#include <itkHilbertPath.h>

Detailed Description

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>
class itk::HilbertPath< TIndexValue, VDimension >

Represent an n-dimensional Hilbert path for a given order.

This class is used to construct a Hilbert spacing-filling curve (or path) for a given order and given dimension. The locality- preserving properties make the Hilbert path an attractive option for mapping multi-dimensional data to a single array.

The path is defined by its dimensionality and order( >= 1 ) with its starting point at [0]^Dimension. The size of the path in each dimension is 2^order where each discrete location is visited by that path. For example, a 2-D Hilbert path of order 8 can map each pixel of a 256x256 image onto a single array. More properties and visualizations can be found in various places on the web.

The implementation is based on Chris Hamilton, "Compact Hilbert Indices", Technical Report CS-2006-07, July 24, 2006. and a direct porting of the Aldo Cortesi's python code found at https://github.com/cortesi/scurve

Author: Nick Tustison

Definition at line 54 of file itkHilbertPath.h.

Inheritance diagram for itk::HilbertPath< TIndexValue, VDimension >:

Collaboration diagram for itk::HilbertPath< TIndexValue, VDimension >:

Public Types
using	ConstPointer = SmartPointer< const Self >

using	HilbertOrderType = unsigned int

using	HilbertPathSizeType = typename HilbertPathType::size_type

using	HilbertPathType = std::vector< IndexType >

using	IndexType = OutputType

using	PathIndexType = InputType

using	Pointer = SmartPointer< Self >

using	Self = HilbertPath< TIndexValue, VDimension >

using	Superclass = Path< unsigned int, Index< VDimension >, VDimension >

Public Types inherited from itk::Path< unsigned int, Index< 3 >, 3 >
using	ConstPointer = SmartPointer< const Self >

using	IndexType = Index< VDimension >

using	InputType = unsigned int

using	OffsetType = Offset< VDimension >

using	OutputType = Index< 3 >

using	Pointer = SmartPointer< Self >

using	Self = Path

using	Superclass = DataObject

Public Types inherited from itk::DataObject
using	ConstPointer = SmartPointer< const Self >

using	DataObjectIdentifierType = std::string

using	DataObjectPointerArraySizeType = std::vector< Pointer >::size_type

using	Pointer = SmartPointer< Self >

using	Self = DataObject

using	Superclass = Object

Public Types inherited from itk::Object
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = Object

using	Superclass = LightObject

Public Types inherited from itk::LightObject
using	ConstPointer = SmartPointer< const Self >

using	Pointer = SmartPointer< Self >

using	Self = LightObject

Public Member Functions
InputType	EndOfInput () const override

OutputType	Evaluate (const PathIndexType &input) const override

virtual InputType	EvaluateInverse (const IndexType &input)

OutputType	EvaluateToIndex (const PathIndexType &input) const override

const char *	GetNameOfClass () const override

OffsetType	IncrementInput (InputType &) const override

virtual HilbertPathSizeType	NumberOfSteps () const

PathIndexType	TransformMultiDimensionalIndexToPathIndex (const IndexType &index)

IndexType	TransformPathIndexToMultiDimensionalIndex (const PathIndexType id)


virtual void	Clear ()


void	Initialize () override


virtual void	SetHilbertOrder (HilbertOrderType _arg)

virtual HilbertOrderType	GetHilbertOrder () const

Public Member Functions inherited from itk::Path< unsigned int, Index< 3 >, 3 >
virtual InputType	EndOfInput () const

virtual OutputType	Evaluate (const InputType &input) const=0

virtual IndexType	EvaluateToIndex (const InputType &input) const=0

const char *	GetNameOfClass () const override

virtual OffsetType	IncrementInput (InputType &input) const=0

virtual InputType	StartOfInput () const

Public Member Functions inherited from itk::DataObject
virtual void	CopyInformation (const DataObject *)

virtual void	DataHasBeenGenerated ()

