#include <itkCompositeTransform.h>

Inheritance diagram for itk::CompositeTransform< TParametersValueType, NDimensions >:

Collaboration diagram for itk::CompositeTransform< TParametersValueType, NDimensions >:

Detailed Description

template<typename TParametersValueType = double, unsigned int NDimensions = 3>
class itk::CompositeTransform< TParametersValueType, NDimensions >

This class contains a list of transforms and concatenates them by composition.

This class concatenates transforms in reverse queue order by means of composition: $ T_0 o T_1 = T_0(T_1(x)) $ Transforms are stored in a container (queue), in the following order: $ T_0, T_1, ... , T_N-1 $ Transforms are added via a single method, AddTransform(). This adds the transforms to the back of the queue. A single method for adding transforms is meant to simplify the interface and prevent errors. One use of the class is to optimize only a subset of included transforms.

The sub transforms are the same dimensionality as this class.

Example: A user wants to optimize two Affine transforms together, then add a Deformation Field (DF) transform, and optimize it separately. He first adds the two Affines, then runs the optimization and both Affines transforms are optimized. Next, he adds the DF transform and calls SetOnlyMostRecentTransformToOptimizeOn, which clears the optimization flags for both of the affine transforms, and leaves the flag set only for the DF transform, since it was the last transform added. Now he runs the optimization and only the DF transform is optimized, but the affines are included in the transformation during the optimization.

Optimization Flags: The m_TransformsToOptimize flags hold one flag for each transform in the queue, designating if each transform is to be used for optimization. Note that all transforms in the queue are applied in TransformPoint, regardless of these flags states'. The methods GetParameters, SetParameters, ComputeJacobianWithRespectToParameters, GetTransformCategory, GetFixedParameters, and SetFixedParameters all query these flags and include only those transforms whose corresponding flag is set. Their input or output is a concatenated array of all transforms set for use in optimization. The goal is to be able to optimize multiple transforms at once, while leaving other transforms fixed. See the above example.

Setting Optimization Flags: A transform's optimization flag is set when it is added to the queue, and remains set as other transforms are added. The methods SetNthTransformToOptimize* and SetAllTransformToOptimize* are used to set and clear flags arbitrarily. SetOnlyMostRecentTransformToOptimizeOn is a convenience method for setting only the most recently added transform for optimization, with the idea that this will be a common practice.

Indexing: The index values used in GetNthTransform and SetNthTransformToOptimize* and SetAllTransformToOptimize* follow the order in which transforms were added. Thus, the first transform added is at index 0, the next at index 1, etc.

Inverse: The inverse transform is created by retrieving the inverse from each sub transform and adding them to a composite transform in reverse order. The m_TransformsToOptimizeFlags is copied in reverse for the inverse.

Examples:: Examples/IO/TransformReadWrite.cxx, Examples/RegistrationITKv4/ImageRegistration1.cxx, Examples/RegistrationITKv4/MultiStageImageRegistration1.cxx, Examples/RegistrationITKv4/MultiStageImageRegistration2.cxx, SphinxExamples/src/Core/Transform/CopyACompositeTransform/Code.cxx, SphinxExamples/src/Registration/Common/Perform2DTranslationRegistrationWithMeanSquares/Code.cxx, and SphinxExamples/src/Registration/Metricsv4/PerformRegistrationOnVectorImages/Code.cxx.

Definition at line 87 of file itkCompositeTransform.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::FixedParametersType	FixedParametersType

typedef Superclass::FixedParametersValueType	FixedParametersValueType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputDiffusionTensor3DType	InputDiffusionTensor3DType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputSymmetricSecondRankTensorType	InputSymmetricSecondRankTensorType

typedef Superclass::InputVectorPixelType	InputVectorPixelType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::JacobianType	JacobianType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputDiffusionTensor3DType	OutputDiffusionTensor3DType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputSymmetricSecondRankTensorType	OutputSymmetricSecondRankTensorType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef CompositeTransform	Self

typedef MultiTransform < TParametersValueType, NDimensions, NDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

