#include <FreeFormTransformation.h>

Inheritance diagram for mirtk::FreeFormTransformation:

Collaboration diagram for mirtk::FreeFormTransformation:

Public Types
typedef GenericExtrapolateImageFunction< CPImage >	CPExtrapolator
	Base type used for extrapolation of control point data.

typedef GenericImage< CPValue >	CPImage
	Type of image representation of free-form transformation.

typedef GenericInterpolateImageFunction< CPImage >	CPInterpolator

typedef Vector3D< DOFStatus >	CPStatus
	Type of vector storing status of control point coefficients.

typedef Vector3D< DOFValue >	CPValue
	Type of vector storing the coefficients at a control point.

typedef CPValue	Vector

Public Types inherited from mirtk::Transformation
typedef Status	DOFStatus
	Type of transforamtion parameter status.

typedef double	DOFValue
	Type of transformation parameter value.

Public Member Functions
int	ActualNumberOfDOFs () const

virtual double	Approximate (const Transformation *, int=1, double=.0)

virtual double	Approximate (const ImageAttributes &, double , double , double *, int=1, double=.0)

virtual double	Approximate (const double , const double , const double , double , double , double , int, int=1, double=.0)

virtual double	Approximate (const double , const double , const double , const double , double , double , double *, int, int=1, double=.0)

virtual double	ApproximateAsNew (const Transformation *, int=1, double=.0)
	Approximate another transformation and return approximation error.

virtual double	ApproximateAsNew (const ImageAttributes &, double , double , double *, int=1, double=.0)

virtual ImageAttributes	ApproximationDomain (const ImageAttributes &, const Transformation *)

const ImageAttributes &	Attributes () const
	Returns attributes of control point grid.

virtual double	BendingEnergy (double, double, double, double=0, double=NaN, bool=true) const
	Calculates the bending of the transformation.

virtual double	BendingEnergy (bool=false, bool=true) const
	Approximates the bending energy on the control point lattice.

virtual double	BendingEnergy (const ImageAttributes &attr, double=NaN, bool=true) const
	Approximates the bending energy on the specified discrete domain.

virtual void	BendingEnergyGradient (double *, double=1.0, bool=false, bool=true, bool=true) const

void	BoundingBox (double &, double &) const
	Gets the temporal bounding box of the free-form deformation (in ms)

void	BoundingBox (double &, double &, double &, double &, double &, double &) const
	Gets the spatial bounding box of the free-form deformation (in mm)

void	BoundingBox (Point &, Point &) const
	Gets the spatial bounding box of the free-form deformation (in mm)

void	BoundingBox (double &, double &, double &, double &, double &, double &, double &, double &) const
	Gets the spatio-temporal bounding box of the free-form deformation (in mm and ms)

void	BoundingBox (Point &, double &, Point &, double &) const
	Gets the spatio-temporal bounding box of the free-form deformation (in mm and ms)

virtual void	BoundingBox (int, double &, double &, double=1) const

virtual void	BoundingBox (int, double &, double &, double &, double &, double &, double &, double=1) const =0

virtual void	BoundingBox (int, double &, double &, double &, double &, double &, double &, double &, double &, double=1) const

void	BoundingBox (int, Point &, Point &, double=1) const

bool	BoundingBox (const ImageAttributes &, int, int &, int &, int &, int &, int &, int &, double=1) const

bool	BoundingBox (const ImageAttributes &, int, int &, int &, int &, int &, int &, int &, int &, int &, double=1) const

bool	BoundingBox (const Image *, int, int &, int &, int &, int &, int &, int &, double=1) const

bool	BoundingBox (const Image *, int, int &, int &, int &, int &, int &, int &, int &, int &, double=1) const

void	ControlPointLocation (int, double &, double &) const
	Gets the location of the given control point (in mm)

void	ControlPointLocation (int, double &, double &, double &) const
	Gets the location of the given control point (in mm)

Point	ControlPointLocation (int) const
	Returns the location of the given control point (in mm)

virtual bool	CopyFrom (const Transformation *)

bool	CropPadPassiveCPs (int=0, bool=false)

virtual bool	CropPadPassiveCPs (int, int, int=0, int=0, bool=false)

bool	DOFBoundingBox (const ImageAttributes &, int, int &, int &, int &, int &, int &, int &, double=1) const

bool	DOFBoundingBox (const Image *, int, int &, int &, int &, int &, int &, int &, double=1) const

virtual double	DOFGradientNorm (const double *) const
	Get norm of the gradient vector.

int	DOFToDimension (int) const
	Get index of dimension corresponding to transformation parameter (DoFs)

int	DOFToIndex (int) const
	Get index of control point corresponding to transformation parameter (DoFs)

double	EvaluateRMSError (const Transformation *) const
	Evaluates RMS error of transformation at control points compared to another.

virtual void	ExtrapolationMode (enum ExtrapolationMode)
	Set extrapolation mode.

const CPExtrapolator *	Extrapolator () const

virtual void	FFDJacobianDetDerivative (double dJ[3], const Matrix &adj, int cp, double x, double y, double z, double=0, double=NaN, bool wrt_world=true, bool use_spacing=true) const

virtual void	FFDJacobianWorld (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t either control point displacements or velocities.

void	Get (int, Vector &) const
	Gets values of the parameters at a control point.

void	Get (int, double &, double &, double &) const
	Gets values of the parameters at a control point.

void	Get (int, int, int, double &, double &, double &) const
	Gets values of the parameters at a control point.

void	Get (int, int, int, int, double &, double &, double &) const
	Gets values of the parameters at a control point.

void	GetOrientation (double , double , double *) const
	Gets the orientation of the free-form deformation lattice.

void	GetSpacing (double &, double &, double &) const
	Gets the control point spacing (in mm)

void	GetSpacing (double &, double &, double &, double &) const
	Gets the control point spacing (in mm)

void	GetStatus (int, CPStatus &) const
	Gets status of the parameters at a control point.

void	GetStatus (int, int, int, DOFStatus &, DOFStatus &, DOFStatus &) const
	Gets status of the parameters at a control point.