void	DisconnectPipeline ()

bool	GetDataReleased () const

const char *	GetNameOfClass () const override

virtual const bool &	GetReleaseDataFlag () const

SmartPointer< ProcessObject >	GetSource () const

DataObjectPointerArraySizeType	GetSourceOutputIndex () const

const DataObjectIdentifierType &	GetSourceOutputName () const

virtual ModifiedTimeType	GetUpdateMTime () const

virtual void	Graft (const DataObject *)

virtual void	Initialize ()

virtual void	PrepareForNewData ()

virtual void	PropagateRequestedRegion ()

void	ReleaseData ()

virtual void	ReleaseDataFlagOn ()

virtual bool	RequestedRegionIsOutsideOfTheBufferedRegion ()

virtual void	ResetPipeline ()

void	SetReleaseDataFlag (bool flag)

virtual void	SetRequestedRegion (const DataObject *)

virtual void	SetRequestedRegionToLargestPossibleRegion ()

bool	ShouldIReleaseData () const

virtual void	Update ()

virtual void	UpdateOutputData ()

virtual void	UpdateOutputInformation ()

void	UpdateSource () const

virtual bool	VerifyRequestedRegion ()

void	SetPipelineMTime (ModifiedTimeType time)

virtual const ModifiedTimeType &	GetPipelineMTime () const

virtual void	SetRealTimeStamp (RealTimeStamp _arg)

virtual const RealTimeStamp &	GetRealTimeStamp () const

Public Member Functions inherited from itk::Object
unsigned long	AddObserver (const EventObject &event, Command *cmd) const

unsigned long	AddObserver (const EventObject &event, std::function< void(const EventObject &)> function) const

LightObject::Pointer	CreateAnother () const override

virtual void	DebugOff () const

virtual void	DebugOn () const

Command *	GetCommand (unsigned long tag)

bool	GetDebug () const

MetaDataDictionary &	GetMetaDataDictionary ()

const MetaDataDictionary &	GetMetaDataDictionary () const

virtual ModifiedTimeType	GetMTime () const

const char *	GetNameOfClass () const override

virtual const TimeStamp &	GetTimeStamp () const

bool	HasObserver (const EventObject &event) const

void	InvokeEvent (const EventObject &)

void	InvokeEvent (const EventObject &) const

virtual void	Modified () const

void	Register () const override

void	RemoveAllObservers ()

void	RemoveObserver (unsigned long tag) const

void	SetDebug (bool debugFlag) const

void	SetReferenceCount (int) override

void	UnRegister () const noexcept override

void	SetMetaDataDictionary (const MetaDataDictionary &rhs)

void	SetMetaDataDictionary (MetaDataDictionary &&rrhs)

virtual void	SetObjectName (std::string _arg)

virtual const std::string &	GetObjectName () const

Public Member Functions inherited from itk::LightObject
Pointer	Clone () const

virtual Pointer	CreateAnother () const

virtual void	Delete ()

virtual const char *	GetNameOfClass () const

virtual int	GetReferenceCount () const

void	Print (std::ostream &os, Indent indent=0) const

virtual void	Register () const

virtual void	SetReferenceCount (int)

virtual void	UnRegister () const noexcept

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from itk::DataObject
static bool	GetGlobalReleaseDataFlag ()

static void	GlobalReleaseDataFlagOff ()

static void	GlobalReleaseDataFlagOn ()

static Pointer	New ()

static void	SetGlobalReleaseDataFlag (bool val)

Static Public Member Functions inherited from itk::Object
static bool	GetGlobalWarningDisplay ()

static void	GlobalWarningDisplayOff ()

static void	GlobalWarningDisplayOn ()

static Pointer	New ()

static void	SetGlobalWarningDisplay (bool val)

Static Public Member Functions inherited from itk::LightObject
static void	BreakOnError ()

static Pointer	New ()

