ITK  4.2.0
Insight Segmentation and Registration Toolkit
Public Types | Public Member Functions | Static Public Member Functions | Static Public Attributes | Protected Member Functions | Private Types | Private Member Functions | Private Attributes | Static Private Attributes
itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep > Class Template Reference

#include <itkWindowedSincInterpolateImageFunction.h>

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

List of all members.

Public Types

typedef SmartPointer< const SelfConstPointer
typedef
Superclass::ContinuousIndexType 
ContinuousIndexType
typedef TInputImage ImageType
typedef Superclass::IndexType IndexType
typedef Superclass::IndexValueType IndexValueType
typedef Superclass::InputImageType InputImageType
typedef Superclass::OutputType OutputType
typedef SmartPointer< SelfPointer
typedef Superclass::RealType RealType
typedef
WindowedSincInterpolateImageFunction 
Self
typedef
InterpolateImageFunction
< TInputImage, TCoordRep > 
Superclass
- Public Types inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
typedef Superclass::PointType PointType
- Public Types inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
typedef TCoordRep CoordRepType
typedef
InputImageType::ConstPointer 
InputImageConstPointer
typedef InputImageType::PixelType InputPixelType
- Public Types inherited from itk::FunctionBase< Point< TCoordRep, TInputImage::ImageDimension >, NumericTraits< TInputImage::PixelType >::RealType >
typedef Point< TCoordRep,
TInputImage::ImageDimension > 
InputType
- Public Types inherited from itk::Object
- Public Types inherited from itk::LightObject

Public Member Functions

virtual ::itk::LightObject::Pointer CreateAnother (void) const
virtual OutputType EvaluateAtContinuousIndex (const ContinuousIndexType &index) const
virtual const char * GetNameOfClass () const
virtual void SetInputImage (const ImageType *image)
- Public Member Functions inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
virtual OutputType Evaluate (const PointType &point) const
virtual OutputType EvaluateAtIndex (const IndexType &index) const
- 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
void ConvertPointToNearestIndex (const PointType &point, IndexType &index) const
virtual NumericTraits
< TInputImage::PixelType >
::RealType 
EvaluateAtContinuousIndex (const ContinuousIndexType &index) const =0
virtual NumericTraits
< TInputImage::PixelType >
::RealType 
EvaluateAtIndex (const IndexType &index) const =0
virtual const ContinuousIndexTypeGetEndContinuousIndex ()
virtual const IndexTypeGetEndIndex ()
const InputImageTypeGetInputImage () const
virtual const ContinuousIndexTypeGetStartContinuousIndex ()
virtual const IndexTypeGetStartIndex ()
virtual bool IsInsideBuffer (const IndexType &index) const
virtual bool IsInsideBuffer (const ContinuousIndexType &index) const
virtual bool IsInsideBuffer (const PointType &point) const

Static Public Member Functions

static Pointer New ()

Static Public Attributes

static const unsigned int ImageDimension = Superclass::ImageDimension
- Static Public Attributes inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
- Static Public Attributes inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >

Protected Member Functions

void PrintSelf (std::ostream &os, Indent indent) const
 WindowedSincInterpolateImageFunction ()
virtual ~WindowedSincInterpolateImageFunction ()
- Protected Member Functions inherited from itk::InterpolateImageFunction< TInputImage, TCoordRep >
 InterpolateImageFunction ()
 ~InterpolateImageFunction ()
- Protected Member Functions inherited from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >
 ImageFunction ()
 ~ImageFunction ()
- Protected Member Functions inherited from itk::FunctionBase< Point< TCoordRep, TInputImage::ImageDimension >, NumericTraits< TInputImage::PixelType >::RealType >
 FunctionBase ()
 ~FunctionBase ()
- Protected Member Functions inherited from itk::Object
 Object ()
bool PrintObservers (std::ostream &os, Indent indent) const
virtual void SetTimeStamp (const TimeStamp &time)
virtual ~Object ()
- 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

typedef
ConstNeighborhoodIterator
< ImageType,
TBoundaryCondition > 
IteratorType

Private Member Functions

void operator= (const Self &)
double Sinc (double x) const
 WindowedSincInterpolateImageFunction (const Self &)

Private Attributes

unsigned int * m_OffsetTable
unsigned int m_OffsetTableSize
unsigned int ** m_WeightOffsetTable
TWindowFunction m_WindowFunction

Static Private Attributes

static const unsigned int m_WindowSize

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 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 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.