void	GetStatus (int, int, int, int, DOFStatus &, DOFStatus &, DOFStatus &) const
	Gets status of the parameters at a control point.

int	GetT () const
	Returns the number of control points in t.

virtual int	GetTAfterSubdivision () const
	Returns the number of control points in t after subdivision.

double	GetTSpacing () const
	Returns the of control point spacing in t.

virtual double	GetTSpacingAfterSubdivision () const
	Returns the control point spacing in t after the subdivision.

int	GetX () const
	Returns the number of control points in x.

virtual int	GetXAfterSubdivision () const
	Returns the number of control points in x after subdivision.

double	GetXSpacing () const
	Returns the of control point spacing in x.

virtual double	GetXSpacingAfterSubdivision () const
	Returns the control point spacing in x after the subdivision.

int	GetY () const
	Returns the number of control points in y.

virtual int	GetYAfterSubdivision () const
	Returns the number of control points in y after subdivision.

double	GetYSpacing () const
	Returns the of control point spacing in y.

virtual double	GetYSpacingAfterSubdivision () const
	Returns the control point spacing in y after the subdivision.

int	GetZ () const
	Returns the number of control points in z.

virtual int	GetZAfterSubdivision () const
	Returns the number of control points in z after subdivision.

double	GetZSpacing () const
	Returns the of control point spacing in z.

virtual double	GetZSpacingAfterSubdivision () const
	Returns the control point spacing in z after the subdivision.

virtual void	GlobalHessian (Matrix [3], double, double, double, double=0, double=NaN) const
	Calculates the Hessian for each component of the global transformation w.r.t world coordinates.

virtual void	GlobalInverse (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the inverse of the global transformation only.

virtual void	GlobalJacobian (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the global transformation w.r.t world coordinates.

virtual void	GlobalTransform (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the global transformation component only.

virtual void	Hessian (Matrix [3], double, double, double, double=0, double=NaN) const
	Calculates the Hessian for each component of the transformation w.r.t world coordinates.

void	HessianToWorld (double &, double &, double &) const

void	HessianToWorld (double &, double &, double &, double &, double &, double &) const

void	HessianToWorld (Matrix &) const

void	HessianToWorld (Matrix [3]) const

void	IndexToDOFs (int, int &, int &) const
	Get indices of transformation parameters (DoFs)

void	IndexToDOFs (int, int &, int &, int &) const
	Get indices of transformation parameters (DoFs)

void	IndexToLattice (int, int &, int &) const
	Get control point lattice coordinates from index.

void	IndexToLattice (int, int &, int &, int &) const
	Get control point lattice coordinates from index.

void	IndexToLattice (int, int &, int &, int &, int &) const
	Get control point lattice coordinates from index.

void	IndexToWorld (int, double &, double &) const
	Get world coordinates (in mm) of control point.

void	IndexToWorld (int, double &, double &, double &) const
	Get world coordinates (in mm) of control point.

void	IndexToWorld (int, Point &) const
	Get world coordinates (in mm) of control point.

Point	IndexToWorld (int) const
	Get world coordinates (in mm) of control point.

virtual void	Initialize (const ImageAttributes &)=0
	Initialize free-form transformation.

void	Initialize (const ImageAttributes &, double, double, double=-1.0, double=-1.0)
	Initialize free-form transformation.

void	Initialize (const CPImage &, bool=false)
	Initialize transformation from existing vector field.

void	Initialize (const GenericImage< double > &, bool=false)
	Initialize transformation from existing 3D+t vector field.

virtual void	Interpolate (const double , const double , const double *)=0

virtual bool	Inverse (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the inverse of the transformation.

virtual bool	IsActive (int) const
	Whether the control point at given lattice index is active.

virtual bool	IsActive (int, int, int=0, int=0) const
	Whether the control point at given lattice coordinates is active.

virtual void	Jacobian (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t world coordinates.

virtual void	JacobianDetDerivative (double dJ[3], const Matrix &adj, int cp, double x, double y, double z, double t=0, double t0=NaN, bool wrt_world=true, bool use_spacing=true) const

virtual void	JacobianDOFs (Matrix &, int, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t the transformation parameters of a control point.

virtual void	JacobianDOFs (TransformationJacobian &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t the transformation parameters.

void	JacobianToWorld (double &, double &) const

void	JacobianToWorld (double &, double &, double &) const

void	JacobianToWorld (Matrix &) const

void	JacobianToWorldOrientation (double &, double &) const
	Reorient 1st order derivatives computed w.r.t 2D lattice coordinates.

void	JacobianToWorldOrientation (double &, double &, double &) const
	Reorient 1st order derivatives computed w.r.t 2D lattice coordinates.

int	KernelRadius () const
	Radius of support region of the used kernel.

virtual int	KernelSize () const =0
	Size of support region of the used kernel.

int	LatticeToIndex (int, int, int=0, int=0) const
	Get control point index from lattice coordinates.

virtual double	LatticeToTime (double) const
	Transforms temporal lattice coordinate to time (in ms)

virtual void	LatticeToWorld (double &, double &) const
	Transforms lattice coordinates to world coordinates (in mm)

virtual void	LatticeToWorld (double &, double &, double &) const
	Transforms lattice coordinates to world coordinates (in mm)

virtual void	LatticeToWorld (Point &) const
	Transforms lattice coordinates to world coordinates (in mm)

	mirtkPublicAttributeMacro (double, SpeedupFactor)
	Speedup factor for gradient computation.

	mirtkReadOnlyAttributeMacro (enum ExtrapolationMode, ExtrapolationMode)
	Mode used for extrapolation of control point image.

int	NumberOfActiveCPs () const
	Number of active control points.

int	NumberOfCPs () const
	Number of control points.

int	NumberOfPassiveCPs () const
	Number of non-active control points.

virtual ParameterList	Parameter () const
	Get (non-DoF) parameters as key/value as string map.

virtual void	ParametricGradient (const GenericImage< double > , double , const WorldCoordsImage , const WorldCoordsImage , double=NaN, double=1) const

virtual void	ParametricGradient (const PointSet &, const Vector3D< double > , double , double=0, double=NaN, double=1) const

virtual void	Print (ostream &, Indent=0) const
	Prints the parameters of the transformation.

