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itk::StandardGradientDescentOptimizer Class Reference

#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:
Inheritance graph
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Public Types

typedef SmartPointer< const SelfConstPointer
 
typedef Superclass::CostFunctionType CostFunctionType
 
typedef Superclass::DerivativeType DerivativeType
 
typedef Superclass::MeasureType MeasureType
 
typedef Superclass::ParametersType ParametersType
 
typedef SmartPointer< SelfPointer
 
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 SelfConstPointer
 
typedef Superclass::CostFunctionType CostFunctionType
 
typedef Superclass::DerivativeType DerivativeType
 
typedef Superclass::MeasureType MeasureType
 
typedef Superclass::ParametersType ParametersType
 
typedef SmartPointer< SelfPointer
 
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 SelfConstPointer
 
typedef Superclass::CostFunctionType CostFunctionType
 
typedef Superclass::DerivativeType DerivativeType
 
typedef Superclass::MeasureType MeasureType
 
typedef Superclass::ParametersType ParametersType
 
typedef SmartPointer< SelfPointer
 
typedef ScaledCostFunctionType::Pointer ScaledCostFunctionPointer
 
typedef ScaledSingleValuedCostFunction ScaledCostFunctionType
 
typedef NonLinearOptimizer::ScalesType ScalesType
 
typedef ScaledSingleValuedNonLinearOptimizer Self
 
typedef SingleValuedNonLinearOptimizer Superclass
 

Public Member Functions

virtual void AdvanceOneStep (void)
 
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)
 
virtual void StartOptimization (void)
 
- Public Member Functions inherited from itk::GradientDescentOptimizer2
virtual unsigned int GetCurrentIteration () const
 
virtual const DerivativeTypeGetGradient ()
 
virtual const doubleGetLearningRate ()
 
virtual const unsigned long & GetNumberOfIterations ()
 
virtual const StopConditionTypeGetStopCondition ()
 
virtual const doubleGetValue ()
 
virtual void MetricErrorResponse (ExceptionObject &err)
 
virtual void ResumeOptimization (void)
 
virtual void SetLearningRate (double _arg)
 
virtual void SetNumberOfIterations (unsigned long _arg)
 
void SetNumberOfThreads (ThreadIdType numberOfThreads)
 
virtual void SetUseEigen (bool _arg)
 
virtual void SetUseMultiThread (bool _arg)
 
virtual void SetUseOpenMP (bool _arg)
 
virtual void StopOptimization (void)
 
- Public Member Functions inherited from itk::ScaledSingleValuedNonLinearOptimizer
virtual const ParametersTypeGetCurrentPosition (void) const
 
virtual bool GetMaximize () const
 
virtual const ScaledCostFunctionTypeGetScaledCostFunction ()
 
virtual const ParametersTypeGetScaledCurrentPosition ()
 
bool GetUseScales (void) const
 
virtual void InitializeScales (void)
 
virtual void MaximizeOff ()
 
virtual void MaximizeOn ()
 
virtual void SetCostFunction (CostFunctionType *costFunction)
 
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)
 
virtual ~StandardGradientDescentOptimizer ()
 
- Protected Member Functions inherited from itk::GradientDescentOptimizer2
 GradientDescentOptimizer2 ()
 
void PrintSelf (std::ostream &os, Indent indent) const
 
virtual ~GradientDescentOptimizer2 ()
 
- 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
 
 ScaledSingleValuedNonLinearOptimizer ()
 
virtual void SetCurrentPosition (const ParametersType &param)
 
virtual void SetScaledCurrentPosition (const ParametersType &parameters)
 
virtual ~ScaledSingleValuedNonLinearOptimizer ()
 

Protected Attributes

double m_CurrentTime
 
- Protected Attributes inherited from itk::GradientDescentOptimizer2
unsigned long m_CurrentIteration
 
DerivativeType m_Gradient
 
double m_LearningRate
 
unsigned long m_NumberOfIterations
 
bool m_Stop
 
StopConditionType m_StopCondition
 
ThreaderType::Pointer m_Threader
 
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
 

Additional Inherited Members

- Protected Types inherited from itk::GradientDescentOptimizer2
typedef itk::MultiThreader ThreaderType
 
typedef ThreaderType::ThreadInfoStruct ThreadInfoType
 

Member Typedef Documentation

Definition at line 75 of file itkStandardGradientDescentOptimizer.h.

