This class implements a finite difference partial differential equation solver for evolving surfaces embedded in volumes as level-sets. More...

#include <itkSparseFieldLevelSetImageFilter.h>

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

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

List of all members.

Public Types
typedef SmartPointer< const Self >	ConstPointer
typedef OutputImageType::IndexType	IndexType
typedef TInputImage	InputImageType
typedef std::vector < LayerPointerType >	LayerListType
typedef ObjectStore < LayerNodeType >	LayerNodeStorageType
typedef SparseFieldLevelSetNode < IndexType >	LayerNodeType
typedef LayerType::Pointer	LayerPointerType
typedef SparseFieldLayer < LayerNodeType >	LayerType
typedef Superclass::NeighborhoodScalesType	NeighborhoodScalesType
typedef TOutputImage	OutputImageType
typedef SmartPointer< Self >	Pointer
typedef Superclass::RadiusType	RadiusType
typedef SparseFieldLevelSetImageFilter	Self
typedef Image< StatusType, itkGetStaticConstMacro(ImageDimension) >	StatusImageType
typedef signed char	StatusType
typedef FiniteDifferenceImageFilter < TInputImage, TOutputImage >	Superclass
typedef Superclass::TimeStepType	TimeStepType
typedef std::vector< ValueType >	UpdateBufferType
typedef OutputImageType::ValueType	ValueType
Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual const char *	GetNameOfClass () const
	typedef (Concept::Convertible< double, typename TOutputImage::PixelType >) DoubleConvertibleToOutputCheck
	typedef (Concept::EqualityComparable< typename TOutputImage::PixelType >) OutputEqualityComparableCheck
	typedef (Concept::OStreamWritable< typename TOutputImage::PixelType >) OutputOStreamWritableCheck

virtual void	SetNumberOfLayers (unsigned int _arg)
virtual unsigned int	GetNumberOfLayers () const

virtual void	SetIsoSurfaceValue (ValueType _arg)
virtual ValueType	GetIsoSurfaceValue () const

virtual void	SetInterpolateSurfaceLocation (bool _arg)
virtual bool	GetInterpolateSurfaceLocation () const

void	InterpolateSurfaceLocationOn ()
void	InterpolateSurfaceLocationOff ()
Static Public Member Functions
static Pointer	New ()
Static Public Attributes
static const unsigned int	ImageDimension = TOutputImage::ImageDimension
Protected Member Functions
void	AllocateUpdateBuffer ()
void	ApplyUpdate (const TimeStepType &dt)
TimeStepType	CalculateChange ()
virtual ValueType	CalculateUpdateValue (const IndexType &, const TimeStepType &dt, const ValueType &value, const ValueType &change)
void	ConstructActiveLayer ()
void	ConstructLayer (StatusType from, StatusType to)
void	CopyInputToOutput ()
virtual ValueType	GetValueOne () const
virtual ValueType	GetValueZero () const
void	Initialize ()
void	InitializeActiveLayerValues ()
virtual void	InitializeBackgroundPixels ()
virtual void	PostProcessOutput ()
void	ProcessOutsideList (LayerType *OutsideList, StatusType ChangeToStatus)
void	ProcessStatusList (LayerType InputList, LayerType OutputList, StatusType ChangeToStatus, StatusType SearchForStatus)
void	PropagateAllLayerValues ()
void	PropagateLayerValues (StatusType from, StatusType to, StatusType promote, int InOrOut)
void	UpdateActiveLayerValues (TimeStepType dt, LayerType StatusUpList, LayerType StatusDownList)

	SparseFieldLevelSetImageFilter ()
	~SparseFieldLevelSetImageFilter ()
virtual void	PrintSelf (std::ostream &os, Indent indent) const
Protected Attributes
double	m_ConstantGradientValue
ValueType	m_IsoSurfaceValue
LayerNodeStorageType::Pointer	m_LayerNodeStore
LayerListType	m_Layers
SparseFieldCityBlockNeighborList < NeighborhoodIterator < OutputImageType > >	m_NeighborList
unsigned int	m_NumberOfLayers
OutputImageType::Pointer	m_ShiftedImage
StatusImageType::Pointer	m_StatusImage
UpdateBufferType	m_UpdateBuffer
Static Protected Attributes
static StatusType	m_StatusActiveChangingDown
static StatusType	m_StatusActiveChangingUp
static StatusType	m_StatusBoundaryPixel
static StatusType	m_StatusChanging
static StatusType	m_StatusNull
static ValueType	m_ValueOne
static ValueType	m_ValueZero
Private Attributes
bool	m_BoundsCheckingActive
bool	m_InterpolateSurfaceLocation
	SparseFieldLevelSetImageFilter (const Self &)
void	operator= (const Self &)

Detailed Description

template<class TInputImage, class TOutputImage>
class itk::SparseFieldLevelSetImageFilter< TInputImage, TOutputImage >

This class implements a finite difference partial differential equation solver for evolving surfaces embedded in volumes as level-sets.