void	Put (int, const Vector &)
	Puts values of the parameters at a control point.

void	Put (int, double, double, double)
	Puts values of the parameters at a control point.

void	Put (int, int, int, double, double, double)
	Puts values of the parameters at a control point.

void	Put (int, int, int, int, double, double, double)
	Puts values of the parameters at a control point.

void	PutBoundingBox (double, double, double, double, double, double)
	Puts the spatial bounding box for the free-form deformation (in mm)

void	PutBoundingBox (const Point &, const Point &)
	Puts the temporal bounding box for the free-form deformation (in mm)

void	PutBoundingBox (double, double)
	Puts the temporal bounding box of the free-form deformation (in ms)

void	PutBoundingBox (double, double, double, double, double, double, double, double)
	Puts the spatio-temporal bounding box for the free-form deformation (in mm)

void	PutOrientation (double , double , double *)
	Puts the orientation of the free-form deformation lattice.

void	PutStatus (int, const CPStatus &)
	Puts status of the parameters at a control point.

void	PutStatus (int, int, int, DOFStatus, DOFStatus, DOFStatus)
	Puts status of the parameters at a control point.

void	PutStatus (int, int, int, int, DOFStatus, DOFStatus, DOFStatus)
	Puts status of the parameters at a control point.

virtual bool	Set (const char , const char )
	Set named (non-DoF) parameter from value as string.

virtual void	Subdivide (bool=true, bool=true, bool=true, bool=true)
	Subdivide lattice of free-form transformation.

void	Subdivide2D ()
	Subdivide lattice in first two dimensions.

void	Subdivide3D ()
	Subdivide lattice in first three dimensions.

void	Subdivide4D ()
	Subdivide lattice in all four dimensions.

int	T () const
	Returns the number of control points in t.

virtual double	TimeToLattice (double) const
	Transforms time (in ms) to temporal lattice coordinate.

virtual void	Transform (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point.

virtual void	WorldToLattice (double &, double &) const
	Transforms world coordinates (in mm) to lattice coordinates.

virtual void	WorldToLattice (double &, double &, double &) const
	Transforms world coordinates (in mm) to lattice coordinates.

virtual void	WorldToLattice (Point &) const
	Transforms world coordinates (in mm) to lattice coordinates.

int	X () const
	Returns the number of control points in x.

int	Y () const
	Returns the number of control points in y.

int	Z () const
	Returns the number of control points in z.

virtual	~FreeFormTransformation ()
	Destructor.

Public Member Functions inherited from mirtk::Transformation
virtual void	Add (const DOFValue *)
	Add change to transformation parameters.

virtual double	Approximate (const ImageAttributes &, const Transformation *, int=1, double=.0)
	Approximate another transformation and return approximation error.

virtual double	Approximate (GenericImage< double > &, int=1, double=.0)

virtual double	ApproximateAsNew (const ImageAttributes &, const Transformation *, int=1, double=.0)
	Approximate another transformation and return approximation error.

virtual double	ApproximateAsNew (GenericImage< double > &, int=1, double=.0)

virtual double	ApproximateAsNew (const double , const double , const double , double , double , double , int, int=1, double=.0)

virtual double	ApproximateAsNew (const double , const double , const double , const double , double , double , double *, int, int=1, double=.0)

virtual void	ApproximateDOFs (const double , const double , const double , const double , const double , const double , const double *, int)

virtual void	ApproximateDOFsGradient (const double , const double , const double , const double , const double , const double , const double , int, double , double=1.0) const

virtual void	ApproximateGradient (const ImageAttributes &, const double , const double , const double , double , double=1.0) const

virtual void	ApproximateGradient (const double , const double , const double , const double , const double , const double , int, double *, double=1.0) const

virtual void	ApproximateGradient (const double , const double , const double , const double , const double , const double , const double , int, double , double=1.0) const

virtual bool	CanModifyDisplacement (int=-1) const

virtual bool	CanRead (TransformationType) const
	Whether this transformation can read a file of specified type (i.e. format)

virtual void	DeriveJacobianWrtDOF (Matrix &, int, double, double, double, double=0, double=NaN) const
	Calculates the derivative of the Jacobian of the transformation (w.r.t. world coordinates) w.r.t. a transformation parameter.

virtual void	Displacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point.

virtual void	Displacement (const ImageAttributes &, double , double , double *) const

virtual void	Displacement (GenericImage< double > &, double=NaN, const WorldCoordsImage *=NULL) const
	Calculates the displacement vectors for a whole image domain.

virtual void	Displacement (GenericImage< float > &, double=NaN, const WorldCoordsImage *=NULL) const
	Calculates the displacement vectors for a whole image domain.

virtual void	Displacement (GenericImage< double > &, double, double, const WorldCoordsImage *=NULL) const

virtual void	Displacement (GenericImage< float > &, double, double, const WorldCoordsImage *=NULL) const

virtual void	DisplacementAfterDOFChange (int dof, double dv, GenericImage< double > &dx, double t, double t0=NaN, const WorldCoordsImage *i2w=NULL) const

double	EvaluateRMSError (const ImageAttributes &, const Transformation *) const
	Evaluates RMS error of transformation compared to another.

double	EvaluateRMSError (const ImageAttributes &, double , double ) const

double	EvaluateRMSError (const ImageAttributes &, double , double , double *) const

double	EvaluateRMSError (const double , const double , const double , double, double , double , double , int no) const
	Evaluates RMS error of transformation compared to displacement field.

double	EvaluateRMSError (const double , const double , const double , const double , double , double , double *, int no) const
	Evaluates RMS error of transformation compared to given displacement field.

virtual double	Get (int) const
	Get value of transformation parameter.

virtual void	Get (DOFValue *) const
	Get values of transformation parameters.

virtual DOFStatus	GetStatus (int) const
	Get status of transformation parameter.

virtual void	GlobalDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the global transformation component only.

virtual void	GlobalInverseDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the inverse of the global transformation only.

virtual double	GlobalJacobian (double, double, double, double=0, double=NaN) const
	Calculates the determinant of the Jacobian of the global transformation w.r.t world coordinates.

