTime { 0.0 }

double	m_Param_A { 1.0 }

double	m_Param_a { 1.0 }

double	m_Param_alpha { 0.602 }

Member Typedef Documentation

◆ ConstPointer

using itk::StandardGradientDescentOptimizer::ConstPointer = SmartPointer<const Self>

Definition at line 75 of file itkStandardGradientDescentOptimizer.h.

◆ Pointer

using itk::StandardGradientDescentOptimizer::Pointer = SmartPointer<Self>

Definition at line 74 of file itkStandardGradientDescentOptimizer.h.

◆ ScaledCostFunctionPointer

using itk::ScaledSingleValuedNonLinearOptimizer::ScaledCostFunctionPointer

Definition at line 78 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ ScaledCostFunctionType

using itk::ScaledSingleValuedNonLinearOptimizer::ScaledCostFunctionType

Definition at line 77 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ ScalesType

using itk::ScaledSingleValuedNonLinearOptimizer::ScalesType

Definition at line 76 of file itkScaledSingleValuedNonLinearOptimizer.h.

◆ Self

using itk::StandardGradientDescentOptimizer::Self = StandardGradientDescentOptimizer

Standard ITK.

Definition at line 71 of file itkStandardGradientDescentOptimizer.h.

◆ Superclass

using itk::StandardGradientDescentOptimizer::Superclass = GradientDescentOptimizer2

Definition at line 72 of file itkStandardGradientDescentOptimizer.h.

Member Enumeration Documentation

◆ StopConditionType

enum itk::GradientDescentOptimizer2::StopConditionType

Codes of stopping conditions The MinimumStepSize stopcondition never occurs, but may be implemented in inheriting classes

Definition at line 83 of file itkGradientDescentOptimizer2.h.

Constructor & Destructor Documentation

◆ StandardGradientDescentOptimizer()

itk::StandardGradientDescentOptimizer::StandardGradientDescentOptimizer ( )

protected

◆ ~StandardGradientDescentOptimizer()

itk::StandardGradientDescentOptimizer::~StandardGradientDescentOptimizer ( )

overrideprotecteddefault

Member Function Documentation

◆ AdvanceOneStep()

void itk::StandardGradientDescentOptimizer::AdvanceOneStep ( )

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

◆ 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

◆ ITK_DISALLOW_COPY_AND_MOVE()

itk::StandardGradientDescentOptimizer::ITK_DISALLOW_COPY_AND_MOVE ( StandardGradientDescentOptimizer )

◆ New()

static Pointer itk::StandardGradientDescentOptimizer::New ( )

static

Method for creation through the object factory.

◆ ResetCurrentTimeToInitialTime()

virtual void itk::StandardGradientDescentOptimizer::ResetCurrentTimeToInitialTime ( )

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 130 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 ( )

override

Set current time to 0 and call superclass' implementation.

◆ UpdateCurrentTime()

virtual void itk::StandardGradientDescentOptimizer::UpdateCurrentTime ( )

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 { 0.0 }

protected

The current time, which serves as input for Compute_a

Definition at line 152 of file itkStandardGradientDescentOptimizer.h.

◆ m_InitialTime

double itk::StandardGradientDescentOptimizer::m_InitialTime { 0.0 }

private

Settings

Definition at line 164 of file itkStandardGradientDescentOptimizer.h.

◆ m_Param_A

double itk::StandardGradientDescentOptimizer::m_Param_A { 1.0 }

private

Definition at line 160 of file itkStandardGradientDescentOptimizer.h.

◆ m_Param_a

double itk::StandardGradientDescentOptimizer::m_Param_a { 1.0 }

private

Parameters, as described by Spall.

Definition at line 159 of file itkStandardGradientDescentOptimizer.h.

◆ m_Param_alpha

double itk::StandardGradientDescentOptimizer::m_Param_alpha { 0.602 }

private

Definition at line 161 of file itkStandardGradientDescentOptimizer.h.

◆ m_UseConstantStep

bool itk::StandardGradientDescentOptimizer::m_UseConstantStep { false }

protected

Constant step size or others, different value of k.

Definition at line 155 of file itkStandardGradientDescentOptimizer.h.

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Private Attributes

Member Typedef Documentation

◆ ConstPointer

◆ Pointer

◆ ScaledCostFunctionPointer

◆ ScaledCostFunctionType

◆ ScalesType

◆ Self

◆ Superclass

Member Enumeration Documentation

◆ StopConditionType

Constructor & Destructor Documentation

◆ StandardGradientDescentOptimizer()

◆ ~StandardGradientDescentOptimizer()

Member Function Documentation

◆ AdvanceOneStep()

◆ Compute_a()

◆ GetClassName()

◆ GetCurrentTime()

◆ GetInitialTime()

◆ GetParam_A()

◆ GetParam_a()

◆ GetParam_alpha()

◆ ITK_DISALLOW_COPY_AND_MOVE()

◆ New()

◆ 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