#include <itkElasticBodySplineKernelTransform.h>

Inheritance diagram for itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >:

Collaboration diagram for itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >:

Detailed Description

template<class TScalarType = double, unsigned int NDimensions = 3>
class itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >

This class defines the elastic body spline (EBS) transformation.

This class defines the elastic body spline (EBS) transformation. It is implemented in as straightforward a manner as possible from the IEEE TMI paper by Davis, Khotanzad, Flamig, and Harms, Vol. 16 No. 3 June 1997 Taken from the paper: The EBS "is based on a physical model of a homogeneous, isotropic, three-dimensional elastic body. The model can approximate the way that some physical objects deform".

Definition at line 43 of file itkElasticBodySplineKernelTransform.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::JacobianType	JacobianType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::ParametersType	ParametersType

typedef SmartPointer< Self >	Pointer

typedef Superclass::ScalarType	ScalarType

typedef ElasticBodySplineKernelTransform	Self

typedef KernelTransform < TScalarType, NDimensions >	Superclass

Public Types inherited from itk::KernelTransform< TScalarType, NDimensions >
typedef vnl_matrix_fixed < TScalarType, NDimensions, NDimensions >	AMatrixType

typedef vnl_vector_fixed < TScalarType, NDimensions >	BMatrixType

typedef vnl_matrix_fixed < TScalarType, NDimensions, 1 >	ColumnMatrixType

typedef SmartPointer< const Self >	ConstPointer

typedef vnl_matrix< TScalarType >	DMatrixType

typedef vnl_matrix_fixed < TScalarType, NDimensions, NDimensions >	GMatrixType

typedef vnl_matrix_fixed < TScalarType, NDimensions, NDimensions >	IMatrixType

typedef Superclass::InputCovariantVectorType	InputCovariantVectorType

typedef Superclass::InputPointType	InputPointType

typedef Superclass::InputVectorType	InputVectorType

typedef Superclass::InputVnlVectorType	InputVnlVectorType

typedef Superclass::JacobianType	JacobianType

typedef vnl_matrix< TScalarType >	KMatrixType

typedef vnl_matrix< TScalarType >	LMatrixType

typedef Superclass::OutputCovariantVectorType	OutputCovariantVectorType

typedef Superclass::OutputPointType	OutputPointType

typedef Superclass::OutputVectorType	OutputVectorType

typedef Superclass::OutputVnlVectorType	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef vnl_matrix< TScalarType >	PMatrixType

typedef SmartPointer< Self >	Pointer

typedef PointSetType::PointIdentifier	PointIdentifier

typedef PointSetType::PointsContainerConstIterator	PointsConstIterator

typedef PointSetType::PointsContainer	PointsContainer

typedef PointSetType::Pointer	PointSetPointer

typedef DefaultStaticMeshTraits < TScalarType, NDimensions, NDimensions, TScalarType, TScalarType >	PointSetTraitsType

typedef PointSet < InputPointType, NDimensions, PointSetTraitsType >	PointSetType

typedef PointSetType::PointsContainerIterator	PointsIterator

typedef vnl_matrix_fixed < TScalarType, 1, NDimensions >	RowMatrixType

typedef Superclass::ScalarType	ScalarType

typedef KernelTransform	Self

typedef Transform< TScalarType, NDimensions, NDimensions >	Superclass

typedef Superclass::TransformCategoryType	TransformCategoryType

typedef VectorSetType::Pointer	VectorSetPointer

typedef itk::VectorContainer < SizeValueType, InputVectorType >	VectorSetType

typedef vnl_matrix< TScalarType >	WMatrixType

typedef vnl_matrix< TScalarType >	YMatrixType

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

typedef Array < ParametersValueType >	DerivativeType

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

typedef CovariantVector < TScalarType, NInputDimensions >	InputCovariantVectorType

typedef DiffusionTensor3D < TScalarType >	InputDiffusionTensor3DType

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

typedef Point< TScalarType, NInputDimensions >	InputPointType

typedef SymmetricSecondRankTensor < TScalarType, NInputDimensions >	InputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalarType >	InputVectorPixelType

typedef Vector< TScalarType, NInputDimensions >	InputVectorType

typedef vnl_vector_fixed < TScalarType, NInputDimensions >	InputVnlVectorType

typedef InverseTransformBaseType::Pointer	InverseTransformBasePointer

typedef Transform< TScalarType, NOutputDimensions, NInputDimensions >	InverseTransformBaseType

typedef Array2D < ParametersValueType >	JacobianType

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

typedef Superclass::NumberOfParametersType	NumberOfParametersType

typedef CovariantVector < TScalarType, NOutputDimensions >	OutputCovariantVectorType

typedef DiffusionTensor3D < TScalarType >	OutputDiffusionTensor3DType

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

typedef Point< TScalarType, NOutputDimensions >	OutputPointType

typedef SymmetricSecondRankTensor < TScalarType, NOutputDimensions >	OutputSymmetricSecondRankTensorType