virtual bool	HasSameDOFsAs (const Transformation *) const
	Checks whether transformation depends on the same vector of parameters.

virtual bool	Inverse (Point &, double=0, double=NaN) const
	Transforms a single point using the inverse of the transformation.

virtual int	Inverse (PointSet &, double=0, double=NaN) const

virtual bool	InverseDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the inverse of the transformation.

virtual int	InverseDisplacement (const ImageAttributes &, double , double , double *) const

virtual int	InverseDisplacement (GenericImage< double > &, double=NaN, const WorldCoordsImage *=NULL) const

virtual int	InverseDisplacement (GenericImage< float > &, double=NaN, const WorldCoordsImage *=NULL) const

virtual int	InverseDisplacement (GenericImage< double > &, double, double, const WorldCoordsImage *=NULL) const

virtual int	InverseDisplacement (GenericImage< float > &, double, double, const WorldCoordsImage *=NULL) const

virtual bool	IsIdentity () const
	Checks whether the transformation is an identity mapping.

virtual double	Jacobian (double, double, double, double=0, double=NaN) const
	Calculates the determinant of the Jacobian of the transformation w.r.t world coordinates.

virtual void	JacobianDOFs (double [3], int, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the transformation w.r.t a transformation parameter.

virtual void	LocalDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the local transformation component only.

virtual void	LocalHessian (Matrix [3], double, double, double, double=0, double=NaN) const
	Calculates the Hessian for each component of the local transformation w.r.t world coordinates.

virtual bool	LocalInverse (double &, double &, double &, double=0, double=NaN) const
	Transforms a single point using the inverse of the local transformation only.

virtual bool	LocalInverseDisplacement (double &, double &, double &, double=0, double=NaN) const
	Calculates the displacement of a single point using the inverse of the local transformation only.

virtual void	LocalJacobian (Matrix &, double, double, double, double=0, double=NaN) const
	Calculates the Jacobian of the local transformation w.r.t world coordinates.

virtual double	LocalJacobian (double, double, double, double=0, double=NaN) const
	Calculates the determinant of the Jacobian of the local transformation w.r.t world coordinates.

virtual void	LocalTransform (double &, double &, double &, double=0, double=NaN) const =0
	Transforms a single point using the local transformation component only.

int	NumberOfActiveDOFs () const
	Get number of active transformation parameters.

virtual int	NumberOfDOFs () const
	Get number of transformation parameters.

int	NumberOfPassiveDOFs () const
	Get number of passive transformation parameters.

void	ParametricGradient (const GenericImage< double > , double , const WorldCoordsImage *, double=NaN, double=1) const

void	ParametricGradient (const GenericImage< double > , double , double=NaN, double=1) const

virtual void	ParametricGradient (const GenericImage< double > *, int, double , const WorldCoordsImage , const WorldCoordsImage , const double *=NULL, double=1) const

void	ParametricGradient (const GenericImage< double > *, int, double , const WorldCoordsImage , const double =NULL, double=1) const

void	ParametricGradient (const GenericImage< double > *, int, double , const double *=NULL, double=1) const

void	Print (Indent=0) const
	Prints information about the transformation.

virtual void	Put (int, double)
	Put value of transformation parameter.

virtual void	Put (const DOFValue *)
	Put values of transformation parameters.

virtual void	PutStatus (int, DOFStatus)
	Put status of transformation parameter.

virtual void	Read (const char *)
	Reads a transformation from a file.

virtual Cifstream &	Read (Cifstream &)
	Reads a transformation from a file stream.

virtual bool	RequiresCachingOfDisplacements () const

virtual void	Reset ()
	Reset transformation.

virtual void	Transform (Point &, double=0, double=NaN) const
	Transforms a single point.

virtual void	Transform (PointSet &, double=0, double=NaN) const
	Transforms a set of points.

virtual void	Transform (int, double , double , double *, double=0, double=NaN) const
	Transforms a set of points.

virtual void	Transform (int, double , double , double , const double , double=NaN) const
	Transforms a set of points.

virtual void	Transform (WorldCoordsImage &, double=NaN) const
	Transforms world coordinates of image voxels.

virtual TransformationType	TypeOfClass () const
	Returns type ID of the instantiated transformation class.

virtual double	Update (const DOFValue *)
	Update transformation parameters given parametric gradient.

virtual void	Verify ()

virtual void	Write (const char *) const
	Writes a transformation to a file.

virtual Cofstream &	Write (Cofstream &) const
	Writes a transformation to a file stream.

virtual	~Transformation ()
	Default destructor.

Public Member Functions inherited from mirtk::Observable
void	AddObserver (Observer &)
	Add observer.

void	Broadcast (Event, const void *=NULL)
	Broadcast event to observers.

void	ClearObservers ()
	Delete all observers.

void	DeleteObserver (Observer &)
	Delete observer.

void	NotifyObservers (Event, const void *=NULL)
	Notify all observers about given event if this object has changed.

int	NumberOfObservers () const
	Number of current observers.

virtual	~Observable ()
	Destructor.

Public Member Functions inherited from mirtk::Object
virtual const char *	NameOfClass () const =0
	Get name of class, which this object is an instance of.

bool	Parameter (const ParameterList &)
	Set parameters from name/value pairs.

virtual	~Object ()
	Destructor.

Static Public Member Functions
static double	Bending3D (const Matrix [3])
	Calculates the bending of the transformation given the 2nd order derivatives.

static ImageAttributes	DefaultAttributes (const ImageAttributes &attr, double dx=-1.0, double dy=-1.0, double dz=-1.0, double dt=-1.0)

static ImageAttributes	DefaultAttributes (double, double, double, double, double, double, double, double, double, double, double, double, const double , const double , const double *)
	Default attributes of free-form transformation lattice.

Static Public Member Functions inherited from mirtk::Transformation
static bool	CheckHeader (const char *)
	Whether magic number in header of given file.

static Transformation *	New (TransformationType)

static Transformation *	New (const Transformation *)

static Transformation *	New (const char *)

static TransformationType	TypeOfClass (const char *)
	Returns type ID corresponding to transformations of the named class.