Static Public Attributes
static constexpr unsigned int	Dimension = VDimension

Static Public Attributes inherited from itk::Path< unsigned int, Index< 3 >, 3 >
static constexpr unsigned int	PathDimension

Protected Member Functions
	HilbertPath ()

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

	~HilbertPath () override=default

Protected Member Functions inherited from itk::Path< unsigned int, Index< 3 >, 3 >
virtual IndexType	GetZeroIndex () const

virtual OffsetType	GetZeroOffset () const

	Path ()

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

	~Path () override=default

Protected Member Functions inherited from itk::DataObject
	DataObject ()

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

virtual void	PropagateResetPipeline ()

	~DataObject () override

Protected Member Functions inherited from itk::Object
	Object ()

bool	PrintObservers (std::ostream &os, Indent indent) const

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

virtual void	SetTimeStamp (const TimeStamp &timeStamp)

	~Object () override

Protected Member Functions inherited from itk::LightObject
virtual LightObject::Pointer	InternalClone () const

	LightObject ()

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

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

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

virtual	~LightObject ()

Private Member Functions
void	ConstructHilbertPath ()

PathIndexType	GetBitRange (const PathIndexType, const PathIndexType, const PathIndexType, const PathIndexType)

PathIndexType	GetDirection (const PathIndexType, const PathIndexType)

PathIndexType	GetEntry (const PathIndexType)

PathIndexType	GetGrayCode (const PathIndexType)

PathIndexType	GetInverseGrayCode (const PathIndexType)

PathIndexType	GetInverseTransform (const PathIndexType, const PathIndexType, const PathIndexType, const PathIndexType)

PathIndexType	GetLeftBitRotation (PathIndexType, PathIndexType, const PathIndexType)

PathIndexType	GetRightBitRotation (PathIndexType, PathIndexType, const PathIndexType)

PathIndexType	GetTrailingSetBits (const PathIndexType, const PathIndexType)

PathIndexType	GetTransform (const PathIndexType, const PathIndexType, const PathIndexType, const PathIndexType)

PathIndexType	SetBit (const PathIndexType, const PathIndexType, const PathIndexType, const PathIndexType)

Private Attributes
HilbertOrderType	m_HilbertOrder { 1 }

HilbertPathType	m_HilbertPath {}

Additional Inherited Members
Protected Attributes inherited from itk::LightObject
std::atomic< int >	m_ReferenceCount {}

Member Typedef Documentation

◆ ConstPointer

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::ConstPointer = SmartPointer<const Self>

Definition at line 63 of file itkHilbertPath.h.

◆ HilbertOrderType

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::HilbertOrderType = unsigned int

Definition at line 81 of file itkHilbertPath.h.

◆ HilbertPathSizeType

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::HilbertPathSizeType = typename HilbertPathType::size_type

Definition at line 83 of file itkHilbertPath.h.

◆ HilbertPathType

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::HilbertPathType = std::vector<IndexType>

Definition at line 82 of file itkHilbertPath.h.

◆ IndexType

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::IndexType = OutputType

Definition at line 80 of file itkHilbertPath.h.

◆ PathIndexType

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::PathIndexType = InputType

The input/output type alias

Definition at line 79 of file itkHilbertPath.h.

◆ Pointer

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::Pointer = SmartPointer<Self>

Definition at line 62 of file itkHilbertPath.h.

◆ Self

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::Self = HilbertPath<TIndexValue, VDimension>

Standard class type aliases.

Definition at line 60 of file itkHilbertPath.h.

◆ Superclass

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

using itk::HilbertPath< TIndexValue, VDimension >::Superclass = Path<unsigned int, Index<VDimension>, VDimension>

Definition at line 61 of file itkHilbertPath.h.

