#include <itkBSplineScatteredDataPointSetToImageFilter.h>

Inheritance diagram for itk::BSplineScatteredDataPointSetToImageFilter< TInputPointSet, TOutputImage >:

Collaboration diagram for itk::BSplineScatteredDataPointSetToImageFilter< TInputPointSet, TOutputImage >:

Detailed Description

template<class TInputPointSet, class TOutputImage>
class itk::BSplineScatteredDataPointSetToImageFilter< TInputPointSet, TOutputImage >

Image filter which provides a B-spline output approximation.

Given an n-D image with scattered data, this filter finds a fast approximation to that irregularly spaced data using uniform B-splines. The traditional method of inverting the observation matrix to find a least-squares fit is made obsolete. Therefore, memory issues are not a concern and inverting large matrices is not applicable. In addition, this allows fitting to be multi-threaded. This class generalizes from Lee's original paper to encompass n-D data in m-D parametric space and any feasible B-spline order as well as the option of specifying a confidence value for each point.

In addition to specifying the input point set, one must specify the number of control points. The specified number of control points must be greater than m_SplineOrder. If one wishes to use the multilevel component of this algorithm, one must also specify the number of levels in the hierarchy. If this is desired, the number of control points becomes the number of control points for the coarsest level. The algorithm then increases the number of control points at each level so that the B-spline n-D grid is refined to twice the previous level.

There are two parts to fitting scattered data: the parameterization assignment problem and the fitting problem given a parameterization. This filter only addresses the second problem in that the user must provide a parametric value for each scattered datum. Different parametric assignment schemes result in different B-spline object outputs.

This filter is general in that it accepts n-D scattered data in m-D parametric dimensions. Input to this filter is an m-D point set with a Vector data type of n dimensions. This means that the parametric values are stored in the points container of the point set whereas the scattered data are stored in the points data container of the point set.

Typical B-spline objects include curves, which have a parametric dimension of 1 and a data dimension of 2 or 3 (depending on the space in which the curve resides) and deformation fields which commonly have parametric and data dimensions of 2 or 3 (again depending on the space of the field). As an example, a curve through a set of 2D points has data dimension 2 and parametric dimension 1. The univariate curve could be represented as: <x(u),y(u)> Another example is a 3D deformation of 3D points, which has parametric dimension 3 and data dimension 3 and can be represented as: <dx(u,v,w), dy(u,v,w), dz(u,v,w)>. However, as mentioned before, the code is general such that, if the user wanted, she could model a time varying 3-D displacement field which resides in 4-D space as <dx(u, v, w, t), dy(u, v, w, t), dz(u, v, w, t)>.

The output is an image defining the sampled B-spline parametric domain where each pixel houses the sampled B-spline object value. For a curve fit to 3-D points, the output is a 1-D image where each voxel contains a vector with the approximated (x,y,z) location. The continuous, finite, rectilinear domain (as well as the sampling rate) is specified via the combination of the SetSpacing() and SetSize() functions. For a 2-D deformation on 2-D points, the output is a 2-D image where each voxel contains the approximated (dx, dy) vector.

The parameterization must be specified using SetPoint, where the actual coordinates of the point are set via SetPointData. For example, to compute a spline through the (ordered) 2D points (5,6) and (7,8), you should use:

typedef itk::Vector< float, 2 > DataType;
PointSetType::PointType param0;
param0[0] = 0.0;
DataType p0;
p0[0] =  10.0; p0[1]= 10.0;
pointSet->SetPoint(0, param0);
pointSet->SetPointData( 0, p0 );
PointSetType::PointType param1;
param1[0] = 1.0;
DataType p1;
p1[0] =  80.0; p1[1]= 50.0;
pointSet->SetPoint(1, param1);
pointSet->SetPointData( 1, p1 );

Author: Nicholas J. Tustison

This code was contributed in the Insight Journal paper: "N-D C^k B-Spline Scattered Data Approximation" by Nicholas J. Tustison, James C. Gee http://hdl.handle.net/1926/140 http://www.insight-journal.org/browse/publication/57

REFERENCE: S. Lee, G. Wolberg, and S. Y. Shin, "Scattered Data Interpolation with Multilevel B-Splines", IEEE Transactions on Visualization and Computer Graphics, 3(3):228-244, 1997.

REFERENCE: N.J. Tustison and J.C. Gee, "Generalized n-D C^k Scattered Data Approximation with Confidence Values", Proceedings of the MIAR conference, August 2006.