Static Public Member Functions inherited from mirtk::Object
static const char *	NameOfType ()
	Get name of this class type.

Protected Member Functions
	FreeFormTransformation (CPInterpolator &, CPInterpolator *=NULL)
	Default constructor.

	FreeFormTransformation (const FreeFormTransformation &, CPInterpolator &, CPInterpolator *=NULL)
	Copy constructor.

void	InitializeCPs (const ImageAttributes &, bool=true)
	Initialize control points.

void	InitializeCPs (const FreeFormTransformation &, bool=true)
	Copy control points from other transformation.

void	InitializeInterpolator ()
	Initialize interpolator of control points.

void	InitializeStatus ()
	Initialize status of control points.

Cofstream &	WriteCPs (Cofstream &) const
	Writes the control point and status information to a file stream.

Protected Member Functions inherited from mirtk::Transformation
void	InitializeDOFs (int)
	Initialize transformation parameters.

void	InitializeDOFs (const Transformation &, int=-1)
	Copy transformation parameters (DoFs) and their status.

virtual Cifstream &	ReadDOFs (Cifstream &, TransformationType)
	Reads transformation parameters from a file stream.

	Transformation (int=0)
	Default constructor.

	Transformation (const Transformation &)
	Copy constructor.

	Transformation (const Transformation &, int)
	Copy constructor.

virtual Cofstream &	WriteDOFs (Cofstream &) const
	Writes transformation parameters to a file stream.

Protected Member Functions inherited from mirtk::Observable
	Observable ()
	Default constructor.

	Observable (const Observable &)
	Copy constructor.

Observable &	operator= (const Observable &)
	Assignment operator.

Protected Member Functions inherited from mirtk::Object
template<typename... Args>
void	Throw (ErrorType err, const char *func, Args... args) const

Protected Attributes
const ImageAttributes &	_attr
	Control point lattice attributes.

CPInterpolator *	_CPFunc

CPImage	_CPImage

CPStatus ****	_CPStatus

CPExtrapolator *	_CPValue
	Infinite discrete representation of free-form transformation coefficients.

const double &	_dt
	Read-only reference to _dt attribute of _CPImage.

const double &	_dx
	Read-only reference to _dx attribute of _CPImage.

const double &	_dy
	Read-only reference to _dy attribute of _CPImage.

const double &	_dz
	Read-only reference to _dz attribute of _CPImage.

const Matrix &	_matL2W
	Read-only reference to _matI2W of _CPImage.

const Matrix &	_matW2L
	Read-only reference to _matW2I of _CPImage.

const int &	_t
	Read-only reference to _t attribute of _CPImage.

const int &	_x
	Read-only reference to _x attribute of _CPImage.

const int &	_y
	Read-only reference to _y attribute of _CPImage.

const int &	_z
	Read-only reference to _z attribute of _CPImage.

Protected Attributes inherited from mirtk::Transformation
int	_NumberOfDOFs
	Number of transformation parameters.

DOFValue *	_Param
	Value of each transformation parameter.

DOFStatus *	_Status
	Status of each transformation parameter (Active or Passive)

Additional Inherited Members
Static Protected Member Functions inherited from mirtk::Object
template<typename... Args>
static void	ThrowStatic (ErrorType err, const char cls, const char func, Args... args)

Detailed Description

Base class for free-form transformations.

Definition at line 41 of file FreeFormTransformation.h.

Member Typedef Documentation

§ CPInterpolator

typedef GenericInterpolateImageFunction<CPImage> mirtk::FreeFormTransformation::CPInterpolator

Base type used for interpolation of control point data

Note: Subclasses may use a particular specialized interpolation type.

Definition at line 83 of file FreeFormTransformation.h.

§ Vector

typedef CPValue mirtk::FreeFormTransformation::Vector

Alias for CPValue type which is preferred when referring to any FFD vector, not only those at control point locations

Definition at line 90 of file FreeFormTransformation.h.

Member Function Documentation

§ ActualNumberOfDOFs()

int mirtk::FreeFormTransformation::ActualNumberOfDOFs ( ) const

inline

Actual number of DoFs, i.e., 2 * NumberOfDOFs for 2D FFD or 3 * NumberOfDOFs for 3D(+t) FFD

Definition at line 830 of file FreeFormTransformation.h.

§ Approximate() [1/4]

virtual double mirtk::FreeFormTransformation::Approximate	(	const Transformation *	,
		int	= `1`,
		double	= `.0`
	)

virtual

Approximate transformation: This function takes a transformation and finds a FFD which approximates this transformation at the control point locations. Returns the approximation error of the resulting FFD at the control point locations.

§ Approximate() [2/4]

virtual double mirtk::FreeFormTransformation::Approximate	(	const ImageAttributes &	,
		double *	,
		double *	,
		double *	,
		int	= `1`,
		double	= `.0`
	)

virtual

Approximate displacements: This function takes a set of points and a set of displacements and finds a transformation which approximates these displacements. After approximation, the displacements are replaced by the residual displacement errors at the points.

Reimplemented from mirtk::Transformation.

§ Approximate() [3/4]

virtual double mirtk::FreeFormTransformation::Approximate	(	const double *	,
		const double *	,
		const double *	,
		double *	,
		double *	,
		double *	,
		int	,
		int	= `1`,
		double	= `.0`
	)

virtual

Approximate displacements: This function takes a set of points and a set of displacements and finds a transformation which approximates these displacements. After approximation, the displacements are replaced by the residual displacement errors at the points.

Reimplemented from mirtk::Transformation.

§ Approximate() [4/4]

virtual double mirtk::FreeFormTransformation::Approximate	(	const double *	,
		const double *	,
		const double *	,
		const double *	,
		double *	,
		double *	,
		double *	,
		int	,
		int	= `1`,
		double	= `.0`
	)

virtual

Approximate displacements: This function takes a set of points and a set of displacements and finds a transformation which approximates these displacements. After approximation, the displacements are replaced by the residual displacement errors at the points.

Reimplemented from mirtk::Transformation.