Constructor & Destructor Documentation

◆ HilbertPath()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

itk::HilbertPath< TIndexValue, VDimension >::HilbertPath ( )

protected

◆ ~HilbertPath()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

itk::HilbertPath< TIndexValue, VDimension >::~HilbertPath ( )

overrideprotecteddefault

Member Function Documentation

◆ Clear()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

virtual void itk::HilbertPath< TIndexValue, VDimension >::Clear ( )

inlinevirtual

Remove all steps from the path

Definition at line 126 of file itkHilbertPath.h.

◆ ConstructHilbertPath()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

void itk::HilbertPath< TIndexValue, VDimension >::ConstructHilbertPath ( )

private

◆ EndOfInput()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

InputType itk::HilbertPath< TIndexValue, VDimension >::EndOfInput ( ) const

inlineoverridevirtual

Where does the path end (what is the last valid input value)?

Reimplemented from itk::Path< unsigned int, Index< 3 >, 3 >.

Definition at line 110 of file itkHilbertPath.h.

◆ Evaluate()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

OutputType itk::HilbertPath< TIndexValue, VDimension >::Evaluate ( const PathIndexType & input ) const

inlineoverridevirtual

Evaluate the hilbert path for the index at the specified path-position.

Implements itk::Path< unsigned int, Index< 3 >, 3 >.

Definition at line 90 of file itkHilbertPath.h.

◆ EvaluateInverse()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

virtual InputType itk::HilbertPath< TIndexValue, VDimension >::EvaluateInverse ( const IndexType & input )

inlinevirtual

Evaluate the hilbert path for the path-position at the specified index.

Definition at line 103 of file itkHilbertPath.h.

◆ EvaluateToIndex()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

OutputType itk::HilbertPath< TIndexValue, VDimension >::EvaluateToIndex ( const PathIndexType & input ) const

inlineoverridevirtual

Like Evaluate(), except always returns an index

Implements itk::Path< unsigned int, Index< 3 >, 3 >.

Definition at line 96 of file itkHilbertPath.h.

◆ GetBitRange()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetBitRange	(	const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType
	)

private

◆ GetDirection()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetDirection	(	const	PathIndexType,
		const	PathIndexType
	)

private

◆ GetEntry()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetEntry ( const PathIndexType )

private

◆ GetGrayCode()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetGrayCode ( const PathIndexType )

private

◆ GetHilbertOrder()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

virtual HilbertOrderType itk::HilbertPath< TIndexValue, VDimension >::GetHilbertOrder ( ) const

virtual

Set/get Hilbert order. The multi-dimensional space is of size 2^(HilbertOrder).

◆ GetInverseGrayCode()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetInverseGrayCode ( const PathIndexType )

private

◆ GetInverseTransform()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetInverseTransform	(	const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType
	)

private

◆ GetLeftBitRotation()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetLeftBitRotation	(	PathIndexType	,
		PathIndexType	,
		const	PathIndexType
	)

private

◆ GetNameOfClass()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

const char * itk::HilbertPath< TIndexValue, VDimension >::GetNameOfClass ( ) const

overridevirtual

See also: LightObject::GetNameOfClass()

Reimplemented from itk::DataObject.

◆ GetRightBitRotation()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetRightBitRotation	(	PathIndexType	,
		PathIndexType	,
		const	PathIndexType
	)

private

◆ GetTrailingSetBits()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetTrailingSetBits	(	const	PathIndexType,
		const	PathIndexType
	)

private

◆ GetTransform()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::GetTransform	(	const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType
	)

private

◆ IncrementInput()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

OffsetType itk::HilbertPath< TIndexValue, VDimension >::IncrementInput ( InputType & ) const

inlineoverridevirtual

Increment the input variable passed by reference and then return the index stored at the new path-position.

Implements itk::Path< unsigned int, Index< 3 >, 3 >.

Definition at line 119 of file itkHilbertPath.h.

◆ Initialize()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

void itk::HilbertPath< TIndexValue, VDimension >::Initialize ( )

inlineoverridevirtual

Needed for Pipelining

Reimplemented from itk::DataObject.