Definition at line 129 of file itkBSplineScatteredDataPointSetToImageFilter.h.

Public Types
typedef SmartPointer< const Self >	ConstPointer

typedef TOutputImage	ImageType

typedef ImageType::IndexType	IndexType

typedef BSplineKernelFunction< 0 >	KernelOrder0Type

typedef BSplineKernelFunction< 1 >	KernelOrder1Type

typedef BSplineKernelFunction< 2 >	KernelOrder2Type

typedef BSplineKernelFunction< 3 >	KernelOrder3Type

typedef CoxDeBoorBSplineKernelFunction< 3 >	KernelType

typedef ImageType::PixelType	PixelType

typedef PointSetType::PointDataContainer	PointDataContainerType

typedef PointSetType::PixelType	PointDataType

typedef SmartPointer< Self >	Pointer

typedef PointSetType::Pointer	PointSetPointer

typedef TInputPointSet	PointSetType

typedef PointSetType::PointType	PointType

typedef float	RealType

typedef ImageType::RegionType	RegionType

typedef BSplineScatteredDataPointSetToImageFilter	Self

typedef ImageType::SizeType	SizeType

typedef PointSetToImageFilter < TInputPointSet, TOutputImage >	Superclass

typedef VectorContainer < unsigned, RealType >	WeightsContainerType


typedef Image< PointDataType, itkGetStaticConstMacro(ImageDimension)>	PointDataImageType

typedef Image< RealType, itkGetStaticConstMacro(ImageDimension)>	RealImageType

typedef RealImageType::Pointer	RealImagePointer

typedef PointDataImageType::Pointer	PointDataImagePointer

typedef FixedArray< unsigned, itkGetStaticConstMacro(ImageDimension)>	ArrayType

Public Types inherited from itk::PointSetToImageFilter< TInputPointSet, TOutputImage >
typedef SmartPointer< const Self >	ConstPointer

typedef TOutputImage::DirectionType	DirectionType

typedef InputPointSetType::ConstPointer	InputPointSetConstPointer

typedef InputPointSetType::Pointer	InputPointSetPointer

typedef TInputPointSet	InputPointSetType

typedef OutputImageType::Pointer	OutputImagePointer

typedef Superclass::OutputImageRegionType	OutputImageRegionType

typedef TOutputImage	OutputImageType

typedef SmartPointer< Self >	Pointer

typedef TOutputImage::PointType	PointType

typedef PointSetToImageFilter	Self

typedef TOutputImage::SizeType	SizeType

typedef TOutputImage::SpacingType	SpacingType

typedef ImageSource< TOutputImage >	Superclass

typedef OutputImageType::ValueType	ValueType

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

typedef Superclass::DataObjectIdentifierType	DataObjectIdentifierType

typedef DataObject::Pointer	DataObjectPointer

typedef Superclass::DataObjectPointerArraySizeType	DataObjectPointerArraySizeType

typedef OutputImageType::PixelType	OutputImagePixelType

typedef OutputImageType::Pointer	OutputImagePointer

typedef OutputImageType::RegionType	OutputImageRegionType

typedef TOutputImage	OutputImageType

typedef SmartPointer< Self >	Pointer

typedef ImageSource	Self

typedef ProcessObject	Superclass

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

typedef DataObject::DataObjectIdentifierType	DataObjectIdentifierType

typedef DataObject::Pointer	DataObjectPointer

typedef std::vector < DataObjectPointer >	DataObjectPointerArray

typedef DataObjectPointerArray::size_type	DataObjectPointerArraySizeType

typedef std::vector < DataObjectIdentifierType >	NameArray

typedef SmartPointer< Self >	Pointer

typedef ProcessObject	Self

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 (void) const

virtual void	GenerateOutputImageOff ()

virtual void	GenerateOutputImageOn ()

virtual const ArrayType &	GetCloseDimension ()

virtual const ArrayType &	GetCurrentNumberOfControlPoints ()

virtual const bool &	GetGenerateOutputImage ()

virtual const ArrayType &	GetNumberOfControlPoints ()

virtual const ArrayType &	GetNumberOfLevels ()

virtual PointDataImagePointer	GetPhiLattice () const

virtual const ArrayType &	GetSplineOrder ()

virtual void	SetCloseDimension (ArrayType _arg)

virtual void	SetGenerateOutputImage (bool _arg)

virtual void	SetNumberOfControlPoints (ArrayType _arg)

void	SetNumberOfLevels (unsigned int)

void	SetNumberOfLevels (const ArrayType &)

void	SetPointWeights (WeightsContainerType *weights)

void	SetSplineOrder (unsigned int)

void	SetSplineOrder (const ArrayType &)

