ITK  6.0.0 Insight Toolkit
itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep > Class Template Reference

#include <itkWindowedSincInterpolateImageFunction.h>

## Detailed Description

### template<typename TInputImage, unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double> class itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >

Use the windowed sinc function to interpolate.

THEORY

This function is intended to provide an interpolation function that has minimum aliasing artifacts, in contrast to linear interpolation. According to sampling theory, the infinite-support sinc filter, whose Fourier transform is the box filter, is optimal for resampling a function. In practice, the infinite support sinc filter is approximated using a limited support 'windowed' sinc filter.

This function is based on the following publication:
Erik H. W. Meijering, Wiro J. Niessen, Josien P. W. Pluim, Max A. Viergever: Quantitative Comparison of Sinc-Approximating Kernels for Medical Image Interpolation. MICCAI 1999, pp. 210-217
In this work, several 'windows' are estimated. In two dimensions, the interpolation at a position (x,y) is given by the following expression:

$I(x,y) = \sum_{i = \lfloor x \rfloor + 1 - m}^{\lfloor x \rfloor + m} \sum_{j = \lfloor y \rfloor + 1 - m}^{\lfloor y \rfloor + m} I_{i,j} K(x-i) K(y-j),$

where m is the 'radius' of the window, (3,4 are reasonable numbers), and K(t) is the kernel function, composed of the sinc function and one of several possible window functions:

$K(t) = w(t) \textrm{sinc}(t) = w(t) \frac{\sin(\pi t)}{\pi t}$

Several window functions are provided here in the itk::Function namespace. The conclusions of the referenced paper suggest to use the Welch, Cosine, Kaiser, and Lanczos windows for m = 4,5. These are based on error in rotating medical images w.r.t. the linear interpolation method. In some cases the results achieve a 20-fold improvement in accuracy.
USING THIS FILTER

Use this filter the way you would use any ImageInterpolationFunction, so for instance, you can plug it into the ResampleImageFilter class. In order to initialize the filter you must choose several template parameters.

The first (TInputImage) is the image type, that's standard.
The second (VRadius) is the radius of the kernel, i.e., the $$m$$ from the formula above.
The third (TWindowFunction) is the window function object, which you can choose from about five different functions defined in this header. The default is the Hamming window, which is commonly used but not optimal according to the cited paper.
The fourth (TBoundaryCondition) is the boundary condition class used to determine the values of pixels that fall off the image boundary. This class has the same meaning here as in the NeighborhoodIterator classes.
The fifth (TCoordRep) is again standard for interpolating functions, and should be float or double.
CAVEATS

There are a few improvements that an enthusiastic ITK developer could make to this filter. One issue is with the way that the kernel is applied. The computational expense comes from two sources: computing the kernel weights K(t) and multiplying the pixels in the window by the kernel weights. The first is done more or less efficiently in $$2 m d$$ operations (where d is the dimensionality of the image). The second can be done better. Presently, each pixel $$I(i,j,k)$$ is multiplied by the weights $$K(x-i), K(y-j), K(z-k)$$ and added to the running total. This results in $$d (2m)^d$$ multiplication operations. However, by keeping intermediate sums, it would be possible to do the operation in $$O ( (2m)^d )$$ operations. This would require some creative coding. In addition, in the case when one of the coordinates is integer, the computation could be reduced by an order of magnitude.

LinearInterpolateImageFunction ResampleImageFilter
Function::HammingWindowFunction
Function::CosineWindowFunction
Function::WelchWindowFunction
Function::LanczosWindowFunction
Function::BlackmanWindowFunction
Examples
Examples/Filtering/ResampleImageFilter8.cxx, and SphinxExamples/src/Core/Transform/ApplyAffineTransformFromHomogeneousMatrixAndResample/Code.cxx.

Definition at line 271 of file itkWindowedSincInterpolateImageFunction.h.