typedef Superclass::TransformQueueType	TransformQueueType

typedef std::deque< bool >	TransformsToOptimizeFlagsType

typedef Superclass::TransformType	TransformType

typedef Superclass::TransformTypePointer	TransformTypePointer

Public Types inherited from itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::DerivativeType	DerivativeType

typedef Superclass::FixedParametersType	FixedParametersType

typedef Superclass::FixedParametersValueType	FixedParametersValueType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputDiffusionTensor3DType	InputDiffusionTensor3DType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputSymmetricSecondRankTensorType	InputSymmetricSecondRankTensorType

typedef Superclass::InputVectorPixelType	InputVectorPixelType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef Superclass::InverseTransformBasePointer	InverseTransformBasePointer

typedef Superclass::JacobianType	JacobianType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputDiffusionTensor3DType	OutputDiffusionTensor3DType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputSymmetricSecondRankTensorType	OutputSymmetricSecondRankTensorType

typedef Superclass::OutputVectorPixelType	OutputVectorPixelType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef ParametersValueType	ScalarType

typedef MultiTransform	Self

typedef TransformType::InverseTransformBasePointer	SubTransformInverseTransformBasePointer

typedef Transform < TParametersValueType, NDimensions, NSubDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

typedef std::deque < TransformTypePointer >	TransformQueueType

typedef Transform < TParametersValueType, NSubDimensions, NSubDimensions >	TransformType

typedef TransformType::Pointer	TransformTypePointer

Public Types inherited from itk::Transform< TParametersValueType, NDimensions, NSubDimensions >
typedef SmartPointer< const Self >	ConstPointer

typedef Array < ParametersValueType >	DerivativeType

typedef Matrix< double, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	DirectionChangeMatrix

typedef Superclass::FixedParametersType	FixedParametersType

typedef Superclass::FixedParametersValueType	FixedParametersValueType

typedef CovariantVector < TParametersValueType, NInputDimensions >	InputCovariantVectorType

typedef DiffusionTensor3D < TParametersValueType >	InputDiffusionTensor3DType

typedef Matrix< double, itkGetStaticConstMacro(InputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	InputDirectionMatrix

typedef Point < TParametersValueType, NInputDimensions >	InputPointType

typedef SymmetricSecondRankTensor < TParametersValueType, NInputDimensions >	InputSymmetricSecondRankTensorType

typedef VariableLengthVector < TParametersValueType >	InputVectorPixelType

typedef Vector < TParametersValueType, NInputDimensions >	InputVectorType

typedef vnl_vector_fixed < TParametersValueType, NInputDimensions >	InputVnlVectorType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Transform < TParametersValueType, NOutputDimensions, NInputDimensions >	InverseTransformBaseType

typedef Array2D < ParametersValueType >	JacobianType

typedef Matrix < TParametersValueType, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(InputSpaceDimension)>	MatrixType

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef CovariantVector < TParametersValueType, NOutputDimensions >	OutputCovariantVectorType

typedef DiffusionTensor3D < TParametersValueType >	OutputDiffusionTensor3DType

typedef Matrix< double, itkGetStaticConstMacro(OutputSpaceDimension), itkGetStaticConstMacro(OutputSpaceDimension)>	OutputDirectionMatrix

typedef Point < TParametersValueType, NOutputDimensions >	OutputPointType

typedef SymmetricSecondRankTensor < TParametersValueType, NOutputDimensions >	OutputSymmetricSecondRankTensorType

typedef VariableLengthVector < TParametersValueType >	OutputVectorPixelType

typedef Vector < TParametersValueType, NOutputDimensions >	OutputVectorType

typedef vnl_vector_fixed < TParametersValueType, NOutputDimensions >	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef ParametersValueType	ScalarType

typedef Transform	Self

typedef TransformBaseTemplate < TParametersValueType >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

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

typedef OptimizerParameters < FixedParametersValueType >	FixedParametersType

typedef double	FixedParametersValueType

typedef IdentifierType	NumberOfParametersType

typedef OptimizerParameters < ParametersValueType >	ParametersType

typedef TParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TransformBaseTemplate	Self

typedef Object	Superclass

enum	TransformCategoryType { UnknownTransformCategory =0, Linear =1, BSpline =2, Spline =3, DisplacementField =4, VelocityField =5 }

