ITK  4.13.0
Insight Segmentation and Registration Toolkit
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itk::LBFGSOptimizerv4 Class Reference
Module ITKOptimizersv4

#include <itkLBFGSOptimizerv4.h>

+ Inheritance diagram for itk::LBFGSOptimizerv4:
+ Collaboration diagram for itk::LBFGSOptimizerv4:

Detailed Description

Wrap of the vnl_lbfgs algorithm for use in ITKv4 registration framework. The vnl_lbfgs is a wrapper for the NETLIB fortran code by Nocedal [1].

LBFGS is a quasi-Newton method. Quasi-Newton methods use an approximate estimate of the inverse Hessian $ (\nabla^2 f(x) )^{-1} $ to scale the gradient step:

\[ x_{n+1} = x_n - s (\nabla^2 f(x_n) )^{-1} \nabla f(x) \]

with $ s $ the step size.

The inverse Hessian is approximated from the gradients of previous iteration and thus only the gradient of the objective function is required.

The step size $ s $ is determined through line search with the approach by More and Thuente [4]. This line search approach finds a step size such that

\[ \lVert \nabla f(x + s (\nabla^2 f(x_n) )^{-1} \nabla f(x) ) \rVert \le \nu \lVert \nabla f(x) \rVert \]

The parameter $ \nu $ is set through SetLineSearchAccuracy() (default 0.9) The default step length, i.e. starting step length for the line search, is set through SetDefaultStepLength() (default 1.0).

The optimization stops when either the gradient satisfies the condition

\[ \lVert \nabla f(x) \rVert \le \epsilon \max(1, \lVert X \rVert) \]

or a maximum number of function evaluations has been reached. The tolerance $\epsilon$ is set through SetGradientConvergenceTolerance() (default 1e-5) and the maximum number of function evaluations is set through SetMaximumNumberOfFunctionEvaluations() (default 2000).

Note: The scaling of the optimization paramaters, set through SetScales(), should be set or left at one. Otherwise the Hessian approximation as well as the line search will be disturbed and the optimizer is unlikely to find a minima.

References:

[1] NETLIB lbfgs

[2] Jorge Nocedal. Updating Quasi-Newton Matrices with Limited Storage. Mathematics of Computation, Vol. 35, No. 151, pp. 773–782, 1980.

[3] Dong C. Liu and Jorge Nocedal. On the limited memory BFGS method for large scale optimization. Mathematical Programming B, Vol. 45, No. 3, pp. 503-528, 1989.

[4] More, J. J. and D. J. Thuente. Line Search Algorithms with Guaranteed Sufficient Decrease. ACM Transactions on Mathematical Software 20, no. 3 (1994): 286–307.

Examples:
Examples/RegistrationITKv4/DeformableRegistration4.cxx, and Examples/RegistrationITKv4/DeformableRegistration6.cxx.

Definition at line 85 of file itkLBFGSOptimizerv4.h.

Public Types

typedef SmartPointer< const Self > ConstPointer
 
typedef Superclass::MetricType MetricType
 
typedef Superclass::ParametersType ParametersType
 
typedef SmartPointer< Self > Pointer
 
typedef Superclass::ScalesType ScalesType
 
typedef LBFGSOptimizerv4 Self
 
typedef LBFGSOptimizerBasev4
< vnl_lbfgs > 		Superclass
 
- Public Types inherited from itk::LBFGSOptimizerBasev4< vnl_lbfgs >
typedef SmartPointer< const Self > ConstPointer
 
typedef
LBFGSOptimizerBaseHelperv4
< vnl_lbfgs > 		InternalOptimizerType
 
typedef Superclass::MetricType MetricType
 
typedef Superclass::ParametersType ParametersType
 
typedef SmartPointer< Self > Pointer
 
typedef Superclass::ScalesType ScalesType
 
typedef LBFGSOptimizerBasev4 Self
 
typedef
Superclass::StopConditionDescriptionType 		StopConditionDescriptionType
 
typedef
Superclass::StopConditionReturnStringType 		StopConditionReturnStringType
 
typedef
SingleValuedNonLinearVnlOptimizerv4 		Superclass
 
- Public Types inherited from itk::SingleValuedNonLinearVnlOptimizerv4
typedef ReceptorMemberCommand
< Self > 		CommandType
 
