This filter integrates a time varying velocity field, using fourth order Runge-Kutta. This filter is basically a tidied up version of that in ANTS: http://www.picsl.upenn.edu/ANTS/ However, ANTS has the four timepoints back to front. I don't know if this is intentional. More...

Inheritance diagram for itk::FourthOrderRungeKuttaVelocityFieldIntegrationFilter< TScalarType, NDimensions >:

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Collaboration diagram for itk::FourthOrderRungeKuttaVelocityFieldIntegrationFilter< TScalarType, NDimensions >:

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Public Types
typedef FourthOrderRungeKuttaVelocityFieldIntegrationFilter	Self

typedef ImageToImageFilter < Image< Vector< TScalarType, NDimensions >, NDimensions+1 > , Image< Vector< TScalarType, NDimensions >, NDimensions > >	Superclass

typedef SmartPointer< Self >	Pointer

typedef SmartPointer< const Self >	ConstPointer

typedef Vector< TScalarType, NDimensions >	TimeVaryingVelocityPixelType

typedef Image < TimeVaryingVelocityPixelType, NDimensions+1 >	TimeVaryingVelocityImageType

typedef TimeVaryingVelocityImageType::RegionType	TimeVaryingVelocityRegionType

typedef TimeVaryingVelocityImageType::IndexType	TimeVaryingVelocityIndexType

typedef TimeVaryingVelocityImageType::SizeType	TimeVaryingVelocitySizeType

typedef TimeVaryingVelocityImageType::PointType	TimeVaryingVelocityPointType

typedef TimeVaryingVelocityImageType::SpacingType	TimeVaryingVelocitySpacingType

typedef TimeVaryingVelocityImageType::DirectionType	TimeVaryingVelocityDirectionType

typedef TScalarType	MaskPixelType

typedef Image< MaskPixelType, NDimensions >	MaskImageType

typedef MaskImageType::Pointer	MaskImagePointer

typedef MaskImageType::IndexType	MaskImageIndexType

typedef MaskImageType::PointType	MaskImagePointType

typedef Vector< TScalarType, NDimensions >	DisplacementPixelType

typedef Image < DisplacementPixelType, NDimensions >	DisplacementImageType

typedef DisplacementImageType::RegionType	DisplacementImageRegionType

typedef DisplacementImageType::IndexType	DisplacementImageIndexType

typedef DisplacementImageType::SizeType	DisplacementImageSizeType

typedef DisplacementImageType::PointType	DisplacementImagePointType

typedef DisplacementImageType::SpacingType	DisplacementImageSpacingType

typedef DisplacementImageType::DirectionType	DisplacementImageDirectionType

typedef VectorLinearInterpolateImageFunction < TimeVaryingVelocityImageType, TScalarType >	TimeVaryingVelocityFieldInterpolatorType

typedef TimeVaryingVelocityFieldInterpolatorType::Pointer	TimeVaryingVelocityFieldInterpolatorPointer

typedef Point< TScalarType, NDimensions+1 >	TimeVaryingPointType

typedef Image< TScalarType, NDimensions >	ThicknessImageType

typedef ThicknessImageType::PixelType	ThicknessImagePixelType

typedef ThicknessImageType::Pointer	ThicknessImagePointer

typedef NearestNeighborInterpolateImageFunction < ThicknessImageType, TScalarType >	ThicknessImageInterpolatorType

typedef ThicknessImageInterpolatorType::Pointer	ThicknessImageInterpolatorPointer

Public Member Functions
virtual const char *	GetClassName () const

	itkStaticConstMacro (Dimension, unsigned int, NDimensions)

virtual void	SetStartTime (float _arg)

virtual float	GetStartTime ()

virtual void	SetFinishTime (float _arg)

virtual float	GetFinishTime ()

virtual void	SetDeltaTime (float _arg)

virtual float	GetDeltaTime ()

virtual void	SetCalculateThickness (bool _arg)

virtual bool	GetCalculateThickness ()

virtual float	GetMaxThickness ()

virtual float	GetMaxDisplacement ()

virtual float	GetFieldEnergy ()

void	SetVoxelsToIntegrateMaskImage (MaskImageType *image)

void	SetMaxDistanceMaskImage (ThicknessImageType *maxDistance)

void	SetGreyWhiteInterfaceMaskImage (MaskImageType *greyWhiteInterface)

ThicknessImageType *	GetCalculatedThicknessImage ()

Static Public Member Functions
static Pointer	New ()

Protected Member Functions
	FourthOrderRungeKuttaVelocityFieldIntegrationFilter ()

	~FourthOrderRungeKuttaVelocityFieldIntegrationFilter ()

void	PrintSelf (std::ostream &os, Indent indent) const

virtual void	BeforeThreadedGenerateData ()

virtual void	ThreadedGenerateData (const DisplacementImageRegionType &regionForThread, ThreadIdType threadId)

virtual void	AfterThreadedGenerateData ()

Detailed Description

template<typename TScalarType, unsigned int NDimensions = 3>
class itk::FourthOrderRungeKuttaVelocityFieldIntegrationFilter< TScalarType, NDimensions >

This filter integrates a time varying velocity field, using fourth order Runge-Kutta. This filter is basically a tidied up version of that in ANTS: http://www.picsl.upenn.edu/ANTS/ However, ANTS has the four timepoints back to front. I don't know if this is intentional.

Also note, that I was reading Numerical Recipes in C, page 711, the bit on fourth-order Runge-Kutta method. If you are reading this, bear in mind that we are integrating through time. This means that for a 3D image, with x,y,z ordinates, and a time ordinate, that it is the time ordinate (index 3) that corresponds to x_n in Numerical Recipes. So, for a small shift in time, given by DeltaTime in this class, and h in Numerical Recipes, we calculate a new point location (x,y,z), analagous to y_n in Numerical Recipes.

Note also that we have start time and end time, normally, 0 and 1 respectively. If you reverse these you are integrating backwards, which computes the inverse. Also delta time controls the size of the step. We essentially start at start time (0), and at each step we add delta time (0.1 say) until we exceed end time (1). So, in effect this can be independent of the size of the time dimension of your velocity field. You could have delta time = 0.1, and have the size of your time dimension = 3.

The mask image, set using SetMaskImage, determines which voxels are integrated. Any value in this mask apart from zero, will cause that voxel to be integrated. It is assumed that this is the same size, as the input image (but obviously, only 1 time dimension).

The max distance mask is used to stop the integration if the Euclidean distance of a point has gone above that in the mask.

Once this class has integrated all the points in the mask, it is possible to compute a thickness image, as described in Das et. al. NeuroImage 2009 doi:10.1016/j.neuroimage.2008.12.016. To do this, a mask is set, currently called the SetGreyWhiteInterfaceMask method. For each of these voxels, the computed thickness value, is propogated through the velocity field. This could be done in another filter, with a small amount of refactoring, but it is in here for now. The result can be obtained by setting CalculateThickness to true, calling an Update and then GetCalculatedThicknessImage after the update.