§ ApproximateAsNew()

virtual double mirtk::FreeFormTransformation::ApproximateAsNew	(	const ImageAttributes &	,
		double *	,
		double *	,
		double *	,
		int	= `1`,
		double	= `.0`
	)

virtual

Approximate displacements: This function takes a set of points and a set of displacements and finds a !new! transformation which approximates these displacements. After approximation, the displacements are replaced by the residual displacement errors at the points.

Reimplemented from mirtk::Transformation.

§ ApproximationDomain()

virtual ImageAttributes mirtk::FreeFormTransformation::ApproximationDomain	(	const ImageAttributes &	,
		const Transformation *
	)

virtual

Get image domain on which this free-form transformation should be defined in order to reduce the error when the given transformation is approximated and the resulting free-form transformation is applied to resample an image that is defined on the specified lattice.

Reimplemented in mirtk::BSplineFreeFormTransformationSV.

§ BendingEnergyGradient()

virtual void mirtk::FreeFormTransformation::BendingEnergyGradient	(	double *	,
		double	= `1.0`,
		bool	= `false`,
		bool	= `true`,
		bool	= `true`
	)		const

virtual

Approximates the gradient of the bending energy on the control point lattice w.r.t the transformation parameters and adds it with the given weight

Reimplemented in mirtk::BSplineFreeFormTransformation3D, mirtk::BSplineFreeFormTransformation4D, mirtk::LinearFreeFormTransformation4D, mirtk::LinearFreeFormTransformation3D, and mirtk::BSplineFreeFormTransformationStatistical.

§ BoundingBox() [1/8]

void mirtk::FreeFormTransformation::BoundingBox	(	int	,
		double &	t1,
		double &	t2,
		double	= `1`
	)		const

inlinevirtual

Gets the temporal bounding box for a control point. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Reimplemented in mirtk::BSplineFreeFormTransformation4D, and mirtk::LinearFreeFormTransformation4D.

Definition at line 1209 of file FreeFormTransformation.h.

§ BoundingBox() [2/8]

void mirtk::FreeFormTransformation::BoundingBox	(	int	,
		double &	x1,
		double &	y1,
		double &	z1,
		double &	x2,
		double &	y2,
		double &	z2,
		double	= `1`
	)		const

inlinepure virtual

Gets the spatial bounding box for a control point. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Implemented in mirtk::BSplineFreeFormTransformation3D, mirtk::BSplineFreeFormTransformation4D, mirtk::LinearFreeFormTransformation4D, and mirtk::LinearFreeFormTransformation3D.

Definition at line 1217 of file FreeFormTransformation.h.

§ BoundingBox() [3/8]

void mirtk::FreeFormTransformation::BoundingBox	(	int	cp,
		double &	x1,
		double &	y1,
		double &	z1,
		double &	t1,
		double &	x2,
		double &	y2,
		double &	z2,
		double &	t2,
		double	fraction = `1`
	)		const

inlinevirtual

Gets the spatio-temporal bounding box for a control point. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Reimplemented in mirtk::BSplineFreeFormTransformation4D, and mirtk::LinearFreeFormTransformation4D.

Definition at line 1230 of file FreeFormTransformation.h.

§ BoundingBox() [4/8]

void mirtk::FreeFormTransformation::BoundingBox	(	int	cp,
		Point &	p1,
		Point &	p2,
		double	fraction = `1`
	)		const

inline

Gets the spatial bounding box for a control point. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Definition at line 1239 of file FreeFormTransformation.h.

§ BoundingBox() [5/8]

bool mirtk::FreeFormTransformation::BoundingBox	(	const ImageAttributes &	domain,
		int	cp,
		int &	i1,
		int &	j1,
		int &	k1,
		int &	i2,
		int &	j2,
		int &	k2,
		double	fraction = `1`
	)		const

inline

Gets the spatial bounding box for a control point in lattice coordinates. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Definition at line 1245 of file FreeFormTransformation.h.

§ BoundingBox() [6/8]

bool mirtk::FreeFormTransformation::BoundingBox	(	const ImageAttributes &	domain,
		int	cp,
		int &	i1,
		int &	j1,
		int &	k1,
		int &	l1,
		int &	i2,
		int &	j2,
		int &	k2,
		int &	l2,
		double	fraction = `1`
	)		const

inline

Gets the spatio-temporal bounding box for a control point in lattice coordinates. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Definition at line 1305 of file FreeFormTransformation.h.

§ BoundingBox() [7/8]

bool mirtk::FreeFormTransformation::BoundingBox	(	const Image *	image,
		int	cp,
		int &	i1,
		int &	j1,
		int &	k1,
		int &	i2,
		int &	j2,
		int &	k2,
		double	fraction = `1`
	)		const

inline

Gets the spatial bounding box for a control point in image coordinates. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Definition at line 1296 of file FreeFormTransformation.h.

§ BoundingBox() [8/8]

bool mirtk::FreeFormTransformation::BoundingBox	(	const Image *	image,
		int	cp,
		int &	i1,
		int &	j1,
		int &	k1,
		int &	l1,
		int &	i2,
		int &	j2,
		int &	k2,
		int &	l2,
		double	fraction = `1`
	)		const

inline

Gets the spatio-temporal bounding box for a control point in image coordinates. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Definition at line 1336 of file FreeFormTransformation.h.

§ CopyFrom()

bool mirtk::FreeFormTransformation::CopyFrom ( const Transformation * other )

inlinevirtual

Copy active transformation parameters (DoFs) from given transformation if possible and return false, otherwise

Reimplemented from mirtk::Transformation.

Definition at line 1381 of file FreeFormTransformation.h.

§ CropPadPassiveCPs() [1/2]

bool mirtk::FreeFormTransformation::CropPadPassiveCPs	(	int	= `0`,
		bool	= `false`
	)

Crop/pad lattice to discard passive control points at the boundary, keeping only a layer of passive control points of given width. The DoF values of passive control points are optionally reset to zero.

