#include <itkMultiphaseSparseFiniteDifferenceImageFilter.h>

Inheritance diagram for itk::MultiphaseSparseFiniteDifferenceImageFilter< TInputImage, TFeatureImage, TOutputImage, TFunction, TIdCell >:

Collaboration diagram for itk::MultiphaseSparseFiniteDifferenceImageFilter< TInputImage, TFeatureImage, TOutputImage, TFunction, TIdCell >:

List of all members.

Classes
struct	SparseDataStruct
Public Types
typedef NeighborhoodAlgorithm::ImageBoundaryFacesCalculator < StatusImageType >	BFCType
typedef SmartPointer< const Self >	ConstPointer
typedef Superclass::FeatureImagePointer	FeatureImagePointer
typedef Superclass::FeatureImageType	FeatureImageType
typedef Superclass::FeaturePointType	FeaturePointType
typedef Superclass::FeatureRegionType	FeatureRegionType
typedef Superclass::FeatureSizeType	FeatureSizeType
typedef Superclass::FeatureSpacingType	FeatureSpacingType
typedef FiniteDifferenceFunctionType::FloatOffsetType	FiniteDifferenceFunctionFloatOffsetType
typedef Superclass::FiniteDifferenceFunctionPointer	FiniteDifferenceFunctionPointer
typedef Superclass::FiniteDifferenceFunctionType	FiniteDifferenceFunctionType
typedef Superclass::IdCellType	IdCellType
typedef Superclass::InputImagePointer	InputImagePointer
typedef Superclass::InputImageType	InputImageType
typedef Superclass::InputIndexType	InputIndexType
typedef Superclass::InputIndexValueType	InputIndexValueType
typedef Superclass::InputOffsetValueType	InputOffsetValueType
typedef Superclass::InputPixelType	InputPixelType
typedef Superclass::InputPointType	InputPointType
typedef Superclass::InputRegionType	InputRegionType
typedef Superclass::InputSizeType	InputSizeType
typedef Superclass::InputSizeValueType	InputSizeValueType
typedef Superclass::InputSpacingType	InputSpacingType
typedef LayerType::ConstIterator	LayerConstIterator
typedef LayerType::Iterator	LayerIterator
typedef LayerListType::const_iterator	LayerListConstIterator
typedef LayerListType::iterator	LayerListIterator
typedef std::vector < LayerPointerType >	LayerListType
typedef LayerNodeStorageType::Pointer	LayerNodeStoragePointer
typedef ObjectStore < LayerNodeType >	LayerNodeStorageType
typedef SparseFieldLevelSetNode < OutputIndexType >	LayerNodeType
typedef LayerType::Pointer	LayerPointerType
typedef SparseFieldLayer < LayerNodeType >	LayerType
typedef SparseFieldCityBlockNeighborList < NeighborhoodIterator < OutputImageType > >	NeighborListType
typedef NeighborListType::OffsetType	OffsetType
typedef Superclass::OutputImagePointer	OutputImagePointer
typedef Superclass::OutputImageType	OutputImageType
typedef Superclass::OutputIndexType	OutputIndexType
typedef Superclass::OutputIndexValueType	OutputIndexValueType
typedef Superclass::OutputPixelType	OutputPixelType
typedef Superclass::OutputRegionType	OutputRegionType
typedef Superclass::OutputSizeType	OutputSizeType
typedef SmartPointer< Self >	Pointer
typedef MultiphaseSparseFiniteDifferenceImageFilter	Self
typedef StatusImageType::Pointer	StatusImagePointer
typedef Image< StatusType, itkGetStaticConstMacro(ImageDimension) >	StatusImageType
typedef signed char	StatusType
typedef MultiphaseFiniteDifferenceImageFilter < TInputImage, TFeatureImage, TOutputImage, TFunction, TIdCell >	Superclass
typedef Superclass::TimeStepType	TimeStepType
typedef UpdateBufferType::const_iterator	UpdateBufferConstIterator
typedef std::vector< ValueType >	UpdateBufferType
typedef InputImageType::ValueType	ValueType
typedef ZeroCrossingFilterType::Pointer	ZeroCrossingFilterPointer
typedef ZeroCrossingImageFilter < InputImageType, InputImageType >	ZeroCrossingFilterType
Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const
virtual const char *	GetNameOfClass () const
void	SetFunctionCount (const IdCellType &n)
	typedef (Concept::EqualityComparable< typename TOutputImage::PixelType >) OutputEqualityComparableCheck
	typedef (Concept::Convertible< double, typename TOutputImage::PixelType >) DoubleConvertibleToOutputCheck
	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 = Superclass::ImageDimension
Protected Member Functions
void	AllocateUpdateBuffer ()
void	ApplyUpdate (TimeStepType dt)
TimeStepType	CalculateChange ()
virtual ValueType	CalculateUpdateValue (const OutputIndexType &, const TimeStepType &dt, const ValueType &value, const ValueType &change)
void	ConstructActiveLayer ()
void	ConstructLayer (SparseDataStruct *sparsePtr, StatusType from, StatusType to)
void	CopyInputToOutput ()
virtual ValueType	GetValueOne () const
virtual ValueType	GetValueZero () const
void	Initialize ()
void	InitializeActiveLayerValues ()
void	InitializeBackgroundConstants ()
virtual void	InitializeBackgroundPixels ()
void	InitializeIteration ()
virtual void	PostProcessOutput ()
virtual void	PrintSelf (std::ostream &os, Indent indent) const
void	ProcessOutsideList (LayerType *OutsideList, StatusType ChangeToStatus)
void	ProcessStatusList (LayerType InputList, LayerType OutputList, StatusType ChangeToStatus, StatusType SearchForStatus)
void	PropagateAllLayerValues ()
void	PropagateFunctionLayerValues (unsigned int functionIndex)
void	PropagateLayerValues (SparseDataStruct *sparsePtr, StatusType from, StatusType to, StatusType promote, int InOrOut)
void	UpdateActiveLayerValues (TimeStepType dt, LayerType StatusUpList, LayerType StatusDownList)
virtual void	UpdatePixel (unsigned int, unsigned int, NeighborhoodIterator< InputImageType > &, ValueType &, bool &)

