This class implements the 4th-order level set anisotropic diffusion (smoothing) PDE. More...

Inheritance diagram for itk::AnisotropicFourthOrderLevelSetImageFilter< TInputImage, TOutputImage >:

Collaboration diagram for itk::AnisotropicFourthOrderLevelSetImageFilter< TInputImage, TOutputImage >:

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef LevelSetFunctionWithRefitTerm < TOutputImage, SparseImageType >	FunctionType
typedef SmartPointer< Self >	Pointer
typedef FunctionType::RadiusType	RadiusType
typedef AnisotropicFourthOrderLevelSetImageFilter	Self
typedef Superclass::SparseImageType	SparseImageType
typedef SparseFieldFourthOrderLevelSetImageFilter < TInputImage, TOutputImage >	Superclass
Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual unsigned int	GetMaxFilterIteration () const
virtual const char *	GetNameOfClass () const
virtual void	SetMaxFilterIteration (unsigned int _arg)
Static Public Member Functions
static Pointer	New ()
Protected Member Functions
	AnisotropicFourthOrderLevelSetImageFilter ()
virtual void	PrintSelf (std::ostream &os, Indent indent) const
	~AnisotropicFourthOrderLevelSetImageFilter ()

virtual bool	Halt ()
Private Member Functions
	AnisotropicFourthOrderLevelSetImageFilter (const Self &)
void	operator= (const Self &)
Private Attributes
FunctionType::Pointer	m_Function
unsigned int	m_MaxFilterIteration

Detailed Description

This class implements the 4th-order level set anisotropic diffusion (smoothing) PDE.

INPUT and OUTPUT: This is a volume to volume filter; however, it is meant to process (smooth) surfaces. The input surface is an isosurface of the input volume. The isosurface value to be processed can be set by calling SetIsoSurfaceValue (default is 0). The output surface is the 0-isosurface of the output volume, regardless of the input isosurface value. To visualize the input/output surfaces to this filter a mesh extraction method such as marching cubes can be used.

: The 4th-order level set PDE framework is proposed as an alternative to 2nd order PDEs. By order we mean the order of differentiation of the level set image function required to compute derivatives for updating the image. For instance, the popular curvature flow uses 2nd-order derivatives of the level set image; hence, it is a 2nd order PDE.

: 2nd-order curvature flow can be used by itself to smooth surfaces as a post-processing filter or it can be used with other PDE terms such as a Canny edge term that attracts the surface to strong edges in a data image. Curvature flow smoothes surfaces by making the surface move in the direction that will decrease surface area.

: The 4th-order PDE framework provides an improvement over curvature flow. Instead of making the surface move to decrease surface area it makes the surface move to decrease total curvature. Similar to curvature flow, these PDEs can be used alone or in conjunction with data terms. The 4th-order PDE framework is implemented in SparseFieldFourthOrderLevelSetImageFilter. This filter class, which is derived from that, uses the 4th-order PDE by itself to implement an anisotropic surface smoothing algorithm. This is a feature preserving surface processing algorithm that smoothes surfaces but will preserve certain features (creases, edges, other sharp features) depending on the NormalProcessConductanceParameter.

PARAMETERS: As mentioned before, the IsoSurfaceValue parameter chooses which isosurface of the input to process. The MaxFilterIterations parameter determine the number of iterations for which this filter will run. The more iterations, the more smoothing. NormalProcessConductanceParameter controls the amount of feature preservation. Its units are in curvature. Reasonable values for almost all surface are in the range 0.1-0.25 . The shape of the surface where the total curvature is above the value of this parameter will tend to stay the same (be preserved) or even be sharpened. The lower the value, the more feature preservation. Notice the difference between the number of iterations parameter and the conductance parameter: for a given conductance parameter, surface features with high enough curvature will be preserved even if the number of iterations is set to be extremely large.