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 void	ClearTransformQueue () override

virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &p, JacobianType &j) const override

virtual ::itk::LightObject::Pointer	CreateAnother () const

virtual void	FlattenTransformQueue ()

virtual const FixedParametersType &	GetFixedParameters () const override

bool	GetInverse (Self *inverse) const

virtual InverseTransformBasePointer	GetInverseTransform () const override

virtual const char *	GetNameOfClass () const

virtual bool	GetNthTransformToOptimize (SizeValueType i) const

virtual NumberOfParametersType	GetNumberOfFixedParameters (void) const override

virtual NumberOfParametersType	GetNumberOfLocalParameters (void) const override

virtual NumberOfParametersType	GetNumberOfParameters (void) const override

virtual const ParametersType &	GetParameters () const override

virtual TransformCategoryType	GetTransformCategory () const override

virtual const TransformsToOptimizeFlagsType &	GetTransformsToOptimizeFlags () const

virtual void	SetAllTransformsToOptimize (bool state)

virtual void	SetAllTransformsToOptimizeOff ()

virtual void	SetAllTransformsToOptimizeOn ()

virtual void	SetFixedParameters (const FixedParametersType &fixedParameters) override

virtual void	SetNthTransformToOptimize (SizeValueType i, bool state)

virtual void	SetNthTransformToOptimizeOff (SizeValueType i)

virtual void	SetNthTransformToOptimizeOn (SizeValueType i)

virtual void	SetOnlyMostRecentTransformToOptimizeOn ()

virtual void	SetParameters (const ParametersType &p) override

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const override

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const override

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &inputVector, const InputPointType &inputPoint) const override

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &inputVector, const InputPointType &inputPoint) const override

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor) const override

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor) const override

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &inputTensor, const InputPointType &inputPoint) const override

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &inputTensor, const InputPointType &inputPoint) const override

virtual OutputPointType	TransformPoint (const InputPointType &inputPoint) const override

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor) const override

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor) const override

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &inputTensor, const InputPointType &inputPoint) const override

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &inputTensor, const InputPointType &inputPoint) const override

virtual OutputVectorType	TransformVector (const InputVectorType &) const override

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &inputVector) const override

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &inputVector) const override

virtual OutputVectorType	TransformVector (const InputVectorType &inputVector, const InputPointType &inputPoint) const override

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &inputVector, const InputPointType &inputPoint) const override

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &inputVector, const InputPointType &inputPoint) const override

virtual void	UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0) override


virtual void	ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &outJacobian, JacobianType &jacobianWithRespectToPosition) const override

Public Member Functions inherited from itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >
virtual void	AddTransform (TransformType *t)

virtual void	AppendTransform (TransformType *t)

virtual const TransformType *	GetBackTransform () const

virtual const TransformType *	GetFrontTransform () const

bool	GetInverse (Self *inverse) const

virtual const TransformTypePointer	GetNthTransform (SizeValueType n) const

virtual const TransformType *	GetNthTransformConstPointer (const SizeValueType n) const

virtual TransformType *	GetNthTransformModifiablePointer (const SizeValueType n) const

virtual SizeValueType	GetNumberOfTransforms () const

virtual const TransformQueueType &	GetTransformQueue () const

virtual bool	IsLinear () const override

virtual bool	IsTransformQueueEmpty () const

virtual void	PrependTransform (TransformType *t)

virtual void	RemoveTransform ()

virtual void	SetFixedParameters (const FixedParametersType &fixedParameters) override

virtual void	SetParameters (const ParametersType &p) override

virtual void	UpdateTransformParameters (const DerivativeType &update, ScalarType factor=1.0) override