Public Member Functions inherited from itk::PointSetToImageFilter< TInputPointSet, TOutputImage >
const InputPointSetType *	GetInput (void)

const InputPointSetType *	GetInput (unsigned int idx)

virtual const char *	GetNameOfClass () const

virtual const PointType &	GetOrigin ()

virtual const SpacingType &	GetSpacing ()

virtual void	SetInput (const InputPointSetType *pointset)

virtual void	SetInput (unsigned int, const InputPointSetType *pointset)

virtual void	SetOrigin (const float *origin)

virtual void	SetSpacing (const float *spacing)

virtual void	SetSpacing (SpacingType _arg)

virtual void	SetSpacing (const double *spacing)

virtual void	SetDirection (DirectionType _arg)

virtual const DirectionType &	GetDirection ()

virtual void	SetOrigin (PointType _arg)

virtual void	SetOrigin (const double *origin)

virtual void	SetInsideValue (ValueType _arg)

virtual ValueType	GetInsideValue () const

virtual void	SetOutsideValue (ValueType _arg)

virtual ValueType	GetOutsideValue () const

virtual void	SetSize (SizeType _arg)

virtual SizeType	GetSize () const

Public Member Functions inherited from itk::ImageSource< TOutputImage >
OutputImageType *	GetOutput (unsigned int idx)

virtual void	GraftNthOutput (unsigned int idx, DataObject *output)

virtual void	GraftOutput (DataObject *output)

virtual void	GraftOutput (const DataObjectIdentifierType &key, DataObject *output)

OutputImageType *	GetOutput (void)

const OutputImageType *	GetOutput (void) const

virtual ProcessObject::DataObjectPointer	MakeOutput (ProcessObject::DataObjectPointerArraySizeType idx)

Public Member Functions inherited from itk::ProcessObject
virtual void	AbortGenerateDataOff ()

virtual void	AbortGenerateDataOn ()

virtual void	EnlargeOutputRequestedRegion (DataObject *)

virtual const bool &	GetAbortGenerateData ()

NameArray	GetInputNames () const

MultiThreader *	GetMultiThreader () const

DataObjectPointerArraySizeType	GetNumberOfIndexedInputs () const

DataObjectPointerArraySizeType	GetNumberOfInputs () const

DataObjectPointerArraySizeType	GetNumberOfOutputs () const

virtual DataObjectPointerArraySizeType	GetNumberOfValidRequiredInputs () const

NameArray	GetOutputNames () const

virtual const float &	GetProgress ()

NameArray	GetRequiredInputNames () const

bool	HasInput (const DataObjectIdentifierType &key) const

bool	HasOutput (const DataObjectIdentifierType &key) const

virtual DataObjectPointer	MakeOutput (const DataObjectIdentifierType &)

virtual void	PrepareOutputs ()

virtual void	PropagateRequestedRegion (DataObject *output)

virtual void	ResetPipeline ()

virtual void	SetAbortGenerateData (bool _arg)

virtual void	SetProgress (float _arg)

virtual void	Update ()

virtual void	UpdateLargestPossibleRegion ()

virtual void	UpdateOutputData (DataObject *output)

virtual void	UpdateOutputInformation ()

void	UpdateProgress (float amount)

DataObjectPointerArray	GetInputs ()

DataObjectPointerArray	GetOutputs ()

DataObjectPointerArray	GetIndexedInputs ()

DataObjectPointerArray	GetIndexedOutputs ()

DataObjectPointerArraySizeType	GetNumberOfIndexedOutputs () const

virtual void	SetReleaseDataFlag (bool flag)

virtual bool	GetReleaseDataFlag () const

void	ReleaseDataFlagOn ()

void	ReleaseDataFlagOff ()

virtual void	SetReleaseDataBeforeUpdateFlag (bool _arg)

virtual const bool &	GetReleaseDataBeforeUpdateFlag ()

virtual void	ReleaseDataBeforeUpdateFlagOn ()

virtual void	ReleaseDataBeforeUpdateFlagOff ()

virtual void	SetNumberOfThreads (ThreadIdType _arg)

virtual const ThreadIdType &	GetNumberOfThreads ()

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 (void)

const MetaDataDictionary &	GetMetaDataDictionary (void) 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