Inheritance diagram for itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >:
Collaboration diagram for itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >:

## Public Types

using ConstPointer = SmartPointer< const Self >

using ImageType = TInputImage

using Pointer = SmartPointer< Self >

using Self = WindowedSincInterpolateImageFunction

using Superclass = InterpolateImageFunction< TInputImage, TCoordRep >

Public Types inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
using ConstPointer = SmartPointer< const Self >

using Pointer = SmartPointer< Self >

using RealType = typename NumericTraits< typename TInputImage::PixelType >::RealType

using Self = InterpolateImageFunction

using SizeType = typename InputImageType::SizeType

using Superclass = ImageFunction< TInputImage, typename NumericTraits< typename TInputImage::PixelType >::RealType, TCoordRep >

Public Types inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
using ConstPointer = SmartPointer< const Self >

using ContinuousIndexType = ContinuousIndex< TCoordRep, Self::ImageDimension >

using CoordRepType = TCoordRep

using IndexType = typename InputImageType::IndexType

using IndexValueType = typename InputImageType::IndexValueType

using InputImageConstPointer = typename InputImageType::ConstPointer

using InputImageType = TInputImage

using InputPixelType = typename InputImageType::PixelType

using OutputType = NumericTraits< TInputImage::PixelType >::RealType

using Pointer = SmartPointer< Self >

using PointType = Point< TCoordRep, Self::ImageDimension >

using Self = ImageFunction

using Superclass = FunctionBase< Point< TCoordRep, Self::ImageDimension >, NumericTraits< TInputImage::PixelType >::RealType >

Public Types inherited from itk::FunctionBase< Point< TCoordRep, TInputImage::ImageDimension >, NumericTraits< TInputImage::PixelType >::RealType >
using ConstPointer = SmartPointer< const Self >

using InputType = Point< TCoordRep, TInputImage::ImageDimension >

using OutputType = NumericTraits< TInputImage::PixelType >::RealType

using Pointer = SmartPointer< Self >

using Self = FunctionBase

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

OutputType EvaluateAtContinuousIndex (const ContinuousIndexType &index) const override

const char * GetNameOfClass () const override

void SetInputImage (const ImageType *image) override

Public Member Functions inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
OutputType EvaluateAtIndex (const IndexType &index) const override

OutputType Evaluate (const PointType &point) const override

Public Member Functions inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
void ConvertContinuousIndexToNearestIndex (const ContinuousIndexType &cindex, IndexType &index) const

void ConvertPointToContinuousIndex (const PointType &point, ContinuousIndexType &cindex) const

virtual const ContinuousIndexTypeGetEndContinuousIndex () const

virtual const IndexTypeGetEndIndex () const

const InputImageTypeGetInputImage () const

const char * GetNameOfClass () const override

virtual const ContinuousIndexTypeGetStartContinuousIndex () const

virtual const IndexTypeGetStartIndex () const

virtual bool IsInsideBuffer (const IndexType &index) const

virtual bool IsInsideBuffer (const ContinuousIndexType &index) const

virtual bool IsInsideBuffer (const PointType &point) const

void ConvertPointToNearestIndex (const PointType &point, IndexType &index) const

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

unsigned long AddObserver (const EventObject &event, Command *) 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

CommandGetCommand (unsigned long tag)

bool GetDebug () const

virtual ModifiedTimeType GetMTime () const

virtual const TimeStampGetTimeStamp () 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

virtual void SetObjectName (std::string _arg)

virtual const std::string & GetObjectName () const

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

virtual void Delete ()

virtual int GetReferenceCount () const

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

## Static Public Member Functions

static Pointer New ()

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 ImageDimension = Superclass::ImageDimension

Static Public Attributes inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
static constexpr unsigned int ImageDimension = Superclass::ImageDimension

Static Public Attributes inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
static constexpr unsigned int ImageDimension

## Protected Member Functions

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

WindowedSincInterpolateImageFunction ()=default

~WindowedSincInterpolateImageFunction () override=default

Protected Member Functions inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
InterpolateImageFunction ()=default

~InterpolateImageFunction () override=default

Protected Member Functions inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
ImageFunction ()

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

~ImageFunction () override=default

Protected Member Functions inherited from itk::FunctionBase< Point< TCoordRep, TInputImage::ImageDimension >, NumericTraits< TInputImage::PixelType >::RealType >
FunctionBase ()=default

~FunctionBase () override=default

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

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

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

virtual ~LightObject ()

