#include <otbWindowedSincInterpolateImageFunctionBase.h>

Inheritance diagram for otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >:

Collaboration diagram for otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >:

Public Types
typedef itk::SmartPointer< const Self >	ConstPointer

typedef Superclass::ContinuousIndexType	ContinuousIndexType

typedef Superclass::FunctionType	FunctionType

typedef Superclass::IndexType	IndexType

typedef Superclass::InputImageType	InputImageType

typedef Superclass::IteratorType	IteratorType

typedef Superclass::OutputType	OutputType

typedef itk::SmartPointer< Self >	Pointer

typedef Superclass::RealType	RealType

typedef WindowedSincInterpolateImageFunctionBase	Self

typedef Superclass::SizeType	SizeType

typedef GenericInterpolateImageFunction< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >	Superclass

typedef std::vector< double >	VectorType

Public Types inherited from otb::GenericInterpolateImageFunction< TInputImage, TWindowFunction, itk::ZeroFluxNeumannBoundaryCondition< TInputImage >, double >
typedef itk::SmartPointer< const Self >	ConstPointer

typedef Superclass::ContinuousIndexType	ContinuousIndexType

typedef TWindowFunction	FunctionType

typedef Superclass::IndexType	IndexType

typedef Superclass::InputImageType	InputImageType

typedef itk::ConstNeighborhoodIterator< InputImageType, itk::ZeroFluxNeumannBoundaryCondition< TInputImage > >	IteratorType

typedef Superclass::OutputType	OutputType

typedef itk::SmartPointer< Self >	Pointer

typedef Superclass::RealType	RealType

typedef GenericInterpolateImageFunction	Self

typedef InputImageType::SizeType	SizeType

typedef itk::InterpolateImageFunction< TInputImage, double >	Superclass

Public Member Functions
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

virtual const char *	GetNameOfClass () const

Public Member Functions inherited from otb::GenericInterpolateImageFunction< TInputImage, TWindowFunction, itk::ZeroFluxNeumannBoundaryCondition< TInputImage >, double >
virtual ::itk::LightObject::Pointer	CreateAnother (void) const

virtual const char *	GetNameOfClass () const

OutputType	EvaluateAtContinuousIndex (const ContinuousIndexType &index) const override

virtual void	SetRadius (unsigned int rad)

virtual unsigned int	GetRadius () const

virtual FunctionType &	GetFunction (void)

virtual void	Initialize ()

virtual void	SetNormalizeWeight (bool _arg)

virtual bool	GetNormalizeWeight ()

Static Public Member Functions
static Pointer	New ()

Static Public Member Functions inherited from otb::GenericInterpolateImageFunction< TInputImage, TWindowFunction, itk::ZeroFluxNeumannBoundaryCondition< TInputImage >, double >
static Pointer	New ()

Static Public Attributes
static const unsigned int	ImageDimension = Superclass::ImageDimension

Static Public Attributes inherited from otb::GenericInterpolateImageFunction< TInputImage, TWindowFunction, itk::ZeroFluxNeumannBoundaryCondition< TInputImage >, double >
static const unsigned int	ImageDimension

Protected Member Functions
void	PrintSelf (std::ostream &os, itk::Indent indent) const override

	WindowedSincInterpolateImageFunctionBase ()

	~WindowedSincInterpolateImageFunctionBase () override

Protected Member Functions inherited from otb::GenericInterpolateImageFunction< TInputImage, TWindowFunction, itk::ZeroFluxNeumannBoundaryCondition< TInputImage >, double >
	GenericInterpolateImageFunction ()

	~GenericInterpolateImageFunction () override

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

void	Modified (void) const override

virtual void	ResetOffsetTable ()

virtual void	InitializeTables ()

virtual void	FillWeightOffsetTable ()

Private Member Functions
void	operator= (const Self &)=delete

	WindowedSincInterpolateImageFunctionBase (const Self &)=delete

Detailed Description

template<class TInputImage, class TWindowFunction, class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>
class otb::WindowedSincInterpolateImageFunctionBase< TInputImage, 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. Most of those functions are inspired of the itk::WindowedSincInterpolateImageFunction source code.

: 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 (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 third (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 NeighborhoodItetator classes.

: The fourth (TCoordRep) is again standard for interpolating functions, and should be float or double.

CAVEATS

There are a few improvements that an enthusiasting 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.

See also: GenericInterpolatorImageFunctionBase; LinearInterpolateImageFunctionBase ResampleImageFilter; Function::HammingWindowFunction; Function::CosineWindowFunction; Function::WelchWindowFunction; Function::LanczosWindowFunction; Function::BlackmanWindowFunction

Definition at line 140 of file otbWindowedSincInterpolateImageFunctionBase.h.