: The ``sparse field'' approach to the level-set model is a logical extension of the classical narrow band technique, which seeks to minimize computational effort by restricting calculations to those pixels in a region of interest around the moving surface (the -level curve). The sparse field method uses a narrow band that is exactly the width needed to calculate changes on the level curve for the next time step. Because the band of grid points under consideration is so sparse, this approach has several advantages: the algorithm does exactly the number of calculations needed to determine the next position of the -level curve, and the distance transform around the level curve can be recomputed at each iteration.

: The sparse field algorithm works by constructing a linked list of indicies that are adjacent to the -level set. These indicies are called the ``active set''. The values at these active set indicies define the position of the -level curve. The active set indicies are shifted to follow the distance transform embedding of the -level curve as their values move in and out of a fixed numerical range about . In this way, the active set is maintained as only those pixels adjacent to the evolving surface. Calculations are then done only at indicies contained in the active set.

: The city-block neighborhoods of the active set indicies are maintained as separate lists called ``layers''. At each iteration, the values at the layers are reinitialized as the distance transform from the active set. The number of layers can be adjusted according to the footprint needed for the calculations on the level curve.

: Briefly, the sparse field solver algorithm is as follows:

: 1. For each active layer index : Compute the change at $u_{x_j}$ , the grid point in the embedding, based on local geometry and external forces and using a stable numerical scheme.

2. For each active layer index $x_j$ , add the change to the grid point value and redefine the active set indicies and those of its layers based on any value changes which have moved outside of the numerical range allowed for the active set.

3. Starting with the first layers adjacent to the active set and moving outwards, reconstruct the distance transform by setting values in the layers according to their neighbors. At the very outer layers, add or remove indicies which have come into or moved out of the sparse field.

HOW TO USE THIS CLASS: Typically, this class should be subclassed with additional functionality for specific applications. It is possible, however to use this solver as a filter directly by instantiating it and supplying it with an appropriate LevelSetFunction object via the SetDifferenceFunction method. See the subclasses and their associated documentation for more information on using this class. Also see the FiniteDifferenceImageFilter documentation for a general overview of this class of solvers.

INPUTS: This filter takes an itk::Image as input. The appropriate type of input image is entirely determined by the application. As a rule, however, the input type is immediately converted to the output type before processing. This is because the input is not assumed to be a real value type and must be converted to signed, real values for the calculations. The input values will also be shifted by the isosurface value so that the algorithm only needs to consider the zero level set.

OUTPUTS: The output of the filter is the distance transform embedding of the isosurface as the zero level set. Values INSIDE the surface will be NEGATIVE and values OUTSIDE the surface will be POSITIVE. The distance transform only holds for those indicies in layers around the active layer. Elsewhere, the values are a fixed positive or negative that is one greater than the layer of greatest magnitude. In other words, if there are three layers, then inside values reach a minimum of -4.0 and outside values a maximum of 4.0.

PARAMETERS: The NumberOfLayers parameter controls the number of layers inside and outside of the active set (see description above). The sparse field will contain 2*NumberOfLayers+1 lists of indices: the active set and city block neighbors inside and outside the active set. It is important to specify enough layers to cover the footprint of your calculations. Curvature calculations require a minimum of 2 layers. Higher order derivatives and other geometrical measures may require more layers. If too few layers are specified, then the calculations will pull values from the background, which may consist of arbitrary or random values.

: The IsoSurfaceValue indicates which value in the input represents the interface of interest. By default, this value is zero. When the solver initializes, it will subtract the IsoSurfaceValue from all values, in the input, shifting the isosurface of interest to zero in the output.

IMPORTANT!: Read the documentation for FiniteDifferenceImageFilter before attempting to use this filter. The solver requires that you specify a FiniteDifferenceFunction to use for calculations. This is set using the method SetDifferenceFunction in the parent class.

REFERENCES: Whitaker, Ross. A Level-Set Approach to 3D Reconstruction from Range Data. International Journal of Computer Vision. V. 29 No. 3, 203-231. 1998.

: Sethian, J.A. Level Set Methods. Cambridge University Press. 1996.

Definition at line 230 of file itkSparseFieldLevelSetImageFilter.h.