## Private Types

using IteratorType = ConstNeighborhoodIterator< ImageType, TBoundaryCondition >

## Private Member Functions

double Sinc (double x) const

## Private Attributes

unsigned int m_OffsetTable [m_OffsetTableSize] {}

unsigned int m_WeightOffsetTable [m_OffsetTableSize][ImageDimension] {}

TWindowFunction m_WindowFunction {}

## Static Private Attributes

static constexpr unsigned int m_OffsetTableSize = Math::UnsignedPower(m_WindowSize, ImageDimension)

static constexpr unsigned int m_WindowSize { 2 * VRadius }

Protected Attributes inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
ContinuousIndexType m_EndContinuousIndex

IndexType m_EndIndex

InputImageConstPointer m_Image

ContinuousIndexType m_StartContinuousIndex

IndexType m_StartIndex

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

## ◆ ConstPointer

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 using itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::ConstPointer = SmartPointer

Definition at line 282 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ ImageType

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 using itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::ImageType = TInputImage

Image type definition

Definition at line 310 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ IteratorType

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 using itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::IteratorType = ConstNeighborhoodIterator
private

Definition at line 343 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ Pointer

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 using itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Pointer = SmartPointer

Definition at line 281 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ Self

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 using itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Self = WindowedSincInterpolateImageFunction

Standard class type aliases.

Definition at line 278 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ Superclass

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 using itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Superclass = InterpolateImageFunction

Definition at line 279 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ WindowedSincInterpolateImageFunction()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::WindowedSincInterpolateImageFunction ( )
protecteddefault

## ◆ ~WindowedSincInterpolateImageFunction()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::~WindowedSincInterpolateImageFunction ( )
overrideprotecteddefault

## ◆ EvaluateAtContinuousIndex()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 OutputType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::EvaluateAtContinuousIndex ( const ContinuousIndexType & index ) const
overridevirtual

Evaluate the function at a ContinuousIndex position

Returns the interpolated image intensity at a specified point position. Bounds checking is based on the type of the TBoundaryCondition specified.

## ◆ GetNameOfClass()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 const char* itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::GetNameOfClass ( ) const
overridevirtual

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
inlineoverridevirtual

Get the radius required for interpolation.

This defines the number of surrounding pixels required to interpolate at a given point.

Definition at line 328 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ New()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 static Pointer itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::New ( )
static

Method for creation through the object factory.

## ◆ PrintSelf()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 void itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::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::InterpolateImageFunction< TInputImage, TCoordRep >.

## ◆ SetInputImage()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 void itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::SetInputImage ( const ImageType * ptr )
overridevirtual

Set the input image.

Warning
this method caches BufferedRegion information. If the BufferedRegion has changed, user must call SetInputImage again to update cached values.

## ◆ Sinc()

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 double itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Sinc ( double x ) const
inlineprivate

The sinc function

Definition at line 363 of file itkWindowedSincInterpolateImageFunction.h.

References itk::Math::pi.

## ◆ ImageDimension

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 constexpr unsigned int itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::ImageDimension = Superclass::ImageDimension
staticconstexpr

Dimension underlying input image.

Definition at line 300 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ m_OffsetTable

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 unsigned int itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::m_OffsetTable[m_OffsetTableSize] {}
private

The offset array, used to keep a list of relevant offsets in the neighborhoodIterator

Definition at line 356 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ m_OffsetTableSize

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 constexpr unsigned int itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::m_OffsetTableSize = Math::UnsignedPower(m_WindowSize, ImageDimension)
staticconstexprprivate

Size of the offset table

Definition at line 352 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ m_WeightOffsetTable

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 unsigned int itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::m_WeightOffsetTable[m_OffsetTableSize][ImageDimension] {}
private

Index into the weights array for each offset

Definition at line 359 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ m_WindowFunction

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 TWindowFunction itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::m_WindowFunction {}
private

The function object, used to compute window

Definition at line 349 of file itkWindowedSincInterpolateImageFunction.h.

## ◆ m_WindowSize

template<typename TInputImage , unsigned int VRadius, typename TWindowFunction = Function::HammingWindowFunction<VRadius>, class TBoundaryCondition = ZeroFluxNeumannBoundaryCondition<TInputImage, TInputImage>, class TCoordRep = double>
 constexpr unsigned int itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::m_WindowSize { 2 * VRadius }
staticconstexprprivate

Definition at line 346 of file itkWindowedSincInterpolateImageFunction.h.

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