#include <itkFEMRegistrationFilter.h>

Inheritance diagram for itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage, TFemObjectType >:

Collaboration diagram for itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage, TFemObjectType >:

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef double	CoordRepType
typedef VectorLinearInterpolateImageFunction < FieldType, CoordRepType >	DefaultInterpolatorType
typedef itk::VectorExpandImageFilter < FieldType, FieldType >	ExpanderType
typedef ExpanderType::ExpandFactorsType	ExpandFactorsType
typedef TFemObjectType	FEMObjectType
typedef itk::ImageRegionIteratorWithIndex < FieldType >	FieldIterator
typedef FieldType::Pointer	FieldPointer
typedef itk::Image< VectorType, itkGetStaticConstMacro(ImageDimension)>	FieldType
typedef TFixedImage	FixedImageType
typedef double	Float
typedef itk::ImageRegionIteratorWithIndex < FloatImageType >	FloatImageIterator
typedef Image< float, itkGetStaticConstMacro(ImageDimension)>	FloatImageType
typedef itk::ImageRegionIteratorWithIndex < FixedImageType >	ImageIterator
typedef FiniteDifferenceFunctionLoad < MovingImageType, FixedImageType >	ImageMetricLoadType
typedef FixedImageType::SizeType	ImageSizeType
typedef itk::fem::ImageToRectilinearFEMObjectFilter < TMovingImage >	ImageToMeshType
typedef itk::VectorIndexSelectionCastImageFilter < FieldType, FloatImageType >	IndexSelectCasterType
typedef InterpolationGridType::PointType	InterpolationGridPointType
typedef InterpolationGridType::SizeType	InterpolationGridSizeType
typedef itk::Image < Element::ConstPointer, ImageDimension >	InterpolationGridType
typedef InterpolatorType::Pointer	InterpolatorPointer
typedef VectorInterpolateImageFunction < FieldType, CoordRepType >	InterpolatorType
typedef std::vector< typename LoadLandmark::Pointer >	LandmarkArrayType
typedef LinearSystemWrapperItpack	LinearSystemSolverType
typedef Load::ArrayType	LoadArray
typedef MaterialLinearElasticity	MaterialType
typedef PDEDeformableRegistrationFunction < FixedImageType, MovingImageType, FieldType >	MetricBaseType
typedef MetricBaseType::Pointer	MetricBaseTypePointer
typedef TMovingImage	MovingImageType
typedef FixedImageType::PixelType	PixelType
typedef SmartPointer< Self >	Pointer
typedef FixedImageType::PointType	PointType
typedef FEMRegistrationFilter	Self
enum	Sign { positive = 1, negative = -1 }
typedef SolverCrankNicolson < ImageDimension >	SolverType
typedef FixedArray< double, ImageDimension >	StandardDeviationsType
typedef ImageToImageFilter < TMovingImage, TFixedImage >	Superclass
typedef itk::Vector< float, itkGetStaticConstMacro(ImageDimension)>	VectorType
typedef itk::WarpImageFilter < MovingImageType, FixedImageType, FieldType >	WarperType
Public Member Functions
void	AddLandmark (PointType source, PointType target)
void	ChooseMetric (unsigned int whichmetric)
void	ClearLandmarks ()
void	ComputeJacobian ()
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
void	DeleteLandmark (unsigned int i)
void	EnforceDiffeomorphism (float thresh, SolverType *S, bool onlywriteimages)
FieldType *	GetDisplacementField ()
Float	GetElasticity (unsigned int which=0)
FixedImageType *	GetFixedImage ()
ImageSizeType	GetImageSize ()
FEMObjectType *	GetInputFEMObject (unsigned int level=0)
virtual InterpolatorType *	GetInterpolator ()
FloatImageType *	GetJacobianImage ()
void	GetLandmark (unsigned int i, PointType &source, PointType &target)
MetricBaseTypePointer	GetMetric ()
unsigned int	GetMetricType ()
MovingImageType *	GetMovingImage ()
virtual const char *	GetNameOfClass () const
MovingImageType *	GetOriginalMovingImage ()
virtual const StandardDeviationsType &	GetStandardDeviations ()
FixedImageType *	GetWarpedImage ()
unsigned int	GetWidthOfMetricRegion (unsigned int which=0)
void	InsertLandmark (unsigned int i, PointType source, PointType target)
void	IterativeSolve (SolverType *S)
void	MultiResSolve ()
void	PrintVectorField (unsigned int modnum=1000)
void	RunRegistration (void)
void	SetDescentDirectionMaximize ()
void	SetDescentDirectionMinimize ()
void	SetElasticity (Float i, unsigned int which=0)
void	SetElement (Element::Pointer e)
void	SetFixedImage (FixedImageType *T)
void	SetGamma (Float r, unsigned int which=0)
void	SetInputFEMObject (FEMObjectType *F, unsigned int level=0)
virtual void	SetInterpolator (InterpolatorType *_arg)
void	SetMaterial (MaterialType::Pointer m)
void	SetMaximumIterations (unsigned int i, unsigned int which)
void	SetMetric (MetricBaseTypePointer MP)
void	SetMovingImage (MovingImageType *R)
void	SetNumberOfIntegrationPoints (unsigned int i, unsigned int which=0)
void	SetRho (Float r, unsigned int which=0)
void	SetUseLandmarksOn ()
void	SetUseNormalizedGradientOn ()
void	SetWidthOfMetricRegion (unsigned int i, unsigned int which=0)
void	WarpImage (const MovingImageType *R)