typedef SmartPointer< const Self > ConstPointer
 
typedef Superclass::DerivativeType DerivativeType
 
typedef Superclass::MetricType MetricType
 
typedef Superclass::ParametersType ParametersType
 
typedef SmartPointer< Self > Pointer
 
typedef Superclass::ScalesType ScalesType
 
typedef
SingleValuedNonLinearVnlOptimizerv4 		Self
 
typedef
Superclass::StopConditionDescriptionType 		StopConditionDescriptionType
 
typedef
Superclass::StopConditionReturnStringType 		StopConditionReturnStringType
 
typedef ObjectToObjectOptimizerBase Superclass
 
- Public Types inherited from itk::ObjectToObjectOptimizerBaseTemplate< double >
typedef SmartPointer< const Self > ConstPointer
 
typedef MetricType::DerivativeType DerivativeType
 
typedef MetricType::MeasureType MeasureType
 
typedef
ObjectToObjectMetricBaseTemplate
< double > 		MetricType
 
typedef MetricType::Pointer MetricTypePointer
 
typedef
MetricType::NumberOfParametersType 		NumberOfParametersType
 
typedef OptimizerParameters
< double > 		ParametersType
 
typedef SmartPointer< Self > Pointer
 
typedef
OptimizerParameterScalesEstimatorTemplate
< double > 		ScalesEstimatorType
 
typedef OptimizerParameters
< double > 		ScalesType
 
typedef
ObjectToObjectOptimizerBaseTemplate 		Self
 
typedef std::ostringstream StopConditionDescriptionType
 
typedef std::string StopConditionReturnStringType
 
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 () const
 
virtual double GetDefaultStepLength () const
 
virtual double GetLineSearchAccuracy () const
 
virtual const char * GetNameOfClass () const
 
void SetDefaultStepLength (double stp)
 
void SetLineSearchAccuracy (double tol)
 
virtual void SetMetric (MetricType *metric) override
 
virtual void StartOptimization (bool doOnlyInitialization=false) override
 
void VerboseOff ()
 
void VerboseOn ()
 
- Public Member Functions inherited from itk::LBFGSOptimizerBasev4< vnl_lbfgs >
virtual double GetGradientConvergenceTolerance () const
 
virtual unsigned int GetMaximumNumberOfFunctionEvaluations () const
 
InternalOptimizerType * GetOptimizer ()
 
virtual const
StopConditionReturnStringType 		GetStopConditionDescription () const override
 
virtual bool GetTrace () const
 
virtual void SetGradientConvergenceTolerance (double gtol)
 
virtual void SetMaximumNumberOfFunctionEvaluations (unsigned int n)
 
virtual void SetTrace (bool flag)
 
virtual void TraceOff ()
 
virtual void TraceOn ()
 
- Public Member Functions inherited from itk::SingleValuedNonLinearVnlOptimizerv4
virtual const DerivativeType & GetCachedDerivative () const
 
virtual const ParametersType & GetCachedCurrentPosition () const
 
- Public Member Functions inherited from itk::ObjectToObjectOptimizerBaseTemplate< double >
virtual SizeValueType GetCurrentIteration () const
 
virtual const MeasureType & GetCurrentMetricValue () const
 
virtual const ParametersType & GetCurrentPosition () const
 
virtual SizeValueType GetNumberOfIterations () const
 
virtual const ThreadIdType & GetNumberOfThreads () const
 
virtual const ScalesType & GetScales () const
 
virtual const bool & GetScalesAreIdentity () const
 
bool GetScalesInitialized () const
 
virtual const MeasureType & GetValue () const
 
virtual const ScalesType & GetWeights () const
 
virtual const bool & GetWeightsAreIdentity () const
 
virtual void SetNumberOfIterations (SizeValueType _arg)
 
virtual void SetNumberOfThreads (ThreadIdType number)
 
virtual void SetScalesEstimator (ScalesEstimatorType *_arg)
 
virtual void SetWeights (ScalesType _arg)
 
virtual void SetMetric (MetricType *_arg)
 
virtual MetricType * GetModifiableMetric ()
 
virtual const MetricType * GetMetric () const
 
virtual void SetScales (const ScalesType &scales)
 
virtual void SetDoEstimateScales (bool _arg)
 
virtual const bool & GetDoEstimateScales () const
 
virtual void DoEstimateScalesOn ()
 
virtual void DoEstimateScalesOff ()
 