See also:
LinearInterpolateImageFunction ResampleImageFilter
Function::HammingWindowFunction
Function::CosineWindowFunction
Function::WelchWindowFunction
Function::LanczosWindowFunction
Function::BlackmanWindowFunction

Definition at line 260 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
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
template<class TInputImage , unsigned int VRadius, class TWindowFunction = Function::HammingWindowFunction< VRadius >, class TBoundaryCondition = ConstantBoundaryCondition< TInputImage >, class TCoordRep = double>
typedef TInputImage itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::ImageType

Image type definition

Definition at line 296 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 292 of file itkWindowedSincInterpolateImageFunction.h.

template<class TInputImage , unsigned int VRadius, class TWindowFunction = Function::HammingWindowFunction< VRadius >, class TBoundaryCondition = ConstantBoundaryCondition< TInputImage >, class TCoordRep = double>
typedef Superclass::IndexValueType itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::IndexValueType
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 283 of file itkWindowedSincInterpolateImageFunction.h.

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

Definition at line 324 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 277 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
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 286 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 266 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

Constructor & Destructor Documentation

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 >::WindowedSincInterpolateImageFunction ( )
protected
template<class TInputImage , unsigned int VRadius, class TWindowFunction = Function::HammingWindowFunction< VRadius >, class TBoundaryCondition = ConstantBoundaryCondition< TInputImage >, class TCoordRep = double>
virtual itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::~WindowedSincInterpolateImageFunction ( )
protectedvirtual
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 >::WindowedSincInterpolateImageFunction ( const Self )
private

Member Function Documentation

template<class TInputImage , unsigned int VRadius, class TWindowFunction = Function::HammingWindowFunction< VRadius >, class TBoundaryCondition = ConstantBoundaryCondition< TInputImage >, class TCoordRep = double>
virtual::itk::LightObject::Pointer itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::CreateAnother ( void  ) const
virtual

Create an object from an instance, potentially deferring to a factory. This method allows you to create an instance of an object that is exactly the same type as the referring object. This is useful in cases where an object has been cast back to a base class.

Reimplemented from itk::Object.

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>
static Pointer itk::WindowedSincInterpolateImageFunction< TInputImage, VRadius, TWindowFunction, TBoundaryCondition, TCoordRep >::New ( )
static

Method for creation through the object factory.

Reimplemented from itk::Object.

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 >::operator= ( const Self )
private

Mutex lock to protect modification to the reference count

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
protectedvirtual

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 >.

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

Set the input image.

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

Reimplemented from itk::ImageFunction< TInputImage, NumericTraits< TInputImage::PixelType >::RealType, TCoordRep >.

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

The sinc function

Definition at line 343 of file itkWindowedSincInterpolateImageFunction.h.

References itk::Math::pi.


Member Data Documentation

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

Dimension underlying input image.

Reimplemented from itk::InterpolateImageFunction< TInputImage, TCoordRep >.

Definition at line 289 of file itkWindowedSincInterpolateImageFunction.h.

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

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

Definition at line 334 of file itkWindowedSincInterpolateImageFunction.h.

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

Size of the offset table

Definition at line 337 of file itkWindowedSincInterpolateImageFunction.h.

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

Index into the weights array for each offset

Definition at line 340 of file itkWindowedSincInterpolateImageFunction.h.

template<class TInputImage , unsigned int VRadius, class TWindowFunction = Function::HammingWindowFunction< VRadius >, class TBoundaryCondition = ConstantBoundaryCondition< 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 330 of file itkWindowedSincInterpolateImageFunction.h.

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

Definition at line 327 of file itkWindowedSincInterpolateImageFunction.h.


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