#include <itkBSplineScatteredDataPointSetToImageFilter.h>

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

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

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 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 &)
Static Public Member Functions
static Pointer	New ()
Static Public Attributes
static const unsigned int	ImageDimension = 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 ()
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

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 continous, 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.