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itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep > Class Template Reference
[Image Functions, Image Interpolators]

Use the windowed sinc function to interpolate. More...

#include <itkWindowedSincInterpolateImageFunction.h>

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

[legend]Collaboration diagram for itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >:

[legend]List of all members.


Public Types
typedef WindowedSincInterpolateImageFunction	Self
typedef InterpolateImageFunction< TInputImage, TCoordRep >	Superclass
typedef SmartPointer< Self >	Pointer
typedef SmartPointer< const Self >	ConstPointer
typedef Superclass::OutputType	OutputType
typedef Superclass::InputImageType	InputImageType
typedef Superclass::RealType	RealType
typedef Superclass::IndexType	IndexType
typedef TInputImage	ImageType
typedef Superclass::ContinuousIndexType	ContinuousIndexType
Public Member Functions
virtual const char *	GetNameOfClass () const
	itkStaticConstMacro (ImageDimension, unsigned int, Superclass::ImageDimension)
virtual void	SetInputImage (const ImageType *image)
virtual OutputType	EvaluateAtContinuousIndex (const ContinuousIndexType &index) const
Static Public Member Functions
Pointer	New ()
Protected Member Functions
	WindowedSincInterpolateImageFunction ()
virtual	~WindowedSincInterpolateImageFunction ()
void	PrintSelf (std::ostream &os, Indent indent) const

Detailed Description

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

Use the windowed sinc function to interpolate.

Author:: Paul A. Yushkevich

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 Lancos 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 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 NeighborhoodItetator classes.

: The fifth (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.

Function::HammingWindowFunction

Function::CosineWindowFunction

Function::WelchWindowFunction

Function::LancosWindowFunction

Function::BlackmanWindowFunction

Definition at line 237 of file itkWindowedSincInterpolateImageFunction.h.

Member Typedef Documentation

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

typedef SmartPointer<const Self> itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::ConstPointer

Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 245 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef Superclass::ContinuousIndexType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::ContinuousIndexType

ContinuousIndex typedef support.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 273 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef Superclass::IndexType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::IndexType

Index typedef support.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 267 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef Superclass::InputImageType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::InputImageType

InputImageType typedef support.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 258 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef Superclass::OutputType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::OutputType

OutputType typedef support.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 255 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef SmartPointer<Self> itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Pointer

Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 244 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef Superclass::RealType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::RealType

RealType typedef support.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 261 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef WindowedSincInterpolateImageFunction itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Self

Standard class typedefs.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 242 of file itkWindowedSincInterpolateImageFunction.h.

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

typedef InterpolateImageFunction<TInputImage,TCoordRep> itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::Superclass

Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.
Definition at line 243 of file itkWindowedSincInterpolateImageFunction.h.

Constructor & Destructor Documentation

Member Function Documentation

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

virtual OutputType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::EvaluateAtContinuousIndex ( const ContinuousIndexType & index ) const [virtual]

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.
Implements itk::InterpolateImageFunction< TInputImage, TCoordRep >.

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

virtual const char* itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::GetNameOfClass ( ) const [virtual]

Run-time type information (and related methods).
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.

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

itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::itkStaticConstMacro ( ImageDimension ,

unsigned int,

Superclass::ImageDimension

)

Dimension underlying input image.
Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.

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

void itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::PrintSelf ( std::ostream & os,

Indent indent

) const [protected, virtual]

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 >.

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

itkWindowedSincInterpolateImageFunction.h

Generated at Thu May 25 02:44:48 2006 for ITK by

itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep > Class Template Reference [Image Functions, Image Interpolators]

Public Types

Public Member Functions

Static Public Member Functions

Protected Member Functions

Detailed Description

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep > Class Template Reference
[Image Functions, Image Interpolators]