Public Member Functions inherited from itk::Transform< TParametersValueType, NDimensions, NSubDimensions >
virtual void	ComputeInverseJacobianWithRespectToPosition (const InputPointType &x, JacobianType &jacobian) const

virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &, JacobianType &) const =0

virtual void	ComputeJacobianWithRespectToParametersCachedTemporaries (const InputPointType &p, JacobianType &jacobian, JacobianType &) const

virtual void	ComputeJacobianWithRespectToPosition (const InputPointType &, JacobianType &) const

virtual void	CopyInFixedParameters (const FixedParametersValueType const begin, const FixedParametersValueType const end) override

virtual void	CopyInParameters (const ParametersValueType const begin, const ParametersValueType const end) override

unsigned int	GetInputSpaceDimension (void) const override

bool	GetInverse (Self *) const

unsigned int	GetOutputSpaceDimension (void) const override

virtual std::string	GetTransformTypeAsString () const override

	itkCloneMacro (Self)

virtual void	SetParametersByValue (const ParametersType &p) override

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformCovariantVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &) const

virtual OutputDiffusionTensor3DType	TransformDiffusionTensor3D (const InputDiffusionTensor3DType &tensor, const InputPointType &point) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformDiffusionTensor3D (const InputVectorPixelType &tensor, const InputPointType &point) const

virtual OutputPointType	TransformPoint (const InputPointType &) const =0

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &tensor, const InputPointType &point) const

virtual OutputSymmetricSecondRankTensorType	TransformSymmetricSecondRankTensor (const InputSymmetricSecondRankTensorType &) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformSymmetricSecondRankTensor (const InputVectorPixelType &tensor, const InputPointType &point) const

virtual OutputVectorType	TransformVector (const InputVectorType &) const

virtual OutputVectorType	TransformVector (const InputVectorType &vector, const InputPointType &point) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &vector, const InputPointType &point) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &) const

virtual OutputVectorPixelType	TransformVector (const InputVectorPixelType &vector, const InputPointType &point) const

virtual void	UpdateTransformParameters (const DerivativeType &update, ParametersValueType factor=1.0)

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 ()

Static Public Attributes

static const unsigned int	InputDimension = NDimensions

static const unsigned int	OutputDimension = NDimensions

Static Public Attributes inherited from itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >
static const unsigned int	SubInputDimension

static const unsigned int	SubOutputDimension

static const unsigned int	InputDimension

static const unsigned int	OutputDimension

Static Public Attributes inherited from itk::Transform< TParametersValueType, NDimensions, NSubDimensions >
static const unsigned int	InputSpaceDimension

static const unsigned int	OutputSpaceDimension

Protected Member Functions
	CompositeTransform ()

TransformQueueType &	GetTransformsToOptimizeQueue () const

virtual LightObject::Pointer	InternalClone () const override

virtual void	PopBackTransform () override

virtual void	PopFrontTransform () override

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

virtual void	PushBackTransform (TransformTypePointer t) override

virtual void	PushFrontTransform (TransformTypePointer t) override

virtual	~CompositeTransform () override

Protected Member Functions inherited from itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >
	MultiTransform ()

virtual	~MultiTransform () override

Protected Member Functions inherited from itk::Transform< TParametersValueType, NDimensions, NSubDimensions >
OutputDiffusionTensor3DType	PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType, const JacobianType) const

	Transform ()

	Transform (NumberOfParametersType NumberOfParameters)

virtual	~Transform () override

Protected Member Functions inherited from itk::TransformBaseTemplate< TParametersValueType >
	TransformBaseTemplate ()

virtual	~TransformBaseTemplate () 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
	LightObject ()

virtual void	PrintHeader (std::ostream &os, Indent indent) const

virtual void	PrintTrailer (std::ostream &os, Indent indent) const

virtual	~LightObject ()

Protected Attributes
TransformsToOptimizeFlagsType	m_TransformsToOptimizeFlags

TransformQueueType	m_TransformsToOptimizeQueue

Protected Attributes inherited from itk::MultiTransform< TParametersValueType, NDimensions, NDimensions >
ModifiedTimeType	m_LocalParametersUpdateTime

NumberOfParametersType	m_NumberOfLocalParameters

TransformQueueType	m_TransformQueue

Protected Attributes inherited from itk::Transform< TParametersValueType, NDimensions, NSubDimensions >
DirectionChangeMatrix	m_DirectionChange

FixedParametersType	m_FixedParameters

ParametersType	m_Parameters

Protected Attributes inherited from itk::LightObject
AtomicInt< int >	m_ReferenceCount

Private Attributes
ModifiedTimeType	m_PreviousTransformsToOptimizeUpdateTime