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag)

void	SetDebug (bool debugFlag) const

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

virtual void	SetReferenceCount (int)

virtual void	UnRegister () 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::PointSetToImageFilter< TInputPointSet, TOutputImage >
static Pointer	New ()

Static Public Attributes
static const unsigned int	ImageDimension = TOutputImage::ImageDimension

Static Public Attributes inherited from itk::PointSetToImageFilter< TInputPointSet, TOutputImage >
static const unsigned int	InputPointSetDimension = InputPointSetType::PointDimension

static const unsigned int	OutputImageDimension = TOutputImage::ImageDimension

Static Public Attributes inherited from itk::ImageSource< TOutputImage >
static const unsigned int	OutputImageDimension = TOutputImage::ImageDimension

Protected Member Functions
void	AfterThreadedGenerateData ()

void	BeforeThreadedGenerateData ()

	BSplineScatteredDataPointSetToImageFilter ()

void	GenerateData ()

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

unsigned int	SplitRequestedRegion (unsigned int, unsigned int, RegionType &)

void	ThreadedGenerateData (const RegionType &, ThreadIdType)

virtual	~BSplineScatteredDataPointSetToImageFilter ()

Protected Member Functions inherited from itk::PointSetToImageFilter< TInputPointSet, TOutputImage >
virtual void	GenerateOutputInformation ()

	PointSetToImageFilter ()

	~PointSetToImageFilter ()

Protected Member Functions inherited from itk::ImageSource< TOutputImage >
virtual void	AllocateOutputs ()

virtual const ImageRegionSplitterBase *	GetImageRegionSplitter (void) const

	ImageSource ()

virtual unsigned int	SplitRequestedRegion (unsigned int i, unsigned int num, OutputImageRegionType &splitRegion)

virtual void	ThreadedGenerateData (const OutputImageRegionType &outputRegionForThread, ThreadIdType threadId)

virtual	~ImageSource ()

Protected Member Functions inherited from itk::ProcessObject
virtual void	AddInput (DataObject *input)

virtual void	AddOutput (DataObject *output)

virtual void	CacheInputReleaseDataFlags ()

virtual void	GenerateInputRequestedRegion ()

virtual void	GenerateOutputRequestedRegion (DataObject *output)

virtual const DataObjectPointerArraySizeType &	GetNumberOfRequiredOutputs ()

bool	IsIndexedInputName (const DataObjectIdentifierType &) const

bool	IsIndexedOutputName (const DataObjectIdentifierType &) const

	itkLegacyMacro (virtual void RemoveOutput(DataObject *output))

	itkLegacyMacro (void SetNumberOfOutputs(DataObjectPointerArraySizeType num))

	itkLegacyMacro (virtual void RemoveInput(DataObject *input))

	itkLegacyMacro (void SetNumberOfInputs(DataObjectPointerArraySizeType num))

DataObjectPointerArraySizeType	MakeIndexFromInputName (const DataObjectIdentifierType &name) const

DataObjectPointerArraySizeType	MakeIndexFromOutputName (const DataObjectIdentifierType &name) const

DataObjectIdentifierType	MakeNameFromInputIndex (DataObjectPointerArraySizeType idx) const

DataObjectIdentifierType	MakeNameFromOutputIndex (DataObjectPointerArraySizeType idx) const

	ProcessObject ()

virtual void	PropagateResetPipeline ()

virtual void	ReleaseInputs ()

virtual void	RemoveInput (const DataObjectIdentifierType &key)

virtual void	RemoveInput (DataObjectPointerArraySizeType)

virtual void	RemoveOutput (const DataObjectIdentifierType &key)

virtual void	RemoveOutput (DataObjectPointerArraySizeType idx)

virtual void	RestoreInputReleaseDataFlags ()

virtual void	SetInput (const DataObjectIdentifierType &key, DataObject *input)

virtual void	SetNthInput (DataObjectPointerArraySizeType num, DataObject *input)

virtual void	SetNthOutput (DataObjectPointerArraySizeType num, DataObject *output)

void	SetNumberOfIndexedInputs (DataObjectPointerArraySizeType num)

void	SetNumberOfIndexedOutputs (DataObjectPointerArraySizeType num)

virtual void	SetNumberOfRequiredOutputs (DataObjectPointerArraySizeType _arg)

virtual void	SetOutput (const DataObjectIdentifierType &key, DataObject *output)

virtual void	SetPrimaryInput (DataObject *input)

virtual void	SetPrimaryOutput (DataObject *output)

virtual void	VerifyInputInformation ()

virtual void	VerifyPreconditions ()