typedef VariableLengthVector < TScalarType >	OutputVectorPixelType

typedef Vector< TScalarType, NOutputDimensions >	OutputVectorType

typedef vnl_vector_fixed < TScalarType, NOutputDimensions >	OutputVnlVectorType

typedef Superclass::ParametersType	ParametersType

typedef Superclass::ParametersValueType	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TScalarType	ScalarType

typedef Transform	Self

typedef TransformBase	Superclass

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

typedef IdentifierType	NumberOfParametersType

typedef OptimizerParameters < ParametersValueType >	ParametersType

typedef double	ParametersValueType

typedef SmartPointer< Self >	Pointer

typedef TransformBase	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 ::itk::LightObject::Pointer	CreateAnother (void) const

virtual TScalarType	GetAlpha () const

virtual const char *	GetNameOfClass () const

virtual void	SetAlpha (TScalarType _arg)

Public Member Functions inherited from itk::KernelTransform< TScalarType, NDimensions >
virtual void	ComputeJacobianWithRespectToParameters (const InputPointType &p, JacobianType &jacobian) const

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

void	ComputeWMatrix (void)

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

virtual VectorSetType *	GetDisplacements ()

virtual const ParametersType &	GetFixedParameters (void) const

virtual const ParametersType &	GetParameters (void) const

virtual PointSetType *	GetSourceLandmarks ()

virtual PointSetType *	GetTargetLandmarks ()

virtual TransformCategoryType	GetTransformCategory () const

virtual void	SetFixedParameters (const ParametersType &)

virtual void	SetParameters (const ParametersType &)

virtual void	SetSourceLandmarks (PointSetType *)

virtual void	SetTargetLandmarks (PointSetType *)

virtual OutputPointType	TransformPoint (const InputPointType &thisPoint) const

virtual OutputVnlVectorType	TransformVector (const InputVnlVectorType &) const

virtual void	UpdateParameters (void) const

virtual OutputVectorType	TransformVector (const InputVectorType &) const

virtual OutputCovariantVectorType	TransformCovariantVector (const InputCovariantVectorType &) const

virtual void	SetStiffness (double _arg)

virtual double	GetStiffness () const

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

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

unsigned int	GetInputSpaceDimension (void) const

bool	GetInverse (Self *) const

virtual InverseTransformBasePointer	GetInverseTransform () const

virtual NumberOfParametersType	GetNumberOfLocalParameters (void) const

virtual NumberOfParametersType	GetNumberOfParameters (void) const

unsigned int	GetOutputSpaceDimension (void) const

virtual std::string	GetTransformTypeAsString () const

virtual bool	IsLinear () const

	itkCloneMacro (Self)

virtual void	SetFixedParameters (const ParametersType &)=0

virtual void	SetParameters (const ParametersType &)=0

virtual void	SetParametersByValue (const ParametersType &p)

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, TScalarType factor=1.0)

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

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::KernelTransform< TScalarType, NDimensions >
static Pointer	New ()

Static Public Attributes
static const unsigned int	SpaceDimension = Superclass::SpaceDimension

Static Public Attributes inherited from itk::KernelTransform< TScalarType, NDimensions >
static const unsigned int	SpaceDimension = NDimensions

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

static const unsigned int	OutputSpaceDimension

Protected Types
typedef Superclass::GMatrixType	GMatrixType

Protected Member Functions
virtual void	ComputeG (const InputVectorType &landmarkVector, GMatrixType &gmatrix) const

	ElasticBodySplineKernelTransform ()

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

virtual	~ElasticBodySplineKernelTransform ()

Protected Member Functions inherited from itk::KernelTransform< TScalarType, NDimensions >
void	ComputeD ()

virtual void	ComputeDeformationContribution (const InputPointType &inputPoint, OutputPointType &result) const

virtual void	ComputeG (const InputVectorType &landmarkVector, GMatrixType &gmatrix) const

void	ComputeK ()

void	ComputeL ()

void	ComputeP ()

virtual const GMatrixType &	ComputeReflexiveG (PointsIterator) const

void	ComputeY ()

	KernelTransform ()

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

void	ReorganizeW (void)

virtual	~KernelTransform ()

Protected Member Functions inherited from itk::Transform< TScalarType, NDimensions, NDimensions >
virtual LightObject::Pointer	InternalClone () const

OutputDiffusionTensor3DType	PreservationOfPrincipalDirectionDiffusionTensor3DReorientation (const InputDiffusionTensor3DType, const JacobianType) const

	Transform ()

	Transform (NumberOfParametersType NumberOfParameters)

virtual	~Transform ()

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

virtual	~TransformBase ()

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

bool	PrintObservers (std::ostream &os, Indent indent) const

virtual void	SetTimeStamp (const TimeStamp &time)

virtual	~Object ()