- 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 ()
 
const MetaDataDictionary & GetMetaDataDictionary () 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 override
 
void RemoveAllObservers ()
 
void RemoveObserver (unsigned long tag)
 
void SetDebug (bool debugFlag) const
 
void SetMetaDataDictionary (const MetaDataDictionary &rhs)
 
virtual void SetReferenceCount (int) override
 
virtual void UnRegister () const noexceptoverride
 
virtual void SetObjectName (std::string _arg)
 
virtual const std::string & GetObjectName () 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::Object
static bool GetGlobalWarningDisplay ()
 
static void GlobalWarningDisplayOff ()
 
static void GlobalWarningDisplayOn ()
 
static Pointer New ()
 
static void SetGlobalWarningDisplay (bool flag)
 
- Static Public Member Functions inherited from itk::LightObject
static void BreakOnError ()
 
static Pointer New ()
 

Protected Types

typedef vnl_lbfgs InternalOptimizerType
 
typedef vnl_vector< double > InternalParametersType
 
- Protected Types inherited from itk::LBFGSOptimizerBasev4< vnl_lbfgs >
typedef
Superclass::CostFunctionAdaptorType 		CostFunctionAdaptorType
 
typedef AutoPointer
< InternalOptimizerType > 		InternalOptimizerAutoPointer
 
- Protected Types inherited from itk::SingleValuedNonLinearVnlOptimizerv4
typedef
SingleValuedVnlCostFunctionAdaptorv4 		CostFunctionAdaptorType
 

Protected Member Functions

 LBFGSOptimizerv4 ()
 
virtual void PrintSelf (std::ostream &os, Indent indent) const override
 
virtual ~LBFGSOptimizerv4 () override
 
- Protected Member Functions inherited from itk::LBFGSOptimizerBasev4< vnl_lbfgs >
 LBFGSOptimizerBasev4 ()
 
virtual ~LBFGSOptimizerBasev4 () override
 
- Protected Member Functions inherited from itk::SingleValuedNonLinearVnlOptimizerv4
const CostFunctionAdaptorType * GetCostFunctionAdaptor () const
 
CostFunctionAdaptorType * GetCostFunctionAdaptor ()
 
CostFunctionAdaptorType * GetNonConstCostFunctionAdaptor () const
 
void SetCostFunctionAdaptor (CostFunctionAdaptorType *adaptor)
 
 SingleValuedNonLinearVnlOptimizerv4 ()
 
virtual ~SingleValuedNonLinearVnlOptimizerv4 () override
 
- Protected Member Functions inherited from itk::ObjectToObjectOptimizerBaseTemplate< double >
 ObjectToObjectOptimizerBaseTemplate ()
 
virtual ~ObjectToObjectOptimizerBaseTemplate () override
 
- Protected Member Functions inherited from itk::Object
 Object ()
 
bool PrintObservers (std::ostream &os, Indent indent) const
 
virtual void SetTimeStamp (const TimeStamp &time)
 
virtual ~Object () override
 
- 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 ()
 

Private Attributes

double m_DefaultStepLength
 
double m_LineSearchAccuracy
 
bool m_Verbose
 

Additional Inherited Members

- Protected Attributes inherited from itk::LBFGSOptimizerBasev4< vnl_lbfgs >
double m_CostFunctionConvergenceFactor
 
double m_GradientConvergenceTolerance
 
double m_InfinityNormOfProjectedGradient
 
unsigned int m_MaximumNumberOfFunctionEvaluations
 
bool m_OptimizerInitialized
 
std::ostringstream m_StopConditionDescription
 
bool m_Trace
 
InternalOptimizerAutoPointer m_VnlOptimizer
 
- Protected Attributes inherited from itk::ObjectToObjectOptimizerBaseTemplate< double >
SizeValueType m_CurrentIteration
 
MeasureType m_CurrentMetricValue
 
bool m_DoEstimateScales
 
MetricTypePointer m_Metric
 
SizeValueType m_NumberOfIterations
 
ThreadIdType m_NumberOfThreads
 
ScalesType m_Scales
 
bool m_ScalesAreIdentity
 
ScalesEstimatorType::Pointer m_ScalesEstimator
 
ScalesType m_Weights
 
bool m_WeightsAreIdentity
 
- Protected Attributes inherited from itk::LightObject
AtomicInt< int > m_ReferenceCount
 

Member Typedef Documentation

typedef SmartPointer< const Self > itk::LBFGSOptimizerv4::ConstPointer

Definition at line 93 of file itkLBFGSOptimizerv4.h.

typedef vnl_lbfgs itk::LBFGSOptimizerv4::InternalOptimizerType
protected

Internal optimizer type.