Member Typedef Documentation

◆ ConstPointer

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef itk::SmartPointer<const Self> otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::ConstPointer

Definition at line 148 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ ContinuousIndexType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::ContinuousIndexType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::ContinuousIndexType

Definition at line 168 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ FunctionType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::FunctionType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::FunctionType

Definition at line 170 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ IndexType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::IndexType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::IndexType

Superclass typedef inheritance.

Definition at line 164 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ InputImageType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::InputImageType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::InputImageType

Input and output images typedef definition.

Definition at line 154 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ IteratorType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::IteratorType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::IteratorType

Definition at line 167 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ OutputType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::OutputType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::OutputType

Definition at line 158 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ Pointer

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef itk::SmartPointer<Self> otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::Pointer

Definition at line 147 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ RealType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::RealType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::RealType

Definition at line 166 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ Self

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef WindowedSincInterpolateImageFunctionBase otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::Self

Standard class typedefs.

Definition at line 145 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ SizeType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef Superclass::SizeType otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::SizeType

Definition at line 165 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ Superclass

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef GenericInterpolateImageFunction<TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep> otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::Superclass

Definition at line 146 of file otbWindowedSincInterpolateImageFunctionBase.h.

◆ VectorType

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

typedef std::vector<double> otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::VectorType

Definition at line 171 of file otbWindowedSincInterpolateImageFunctionBase.h.

Constructor & Destructor Documentation

◆ WindowedSincInterpolateImageFunctionBase() [1/2]

template<class TInputImage , class TWindowFunction , class TBoundaryCondition , class TCoordRep >

otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::WindowedSincInterpolateImageFunctionBase

protected

Compute a resampled profil according to the window size.

Constructor

Definition at line 30 of file otbWindowedSincInterpolateImageFunctionBase.hxx.

◆ ~WindowedSincInterpolateImageFunctionBase()

template<class TInputImage , class TWindowFunction , class TBoundaryCondition , class TCoordRep >

otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::~WindowedSincInterpolateImageFunctionBase

overrideprotected

Destructor

Definition at line 36 of file otbWindowedSincInterpolateImageFunctionBase.hxx.

◆ WindowedSincInterpolateImageFunctionBase() [2/2]

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::WindowedSincInterpolateImageFunctionBase ( const Self & )

privatedelete

Member Function Documentation

◆ CreateAnother()

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

virtual::itk::LightObject::Pointer otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::CreateAnother ( void ) const

◆ GetNameOfClass()

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

virtual const char* otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::GetNameOfClass ( ) const

virtual

Run-time type information (and related methods).

◆ New()

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

static Pointer otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::New ( )

static

Method for creation through the object factory.

◆ operator=()

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

void otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::operator= ( const Self & )

privatedelete

◆ PrintSelf()

template<class TInputImage , class TWindowFunction , class TBoundaryCondition , class TCoordRep >

void otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::PrintSelf	(	std::ostream &	os,
		itk::Indent	indent
	)		const

overrideprotected

Definition at line 41 of file otbWindowedSincInterpolateImageFunctionBase.hxx.

Member Data Documentation

◆ ImageDimension

template<class TInputImage , class TWindowFunction , class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>

const unsigned int otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >::ImageDimension = Superclass::ImageDimension

static

Dimension underlying input image.

Definition at line 161 of file otbWindowedSincInterpolateImageFunctionBase.h.

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

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Member Functions

Private Member Functions

Detailed Description

template<class TInputImage, class TWindowFunction, class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double> class otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >

Member Typedef Documentation

◆ ConstPointer

◆ ContinuousIndexType

◆ FunctionType

◆ IndexType

◆ InputImageType

◆ IteratorType

◆ OutputType

◆ Pointer

◆ RealType

◆ Self

◆ SizeType

◆ Superclass

◆ VectorType

Constructor & Destructor Documentation

◆ WindowedSincInterpolateImageFunctionBase() [1/2]

◆ ~WindowedSincInterpolateImageFunctionBase()

◆ WindowedSincInterpolateImageFunctionBase() [2/2]

Member Function Documentation

◆ CreateAnother()

◆ GetNameOfClass()

◆ New()

◆ operator=()

◆ PrintSelf()

Member Data Documentation

◆ ImageDimension

template<class TInputImage, class TWindowFunction, class TBoundaryCondition = itk::ZeroFluxNeumannBoundaryCondition<TInputImage>, class TCoordRep = double>
class otb::WindowedSincInterpolateImageFunctionBase< TInputImage, TWindowFunction, TBoundaryCondition, TCoordRep >