§ CropPadPassiveCPs() [2/2]

virtual bool mirtk::FreeFormTransformation::CropPadPassiveCPs	(	int	,
		int	,
		int	= `0`,
		int	= `0`,
		bool	= `false`
	)

virtual

Crop/pad lattice to discard passive control points at the boundary, keeping only a layer of passive control points of given width. The DoF values of passive control points are optionally reset to zero.

Reimplemented in mirtk::BSplineFreeFormTransformationStatistical.

§ DefaultAttributes()

static ImageAttributes mirtk::FreeFormTransformation::DefaultAttributes	(	const ImageAttributes &	attr,
		double	dx = `-1.0`,
		double	dy = `-1.0`,
		double	dz = `-1.0`,
		double	dt = `-1.0`
	)

static

Default attributes of free-form transformation lattice

Parameters

[in]	attr	(Target) image attributes.
[in]	dx	Control point spacing in x.
[in]	dy	Control point spacing in y.
[in]	dz	Control point spacing in z.
[in]	dt	Control point spacing in t.

Note: If a control point number/spacing is negative, it is set to the specified number/size.

§ DOFBoundingBox() [1/2]

bool mirtk::FreeFormTransformation::DOFBoundingBox	(	const ImageAttributes &	domain,
		int	dof,
		int &	i1,
		int &	j1,
		int &	k1,
		int &	i2,
		int &	j2,
		int &	k2,
		double	fraction = `1`
	)		const

inline

Gets the spatial bounding box for a transformation parameter in lattice coordinates. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Definition at line 1345 of file FreeFormTransformation.h.

§ DOFBoundingBox() [2/2]

bool mirtk::FreeFormTransformation::DOFBoundingBox	(	const Image *	image,
		int	dof,
		int &	i1,
		int &	j1,
		int &	k1,
		int &	i2,
		int &	j2,
		int &	k2,
		double	fraction = `1`
	)		const

inlinevirtual

Gets the spatial bounding box for a transformation parameter in image coordinates. The last parameter specifies what fraction of the bounding box to return. The default is 1 which equals 100% of the bounding box.

Reimplemented from mirtk::Transformation.

Definition at line 1354 of file FreeFormTransformation.h.

§ Extrapolator()

const FreeFormTransformation::CPExtrapolator * mirtk::FreeFormTransformation::Extrapolator ( ) const

inline

Get access to control point coefficients extrapolator Intended for use by non-member auxiliary functions of subclass implementations.

Definition at line 786 of file FreeFormTransformation.h.

§ FFDJacobianDetDerivative()

virtual void mirtk::FreeFormTransformation::FFDJacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		int	cp,
		double	x,
		double	y,
		double	z,
		double	= `0`,
		double	= `NaN`,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

virtual

Calculates derivatives of the Jacobian determinant of spline function w.r.t. DoFs of a control point

This function is identical to JacobianDetDerivative when the DoFs of the control points are displacements. When the DoFs are velocities, however, this function computes the derivatives of the Jacobian determinant of the velocity field instead.

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant at (x, y, z) w.r.t. DoFs of control point.
[in]	cp	Index of control point w.r.t. whose DoFs the derivatives are computed.
[in]	x	World coordinate along x axis at which to evaluate derivatives.
[in]	y	World coordinate along y axis at which to evaluate derivatives.
[in]	z	World coordinate along z axis at which to evaluate derivatives.
[in]	adj	Adjugate of Jacobian matrix evaluated at (x, y, z).
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

Reimplemented in mirtk::BSplineFreeFormTransformation3D.

§ HessianToWorld() [1/4]

void mirtk::FreeFormTransformation::HessianToWorld	(	double &	duu,
		double &	duv,
		double &	dvv
	)		const

inline

Convert 2nd order derivatives computed w.r.t 2D lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1590 of file FreeFormTransformation.h.

§ HessianToWorld() [2/4]

void mirtk::FreeFormTransformation::HessianToWorld	(	double &	duu,
		double &	duv,
		double &	duw,
		double &	dvv,
		double &	dvw,
		double &	dww
	)		const

inline

Convert 2nd order derivatives computed w.r.t 3D lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1614 of file FreeFormTransformation.h.

§ HessianToWorld() [3/4]

void mirtk::FreeFormTransformation::HessianToWorld ( Matrix & hessian ) const

inline

Convert 2nd order derivatives of single transformed coordinate computed w.r.t lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1652 of file FreeFormTransformation.h.

§ HessianToWorld() [4/4]

void mirtk::FreeFormTransformation::HessianToWorld ( Matrix hessian[3] ) const

inline

Convert 2nd order derivatives computed w.r.t lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1668 of file FreeFormTransformation.h.

§ Interpolate()

virtual void mirtk::FreeFormTransformation::Interpolate	(	const double *	,
		const double *	,
		const double *
	)

pure virtual

Interpolates displacements: This function takes a set of displacements defined at the control points and finds a FFD which interpolates these displacements.

Implemented in mirtk::BSplineFreeFormTransformationSV, mirtk::BSplineFreeFormTransformation3D, mirtk::LinearFreeFormTransformationTD, mirtk::BSplineFreeFormTransformationTD, mirtk::LinearFreeFormTransformation3D, mirtk::BSplineFreeFormTransformation4D, mirtk::LinearFreeFormTransformation4D, and mirtk::BSplineFreeFormTransformationStatistical.

§ JacobianDetDerivative()

void mirtk::FreeFormTransformation::JacobianDetDerivative	(	double	dJ[3],
		const Matrix &	adj,
		int	cp,
		double	x,
		double	y,
		double	z,
		double	t = `0`,
		double	t0 = `NaN`,
		bool	wrt_world = `true`,
		bool	use_spacing = `true`
	)		const

inlinevirtual

Calculates derivatives of the Jacobian determinant at world point w.r.t. DoFs of a control point

Parameters

[out]	dJ	Partial derivatives of Jacobian determinant w.r.t. DoFs of control point.
[in]	adj	Pre-computed adjugate of Jacobian matrix at this world point.
[in]	cp	Index of control point w.r.t. whose DoFs the derivatives are computed.
[in]	x	World coordinate along x axis at which to evaluate derivatives.
[in]	y	World coordinate along y axis at which to evaluate derivatives.
[in]	z	World coordinate along z axis at which to evaluate derivatives.
[in]	t	Temporal coordinate of point at which to evaluate derivatives.
[in]	t0	Temporal coordinate of co-domain (target). Used by velocity-based models.
[in]	wrt_world	Whether derivatives are computed w.r.t. world coordinate system.
[in]	use_spacing	Whether to use grid spacing when `wrt_world` is `true`.