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

Definition at line 87 of file itkStandardGradientDescentOptimizer.h.

Definition at line 86 of file itkStandardGradientDescentOptimizer.h.

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

Typedefs inherited from the superclass.

Definition at line 81 of file itkStandardGradientDescentOptimizer.h.

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

Definition at line 85 of file itkStandardGradientDescentOptimizer.h.

Definition at line 74 of file itkStandardGradientDescentOptimizer.h.

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

Definition at line 90 of file itkStandardGradientDescentOptimizer.h.

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

Definition at line 89 of file itkStandardGradientDescentOptimizer.h.

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

Definition at line 88 of file itkStandardGradientDescentOptimizer.h.

Standard ITK.

Definition at line 71 of file itkStandardGradientDescentOptimizer.h.

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

Definition at line 91 of file itkStandardGradientDescentOptimizer.h.

Definition at line 72 of file itkStandardGradientDescentOptimizer.h.

Constructor & Destructor Documentation

itk::StandardGradientDescentOptimizer::StandardGradientDescentOptimizer ( )
protected
virtual itk::StandardGradientDescentOptimizer::~StandardGradientDescentOptimizer ( )
inlineprotectedvirtual

Definition at line 136 of file itkStandardGradientDescentOptimizer.h.

itk::StandardGradientDescentOptimizer::StandardGradientDescentOptimizer ( const Self )
private

Member Function Documentation

virtual void itk::StandardGradientDescentOptimizer::AdvanceOneStep ( void  )
virtual

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

Reimplemented from itk::GradientDescentOptimizer2.

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

Function to compute the parameter at time/iteration k.

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

virtual double itk::StandardGradientDescentOptimizer::GetInitialTime ( ) const
virtual
virtual double itk::StandardGradientDescentOptimizer::GetParam_a ( ) const
virtual
virtual double itk::StandardGradientDescentOptimizer::GetParam_A ( ) const
virtual
virtual double itk::StandardGradientDescentOptimizer::GetParam_alpha ( ) const
virtual
static Pointer itk::StandardGradientDescentOptimizer::New ( )
static

Method for creation through the object factory.

void itk::StandardGradientDescentOptimizer::operator= ( const Self )
private
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.

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

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

Set/Get a.

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

Set/Get A.

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

Set/Get alpha.

virtual void itk::StandardGradientDescentOptimizer::StartOptimization ( void  )
virtual

Set current time to 0 and call superclass' implementation.

Reimplemented from itk::GradientDescentOptimizer2.

Reimplemented in elastix::AdaptiveStochasticGradientDescent< TElastix >, and elastix::StandardGradientDescent< TElastix >.

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::AdaptiveStochasticGradientDescentOptimizer.

Field Documentation

double itk::StandardGradientDescentOptimizer::m_CurrentTime
protected

The current time, which serves as input for Compute_a

Definition at line 148 of file itkStandardGradientDescentOptimizer.h.

double itk::StandardGradientDescentOptimizer::m_InitialTime
private

Settings

Definition at line 161 of file itkStandardGradientDescentOptimizer.h.

double itk::StandardGradientDescentOptimizer::m_Param_a
private

Parameters, as described by Spall.

Definition at line 156 of file itkStandardGradientDescentOptimizer.h.

double itk::StandardGradientDescentOptimizer::m_Param_A
private

Definition at line 157 of file itkStandardGradientDescentOptimizer.h.

double itk::StandardGradientDescentOptimizer::m_Param_alpha
private

Definition at line 158 of file itkStandardGradientDescentOptimizer.h.



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