	~ProcessObject ()

DataObject *	GetInput (const DataObjectIdentifierType &key)

const DataObject *	GetInput (const DataObjectIdentifierType &key) const

DataObject *	GetInput (DataObjectPointerArraySizeType idx)

const DataObject *	GetInput (DataObjectPointerArraySizeType idx) const

virtual void	PushBackInput (const DataObject *input)

virtual void	PopBackInput ()

virtual void	PushFrontInput (const DataObject *input)

virtual void	PopFrontInput ()

DataObject *	GetPrimaryInput ()

const DataObject *	GetPrimaryInput () const

virtual void	SetPrimaryInputName (const DataObjectIdentifierType &key)

virtual const char *	GetPrimaryInputName (void) const

virtual void	SetNumberOfRequiredInputs (DataObjectPointerArraySizeType)

virtual const DataObjectPointerArraySizeType &	GetNumberOfRequiredInputs ()

bool	AddRequiredInputName (const DataObjectIdentifierType &)

bool	AddRequiredInputName (const DataObjectIdentifierType &, DataObjectPointerArraySizeType idx)

bool	RemoveRequiredInputName (const DataObjectIdentifierType &)

bool	IsRequiredInputName (const DataObjectIdentifierType &) const

void	SetRequiredInputNames (const NameArray &)

DataObject *	GetOutput (const DataObjectIdentifierType &key)

const DataObject *	GetOutput (const DataObjectIdentifierType &key) const

virtual void	SetPrimaryOutputName (const DataObjectIdentifierType &key)

virtual const char *	GetPrimaryOutputName (void) const

DataObject *	GetOutput (DataObjectPointerArraySizeType idx)

const DataObject *	GetOutput (DataObjectPointerArraySizeType idx) const

DataObject *	GetPrimaryOutput ()

const DataObject *	GetPrimaryOutput () const

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
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 Member Functions
	BSplineScatteredDataPointSetToImageFilter (const Self &)

void	CollapsePhiLattice (PointDataImageType , PointDataImageType , const RealType, const unsigned int)

void	GenerateOutputImage ()

IndexType	NumberToIndex (const unsigned int, const SizeType)

void	operator= (const Self &)

void	RefineControlPointLattice ()

void	SetPhiLatticeParametricDomainParameters ()

void	ThreadedGenerateDataForFitting (const RegionType &, ThreadIdType)

void	ThreadedGenerateDataForReconstruction (const RegionType &, ThreadIdType)

void	UpdatePointSet ()

Private Attributes
RealType	m_BSplineEpsilon

ArrayType	m_CloseDimension

unsigned int	m_CurrentLevel

ArrayType	m_CurrentNumberOfControlPoints

std::vector < PointDataImagePointer >	m_DeltaLatticePerThread

bool	m_DoMultilevel

bool	m_GenerateOutputImage

PointDataContainerType::Pointer	m_InputPointData

bool	m_IsFittingComplete

KernelType::Pointer	m_Kernel [ImageDimension]

KernelOrder0Type::Pointer	m_KernelOrder0

KernelOrder1Type::Pointer	m_KernelOrder1

KernelOrder2Type::Pointer	m_KernelOrder2

KernelOrder3Type::Pointer	m_KernelOrder3

unsigned int	m_MaximumNumberOfLevels

ArrayType	m_NumberOfControlPoints

ArrayType	m_NumberOfLevels

std::vector< RealImagePointer >	m_OmegaLatticePerThread

PointDataContainerType::Pointer	m_OutputPointData

PointDataImageType::Pointer	m_PhiLattice

WeightsContainerType::Pointer	m_PointWeights

PointDataImageType::Pointer	m_PsiLattice

vnl_matrix< RealType >	m_RefinedLatticeCoefficients [ImageDimension]

ArrayType	m_SplineOrder

bool	m_UsePointWeights

Additional Inherited Members
Protected Types inherited from itk::LightObject
typedef int	InternalReferenceCountType

Static Protected Member Functions inherited from itk::ImageSource< TOutputImage >
static const ImageRegionSplitterBase *	GetGlobalDefaultSplitter ()

static ITK_THREAD_RETURN_TYPE	ThreaderCallback (void *arg)

Protected Attributes inherited from itk::PointSetToImageFilter< TInputPointSet, TOutputImage >
DirectionType	m_Direction

ValueType	m_InsideValue

PointType	m_Origin

ValueType	m_OutsideValue

SizeType	m_Size

SpacingType	m_Spacing