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
TScalarType	m_Alpha

Protected Attributes inherited from itk::KernelTransform< TScalarType, NDimensions >
AMatrixType	m_AMatrix

BMatrixType	m_BVector

VectorSetPointer	m_Displacements

DMatrixType	m_DMatrix

GMatrixType	m_GMatrix

IMatrixType	m_I

KMatrixType	m_KMatrix

LMatrixType	m_LMatrix

PMatrixType	m_PMatrix

PointSetPointer	m_SourceLandmarks

double	m_Stiffness

PointSetPointer	m_TargetLandmarks

WMatrixType	m_WMatrix

bool	m_WMatrixComputed

YMatrixType	m_YMatrix

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

ParametersType	m_FixedParameters

ParametersType	m_Parameters

Private Member Functions
	ElasticBodySplineKernelTransform (const Self &)

void	operator= (const Self &)

Member Typedef Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef SmartPointer< const Self > itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::ConstPointer

Definition at line 53 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::GMatrixType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::GMatrixType

protected

Definition at line 93 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::InputCovariantVectorType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::InputCovariantVectorType

Definition at line 85 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::InputPointType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::InputPointType

Definition at line 79 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::InputVectorType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::InputVectorType

Definition at line 83 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::JacobianType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::JacobianType

Jacobian type.

Definition at line 68 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::OutputCovariantVectorType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::OutputCovariantVectorType

Definition at line 86 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::OutputPointType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::OutputPointType

Definition at line 82 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::OutputVectorType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::OutputVectorType

Definition at line 84 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::ParametersType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::ParametersType

Parameters type.

Definition at line 65 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef SmartPointer< Self > itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::Pointer

Definition at line 52 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef Superclass::ScalarType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::ScalarType

Scalar type.

Definition at line 59 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef ElasticBodySplineKernelTransform itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::Self

Standard class typedefs.

Definition at line 48 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

typedef KernelTransform< TScalarType, NDimensions > itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::Superclass

Definition at line 50 of file itkElasticBodySplineKernelTransform.h.

Constructor & Destructor Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::ElasticBodySplineKernelTransform ( )

protected

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::~ElasticBodySplineKernelTransform ( )

protectedvirtual

template<class TScalarType = double, unsigned int NDimensions = 3>

itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::ElasticBodySplineKernelTransform ( const Self & )

private

Member Function Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual void itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::ComputeG	(	const InputVectorType &	landmarkVector,
		GMatrixType &	gmatrix
	)		const

protectedvirtual

Compute G(x) For the elastic body spline, this is: $ G(x) = [alpha*r(x)^2*I - 3*x*x']*r(x) $ $G(x) = [\alpha*r(x)^2*I - 3*x*x']*r(x)$ where $\alpha = 12 ( 1 - \nu ) - 1$ $\nu$ is Poisson's Ratio $ r(x) = Euclidean norm = sqrt[x1^2 + x2^2 + x3^2] $

$r(x) = \sqrt{ x_1^2 + x_2^2 + x_3^2 }$

I = identity matrix

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual::itk::LightObject::Pointer itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::CreateAnother ( void ) 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.

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual TScalarType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::GetAlpha ( ) const

virtual

Get alpha

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual const char* itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

Reimplemented from itk::KernelTransform< TScalarType, NDimensions >.

template<class TScalarType = double, unsigned int NDimensions = 3>

static Pointer itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::New ( )

static

New macro for creation of through a Smart Pointer

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::operator= ( const Self & )

private

template<class TScalarType = double, unsigned int NDimensions = 3>

void itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

protectedvirtual

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::Object.

template<class TScalarType = double, unsigned int NDimensions = 3>

virtual void itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::SetAlpha ( TScalarType _arg )

virtual

Set alpha. Alpha is related to Poisson's Ratio ( $\nu$ ) as $\alpha = 12 ( 1 - \nu ) - 1$

Member Data Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>

TScalarType itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::m_Alpha

protected

alpha, Alpha is related to Poisson's Ratio ( $\nu$ ) as $\alpha = 12 ( 1 - \nu ) - 1$

Definition at line 110 of file itkElasticBodySplineKernelTransform.h.

template<class TScalarType = double, unsigned int NDimensions = 3>

const unsigned int itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >::SpaceDimension = Superclass::SpaceDimension

static

Dimension of the domain space.

Definition at line 71 of file itkElasticBodySplineKernelTransform.h.

The documentation for this class was generated from the following file:

itkElasticBodySplineKernelTransform.h

Detailed Description

template<class TScalarType = double, unsigned int NDimensions = 3> class itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Types

Protected Member Functions

Protected Attributes

Private Member Functions

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class TScalarType = double, unsigned int NDimensions = 3>
class itk::ElasticBodySplineKernelTransform< TScalarType, NDimensions >