Definition at line 142 of file itkHilbertPath.h.

◆ New()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

static Pointer itk::HilbertPath< TIndexValue, VDimension >::New ( )

static

New() method for dynamic construction

◆ NumberOfSteps()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

virtual HilbertPathSizeType itk::HilbertPath< TIndexValue, VDimension >::NumberOfSteps ( ) const

inlinevirtual

How many steps in the path?

Definition at line 135 of file itkHilbertPath.h.

◆ PrintSelf()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

void itk::HilbertPath< TIndexValue, VDimension >::PrintSelf	(	std::ostream &	os,
		Indent	indent
	)		const

overrideprotectedvirtual

Methods invoked by Print() to print information about the object including superclasses. Typically not called by the user (use Print() instead) but used in the hierarchical print process to combine the output of several classes.

Reimplemented from itk::DataObject.

◆ SetBit()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::SetBit	(	const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType,
		const	PathIndexType
	)

private

◆ SetHilbertOrder()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

virtual void itk::HilbertPath< TIndexValue, VDimension >::SetHilbertOrder ( HilbertOrderType _arg )

virtual

Set/get Hilbert order. The multi-dimensional space is of size 2^(HilbertOrder).

◆ TransformMultiDimensionalIndexToPathIndex()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

PathIndexType itk::HilbertPath< TIndexValue, VDimension >::TransformMultiDimensionalIndexToPathIndex ( const IndexType & index )

Convert the multidimensional index to the path index

◆ TransformPathIndexToMultiDimensionalIndex()

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

IndexType itk::HilbertPath< TIndexValue, VDimension >::TransformPathIndexToMultiDimensionalIndex ( const PathIndexType id )

Convert the path index to the multidimensional index location

Member Data Documentation

◆ Dimension

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

constexpr unsigned int itk::HilbertPath< TIndexValue, VDimension >::Dimension = VDimension

staticconstexpr

Dimension underlying input image.

Definition at line 72 of file itkHilbertPath.h.

◆ m_HilbertOrder

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

HilbertOrderType itk::HilbertPath< TIndexValue, VDimension >::m_HilbertOrder { 1 }

private

Definition at line 207 of file itkHilbertPath.h.

◆ m_HilbertPath

template<typename TIndexValue = unsigned int, unsigned int VDimension = 3>

HilbertPathType itk::HilbertPath< TIndexValue, VDimension >::m_HilbertPath {}

private

Definition at line 208 of file itkHilbertPath.h.

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

itkHilbertPath.h

Detailed Description

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Member Typedef Documentation

◆ ConstPointer

◆ HilbertOrderType

◆ HilbertPathSizeType

◆ HilbertPathType

◆ IndexType

◆ PathIndexType

◆ Pointer

◆ Self

◆ Superclass

Constructor & Destructor Documentation

◆ HilbertPath()

◆ ~HilbertPath()

Member Function Documentation

◆ Clear()

◆ ConstructHilbertPath()

◆ EndOfInput()

◆ Evaluate()

◆ EvaluateInverse()

◆ EvaluateToIndex()

◆ GetBitRange()

◆ GetDirection()

◆ GetEntry()

◆ GetGrayCode()

◆ GetHilbertOrder()

◆ GetInverseGrayCode()

◆ GetInverseTransform()

◆ GetLeftBitRotation()

◆ GetNameOfClass()

◆ GetRightBitRotation()

◆ GetTrailingSetBits()

◆ GetTransform()

◆ IncrementInput()

◆ Initialize()

◆ New()

◆ NumberOfSteps()

◆ PrintSelf()

◆ SetBit()

◆ SetHilbertOrder()

◆ TransformMultiDimensionalIndexToPathIndex()

◆ TransformPathIndexToMultiDimensionalIndex()

Member Data Documentation

◆ Dimension

◆ m_HilbertOrder

◆ m_HilbertPath