Reimplemented in mirtk::BSplineFreeFormTransformationSV.

Definition at line 1789 of file FreeFormTransformation.h.

§ JacobianToWorld() [1/3]

void mirtk::FreeFormTransformation::JacobianToWorld	(	double &	du,
		double &	dv
	)		const

inline

Convert 1st order derivatives computed w.r.t 2D lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1542 of file FreeFormTransformation.h.

§ JacobianToWorld() [2/3]

void mirtk::FreeFormTransformation::JacobianToWorld	(	double &	du,
		double &	dv,
		double &	dw
	)		const

inline

Convert 1st order derivatives computed w.r.t 3D lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1550 of file FreeFormTransformation.h.

§ JacobianToWorld() [3/3]

void mirtk::FreeFormTransformation::JacobianToWorld ( Matrix & jac ) const

inline

Convert 1st order derivatives computed w.r.t lattice coordinates to derivatives w.r.t world coordinates

Definition at line 1559 of file FreeFormTransformation.h.

§ ParametricGradient() [1/2]

virtual void mirtk::FreeFormTransformation::ParametricGradient	(	const GenericImage< double > *	,
		double *	,
		const WorldCoordsImage *	,
		const WorldCoordsImage *	,
		double	= `NaN`,
		double	= `1`
	)		const

virtual

Applies the chain rule to convert spatial non-parametric gradient to a gradient w.r.t the parameters of this transformation.

If the transformation itself is non-parametric, the gradient will be passed through unchanged. The default implementation uses the full Jacobian matrix computed for each DoF separately (i.e., calls JacobianDOFs for each DoF).

For 4D transformations, the temporal coordinate t used for the computation of the Jacobian of the transformation w.r.t the transformation parameters for all spatial (x, y, z) voxel coordinates in world units, is assumed to correspond to the temporal origin of the given gradient image. For 4D transformations parameterized by velocities, a second time for the upper integration bound can be provided as last argument to this method. This last argument is ignored by transformations parameterized by displacements.

See also: ImageSimilarityMetric::EvaluateGradient

Reimplemented from mirtk::Transformation.

Reimplemented in mirtk::BSplineFreeFormTransformationSV, mirtk::BSplineFreeFormTransformation3D, mirtk::BSplineFreeFormTransformation4D, mirtk::BSplineFreeFormTransformationTD, mirtk::BSplineFreeFormTransformationStatistical, mirtk::FreeFormTransformation3D, and mirtk::FreeFormTransformation4D.

§ ParametricGradient() [2/2]

virtual void mirtk::FreeFormTransformation::ParametricGradient	(	const PointSet &	,
		const Vector3D< double > *	,
		double *	,
		double	= `0`,
		double	= `NaN`,
		double	= `1`
	)		const

virtual

Applies the chain rule to convert point-wise non-parametric gradient to a gradient w.r.t the parameters of this transformation.

Reimplemented from mirtk::Transformation.

Reimplemented in mirtk::BSplineFreeFormTransformationSV, mirtk::BSplineFreeFormTransformationTD, and mirtk::FreeFormTransformation3D.

Member Data Documentation

§ _CPFunc

CPInterpolator* mirtk::FreeFormTransformation::_CPFunc

protected

Infinite continuous function of free-form transformation

Note that the actual interpolator object is (at the moment) attribute of the specific FFD implementation. The base class pointer here is only used to update the interpolator when necessary, e.g., when the extrapolation mode has changed. It is set by the base class constructor to the respective interpolate image function attribute of the subclass.

Definition at line 131 of file FreeFormTransformation.h.

§ _CPImage

CPImage mirtk::FreeFormTransformation::_CPImage

protected

Finite discrete representation of free-form transformation coefficients

Note that this image instance stores all the attributes of the control point lattice. The actual control point data is stored in the parameters of the transformation, the memory of which is managed by the base class. The image only wraps this memory and interprets it as an image. This allows the use of image functions such as interpolators and efficient image filters.

Definition at line 119 of file FreeFormTransformation.h.

§ _CPStatus

CPStatus**** mirtk::FreeFormTransformation::_CPStatus

protected

Status of control points

Note that the actual status values are stored by the base class member Transformation::_Status in a contiguous memory block.

Definition at line 138 of file FreeFormTransformation.h.

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

FreeFormTransformation.h

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Member Typedef Documentation

§ CPInterpolator

§ Vector

Member Function Documentation

§ ActualNumberOfDOFs()

§ Approximate() [1/4]

§ Approximate() [2/4]

§ Approximate() [3/4]

§ Approximate() [4/4]

§ ApproximateAsNew()

§ ApproximationDomain()

§ BendingEnergyGradient()

§ BoundingBox() [1/8]

§ BoundingBox() [2/8]

§ BoundingBox() [3/8]

§ BoundingBox() [4/8]

§ BoundingBox() [5/8]

§ BoundingBox() [6/8]

§ BoundingBox() [7/8]

§ BoundingBox() [8/8]

§ CopyFrom()

§ CropPadPassiveCPs() [1/2]

§ CropPadPassiveCPs() [2/2]

§ DefaultAttributes()

§ DOFBoundingBox() [1/2]

§ DOFBoundingBox() [2/2]

§ Extrapolator()

§ FFDJacobianDetDerivative()

§ HessianToWorld() [1/4]

§ HessianToWorld() [2/4]

§ HessianToWorld() [3/4]

§ HessianToWorld() [4/4]

§ Interpolate()

§ JacobianDetDerivative()

§ JacobianToWorld() [1/3]

§ JacobianToWorld() [2/3]

§ JacobianToWorld() [3/3]

§ ParametricGradient() [1/2]

§ ParametricGradient() [2/2]

Member Data Documentation

§ _CPFunc

§ _CPImage

§ _CPStatus