void	SetDisplacementField (FieldType *F)

void	SetMeshPixelsPerElementAtEachResolution (unsigned int i, unsigned int which=0)

virtual void	SetTimeStep (Float _arg)
virtual Float	GetTimeStep ()

virtual void	SetAlpha (Float _arg)
virtual Float	GetAlpha ()

virtual void	SetUseLandmarks (bool _arg)
virtual bool	GetUseLandmarks ()
void	SetUseLandmarksOff ()

virtual void	SetUseMassMatrix (bool _arg)
virtual bool	GetUseMassMatrix ()

virtual void	SetEnergyReductionFactor (Float _arg)
virtual Float	GetEnergyReductionFactor ()

virtual void	SetDoLineSearchOnImageEnergy (unsigned int _arg)
virtual unsigned int	GetDoLineSearchOnImageEnergy ()

virtual void	SetUseNormalizedGradient (bool _arg)
virtual bool	GetUseNormalizedGradient ()
void	SetUseNormalizedGradientOff ()

virtual void	SetEmployRegridding (unsigned int _arg)
virtual unsigned int	GetEmployRegridding ()

virtual void	SetLineSearchMaximumIterations (unsigned int _arg)
virtual unsigned int	GetLineSearchMaximumIterations ()

void	SetMaxLevel (unsigned int level)
virtual unsigned int	GetMaxLevel ()

virtual void	SetCreateMeshFromImage (bool _arg)
void	SetCreateMeshFromImageOn ()
void	SetCreateMeshFromImageOff ()
virtual bool	GetCreateMeshFromImage ()

virtual void	SetStandardDeviations (StandardDeviationsType _arg)
virtual void	SetStandardDeviations (double value)

virtual void	SetMaximumKernelWidth (unsigned int _arg)
virtual unsigned int	GetMaximumKernelWidth () const

virtual void	SetMaximumError (double _arg)
virtual double	GetMaximumError () const
Static Public Member Functions
static Pointer	New ()
Static Public Attributes
static const unsigned int	ImageDimension = FixedImageType::ImageDimension
Protected Member Functions
void	ApplyImageLoads (MovingImageType i1, FixedImageType i2)
void	ApplyLoads (ImageSizeType Isz, double *spacing=NULL)
void	CreateLinearSystemSolver ()
void	CreateMesh (unsigned int ElementsPerSide, SolverType *solver)
Float	EvaluateEnergy ()
Float	EvaluateResidual (SolverType *mySolver, Float t)
FieldPointer	ExpandVectorField (ExpandFactorsType expandFactors, FieldType f)
	FEMRegistrationFilter ()
void	FindBracketingTriplet (SolverType mySolver, Float a, Float b, Float c)
FloatImageType *	GetMetricImage (FieldType *F)
Float	GoldenSection (SolverType *mySolver, Float tol=0.01, unsigned int MaxIters=25)
void	InterpolateVectorField (SolverType *S)
void	PrintSelf (std::ostream &os, Indent indent) const
void	SampleVectorFieldAtNodes (SolverType *S)
void	SmoothDisplacementField ()
	~FEMRegistrationFilter ()