	MultiphaseSparseFiniteDifferenceImageFilter ()
	~MultiphaseSparseFiniteDifferenceImageFilter ()
Protected Attributes
ValueType	m_BackgroundValue
ValueType	m_IsoSurfaceValue
NeighborListType	m_NeighborList
unsigned int	m_NumberOfLayers
std::vector< ValueType >	m_PixelDistance
std::vector< SparseDataStruct * >	m_SparseData
Static Protected Attributes
static double	m_ConstantGradientValue
static const StatusType	m_StatusActiveChangingDown
static const StatusType	m_StatusActiveChangingUp
static const StatusType	m_StatusBoundaryPixel
static const StatusType	m_StatusChanging
static const StatusType	m_StatusNull
static const ValueType	m_ValueOne
static const ValueType	m_ValueZero
Private Attributes
bool	m_BoundsCheckingActive
unsigned int	m_CurrentFunctionIndex
unsigned int	m_RMSCounter
double	m_RMSSum
bool	m_InterpolateSurfaceLocation
	MultiphaseSparseFiniteDifferenceImageFilter (const Self &)
void	operator= (const Self &)

Detailed Description

template<class TInputImage, class TFeatureImage, class TOutputImage, class TFunction, typename TIdCell = unsigned int>
class itk::MultiphaseSparseFiniteDifferenceImageFilter< TInputImage, TFeatureImage, TOutputImage, TFunction, TIdCell >

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 indices that are adjacent to the -level set. These indices are called the "active set". The values at these active set indices define the position of the -level curve. The active set indices 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 indices contained in the active set.

: The city-block neighborhoods of the active set indices 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 indices 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 indices 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 FiniteDifferenceImageFilter2 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 indices 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.IndexType this->SetNumberOfLayers(5);

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 in three dimensions, for example, require 3 layers. In two dimensions, a minimum of 2 layers is probably required. 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 FiniteDifferenceImageFilter2 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.

This code was adapted from the paper

"An active contour model without edges" T. Chan and L. Vese. In Scale-Space Theories in Computer Vision, pages 141-151, 1999.

Author:: Mosaliganti K., Smith B., Gelas A., Gouaillard A., Megason S.

This code was taken from the Insight Journal paper:

"Cell Tracking using Coupled Active Surfaces for Nuclei and Membranes" http://www.insight-journal.org/browse/publication/642 http://hdl.handle.net/10380/3055

That is based on the papers:

"Level Set Segmentation: Active Contours without edge" http://www.insight-journal.org/browse/publication/322 http://hdl.handle.net/1926/1532

and

"Level set segmentation using coupled active surfaces" http://www.insight-journal.org/browse/publication/323 http://hdl.handle.net/1926/1533

Definition at line 178 of file itkMultiphaseSparseFiniteDifferenceImageFilter.h.