Definition at line 141 of file itkLBFGSOptimizerv4.h.

typedef vnl_vector< double > itk::LBFGSOptimizerv4::InternalParametersType
protected

InternalParameters typedef.

Definition at line 138 of file itkLBFGSOptimizerv4.h.

typedef Superclass::MetricType itk::LBFGSOptimizerv4::MetricType

Definition at line 95 of file itkLBFGSOptimizerv4.h.

typedef Superclass::ParametersType itk::LBFGSOptimizerv4::ParametersType

Definition at line 96 of file itkLBFGSOptimizerv4.h.

typedef SmartPointer< Self > itk::LBFGSOptimizerv4::Pointer

Definition at line 92 of file itkLBFGSOptimizerv4.h.

typedef Superclass::ScalesType itk::LBFGSOptimizerv4::ScalesType

Definition at line 97 of file itkLBFGSOptimizerv4.h.

typedef LBFGSOptimizerv4 itk::LBFGSOptimizerv4::Self

Standard "Self" typedef.

Definition at line 90 of file itkLBFGSOptimizerv4.h.

typedef LBFGSOptimizerBasev4<vnl_lbfgs> itk::LBFGSOptimizerv4::Superclass

Definition at line 91 of file itkLBFGSOptimizerv4.h.

Constructor & Destructor Documentation

itk::LBFGSOptimizerv4::LBFGSOptimizerv4 ( )
protected
virtual itk::LBFGSOptimizerv4::~LBFGSOptimizerv4 ( )
overrideprotectedvirtual

Member Function Documentation

virtual::itk::LightObject::Pointer itk::LBFGSOptimizerv4::CreateAnother ( ) 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::Object.

virtual double itk::LBFGSOptimizerv4::GetDefaultStepLength ( ) const
virtual
virtual double itk::LBFGSOptimizerv4::GetLineSearchAccuracy ( ) const
virtual
virtual const char* itk::LBFGSOptimizerv4::GetNameOfClass ( ) const
virtual

Run-time type information (and related methods).

Reimplemented from itk::LBFGSOptimizerBasev4< vnl_lbfgs >.

static Pointer itk::LBFGSOptimizerv4::New ( )
static

Method for creation through the object factory.

virtual void itk::LBFGSOptimizerv4::PrintSelf ( std::ostream &  os,
Indent  indent 
) const
overrideprotectedvirtual

Print out internal state

Reimplemented from itk::LBFGSOptimizerBasev4< vnl_lbfgs >.

void itk::LBFGSOptimizerv4::SetDefaultStepLength ( double  stp)

Set/Get the default step size. This is a positive real number with a default value of 1.0 which determines the step size in the line search.

void itk::LBFGSOptimizerv4::SetLineSearchAccuracy ( double  tol)

Set/Get the line search accuracy. This is a positive real number with a default value of 0.9, which controls the accuracy of the line search. If the function and gradient evalutions are inexpensive with respect to the cost of the iterations it may be advantageous to set the value to a small value (say 0.1).

virtual void itk::LBFGSOptimizerv4::SetMetric ( MetricType *  metric)
overridevirtual

Plug in a Cost Function into the optimizer

Reimplemented from itk::LBFGSOptimizerBasev4< vnl_lbfgs >.

virtual void itk::LBFGSOptimizerv4::StartOptimization ( bool  doOnlyInitialization = false)
overridevirtual

Start optimization with an initial value.

Reimplemented from itk::LBFGSOptimizerBasev4< vnl_lbfgs >.

void itk::LBFGSOptimizerv4::VerboseOff ( )
void itk::LBFGSOptimizerv4::VerboseOn ( )

Member Data Documentation

double itk::LBFGSOptimizerv4::m_DefaultStepLength
private

Definition at line 148 of file itkLBFGSOptimizerv4.h.

double itk::LBFGSOptimizerv4::m_LineSearchAccuracy
private

Definition at line 147 of file itkLBFGSOptimizerv4.h.

bool itk::LBFGSOptimizerv4::m_Verbose
private

Definition at line 144 of file itkLBFGSOptimizerv4.h.

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