virtual const ImageMetricLoadType *	GetLoad ()
virtual void	SetLoad (ImageMetricLoadType *_arg)
Private Member Functions
	FEMRegistrationFilter (const Self &)
void	InitializeField ()
void	operator= (const Self &)
Private Attributes
Float	m_Alpha
bool	m_CreateMeshFromImage
ImageSizeType	m_CurrentImageScaling
unsigned int	m_CurrentLevel
FixedImageType::SizeType	m_CurrentLevelImageSize
Sign	m_DescentDirection
unsigned int	m_DoLineSearchOnImageEnergy
vnl_vector< Float >	m_E
Element::Pointer	m_Element
unsigned int	m_EmployRegridding
Float	m_Energy
Float	m_EnergyReductionFactor
FEMObjectType::Pointer	m_FEMObject
FieldType::Pointer	m_Field
FieldType::RegionType	m_FieldRegion
FieldType::SizeType	m_FieldSize
unsigned int	m_FileCount
FixedImageType::Pointer	m_FixedImage
FloatImageType::Pointer	m_FloatImage
ImageSizeType	m_FullImageSize
vnl_vector< Float >	m_Gamma
ImageSizeType	m_ImageOrigin
ImageSizeType	m_ImageScaling
InterpolatorPointer	m_Interpolator
LandmarkArrayType	m_LandmarkArray
unsigned int	m_LineSearchMaximumIterations
ImageMetricLoadType::Pointer	m_Load
MaterialType::Pointer	m_Material
double	m_MaximumError
unsigned int	m_MaximumKernelWidth
vnl_vector< unsigned int >	m_Maxiters
unsigned int	m_MaxLevel
vnl_vector< unsigned int >	m_MeshPixelsPerElementAtEachResolution
MetricBaseTypePointer	m_Metric
vnl_vector< unsigned int >	m_MetricWidth
Float	m_MinE
Float	m_MinJacobian
MovingImageType::Pointer	m_MovingImage
vnl_vector< unsigned int >	m_NumberOfIntegrationPoints
MovingImageType::Pointer	m_OriginalMovingImage
vnl_vector< Float >	m_Rho
StandardDeviationsType	m_StandardDeviations
Float	m_TimeStep
FieldType::Pointer	m_TotalField
unsigned int	m_TotalIterations
bool	m_UseLandmarks
bool	m_UseMassMatrix
bool	m_UseNormalizedGradient
FixedImageType::Pointer	m_WarpedImage
WarperType::Pointer	m_Warper
unsigned int	m_WhichMetric
FixedImageType::IndexType	m_Windex
FixedImageType::RegionType	m_Wregion

Detailed Description

template<class TMovingImage, class TFixedImage, class TFemObjectType>
class itk::fem::FEMRegistrationFilter< TMovingImage, TFixedImage, TFemObjectType >

FEM Image registration filter. The image registration problem is modeled here with the finite element method. Image registration is, in general, an ill-posed problem. Thus, we use an optimization scheme where the optimization criterion is given by a regularized variational energy. The variational energy arises from modeling the image as a physical body on which external forces act. The body is allowed to deform so as to minimize the applied force. The resistance of the physical body to deformation, determined by the physics associated with the body, serves to regularize the solution. The forces applied to the body are, generally, highly non-linear and so the body is allowed to deform slowly and incrementally. The direction it deforms follows the gradient of the potential energy (the force) we define. The potential energies we may choose from are given by the itk image-to-image metrics. The choices and the associated direction of descent are : Mean Squares (minimize), Normalized Cross-Correlation (maximize), and Mutual Information (maximize). Note that we have to set the direction (SetDescentDirection) when we choose a metric.

The forces driving the problem may also be given by user-supplied landmarks. The corners of the image, in this example, are always pinned. This example is designed for 2D or 3D images. A rectilinear mesh is generated automatically given the correct element type (Quadrilateral or Hexahedral). Our specific Solver for this example uses trapezoidal time stepping. This is a method for solving a second-order PDE in time. The solution is penalized by the zeroth (mass matrix) and first derivatives (stiffness matrix) of the shape functions. There is an option to perform a line search on the energy after each iteration. Optimal parameter settings require experimentation. The following approach tends to work well : Choose the relative size of density to elasticity (e.g. Rho / E ~= 1.) such that the image deforms locally and slowly. This also affects the stability of the solution. Choose the time step to control the size of the deformation at each step. Choose enough iterations to allow the solution to converge (this may be automated).

To use this filter the user will at a minimum set the Fixed and Moving images. If the user does not specify a mesh using the SetInputFEMObject() then a mesh will be created automatically of the approriate type (2d=quads and 3d=hex). The user has significant control over the registration process including setting number of resolution levels, material properties, and the metric used to define correspondence between images.

Note:: This code works for only 2 or 3 dimensions b/c we do not have > 3D elements.; TODO : Keep the full field around (if using re-gridding). Introduce compensation for kinematic non-linearity in time (if using Eulerian frame).

Definition at line 118 of file itkFEMRegistrationFilter.h.