stir::SeparableMetzArrayFilter< num_dimensions, elemT > Class Template Reference

Separable Metz filtering in n - dimensions. More...

#include "stir/SeparableMetzArrayFilter.h"

Inheritance diagram for stir::SeparableMetzArrayFilter< num_dimensions, elemT >:

Public Member Functions
	SeparableMetzArrayFilter ()
	Default constructor. More...
	SeparableMetzArrayFilter (const VectorWithOffset< float > &fwhms, const VectorWithOffset< float > &metz_powers, const BasicCoordinate< num_dimensions, float > &sampling_distances, const VectorWithOffset< int > &max_kernel_sizes)
	Constructor. More...
Public Member Functions inherited from stir::SeparableArrayFunctionObject< num_dimensions, elemT >
	SeparableArrayFunctionObject ()
	Default constructor, results in a trivial ArrayFunctionObject.
	SeparableArrayFunctionObject (const VectorWithOffset< shared_ptr< ArrayFunctionObject< 1, elemT >>> &)
	Constructor taking 1D ArrayFunctionObjects. More...
bool	is_trivial () const override
	Should return true when the operations won't modify the object at all. More...
Public Member Functions inherited from stir::ArrayFunctionObject_1ArgumentImplementation< num_dimensions, elemT >
void	operator() (Array< num_dimensions, elemT > &array) const override
	in-place modification More...
void	operator() (Array< num_dimensions, elemT > &out_array, const Array< num_dimensions, elemT > &in_array) const override
	result stored in another array, implemented inline
Public Member Functions inherited from stir::ArrayFunctionObject< num_dimensions, elemT >
virtual Succeeded	get_influencing_indices (IndexRange< num_dimensions > &influencing_indices, const IndexRange< num_dimensions > &output_indices) const
	sets the range of indices that influences the result in a set of coordinates output_indices More...
virtual Succeeded	get_influenced_indices (IndexRange< num_dimensions > &influenced_indices, const IndexRange< num_dimensions > &input_indices) const
	sets the range of indices that gets influenced by a set of coordinate input_indices More...

Additional Inherited Members
Protected Member Functions inherited from stir::SeparableArrayFunctionObject< num_dimensions, elemT >
void	do_it (Array< num_dimensions, elemT > &array) const override
Protected Member Functions inherited from stir::ArrayFunctionObject_1ArgumentImplementation< num_dimensions, elemT >
virtual void	do_it (Array< num_dimensions, elemT > &array) const =0
Protected Attributes inherited from stir::SeparableArrayFunctionObject< num_dimensions, elemT >
VectorWithOffset< shared_ptr< ArrayFunctionObject< 1, elemT > > >	all_1d_array_filters

Detailed Description

template<int num_dimensions, typename elemT>
class stir::SeparableMetzArrayFilter< num_dimensions, elemT >

Separable Metz filtering in n - dimensions.

The Metz filter is easiest defined in frequency space. For a fwhm s and power P, its (continuous) Fourier transform is given by

where is the Fourier transform of a Gaussian with FWHM s, normalised such that .

For power 0, the Metz filter is just a Gaussian. For higher power, mid-range frequencies are more and more amplified. The first figure shows the FT of the Metz filter with fwhm 1, for powers 0, 0.5, 1, ... 3 (lowest curve is Gaussian).

Spatially, the Metz filter has negative lobes. The 2nd figure shows the Metz kernel in space, again with fwhm 1, powers 0 (long dashes),1,2,3 (no dashes)

Note that from the definition it follows that

The final figure illustrates the relation between the actual FWHM of the Metz filter and the FWHM of the underlying Gaussian.

This implementation discretises the Metz filter currently in the following way. it assumes that the input data are band-limited. For such data, it is possible to compute the filtering with the continuous Metz filter exactly. This is done with linear convolution of the sampled data with samples of the spatial Metz cut off at the same frequency as the input data.

Warning

Currently, this implements a Metz filter cut off at 1/sampling_distance.

The Metz filter does not preserve positivity.

Constructor & Destructor Documentation

SeparableMetzArrayFilter() [1/2]

template<int num_dimensions, typename elemT>

stir::SeparableMetzArrayFilter< num_dimensions, elemT >::SeparableMetzArrayFilter ( )

inline

Default constructor.

Warning

This currently does not set things properly for a trivial filter.

SeparableMetzArrayFilter() [2/2]

template<int num_dimensions, typename elemT >

stir::SeparableMetzArrayFilter< num_dimensions, elemT >::SeparableMetzArrayFilter	(	const VectorWithOffset< float > &	fwhms,
		const VectorWithOffset< float > &	metz_powers,
		const BasicCoordinate< num_dimensions, float > &	sampling_distances,
		const VectorWithOffset< int > &	max_kernel_sizes
	)

Constructor.

Parameters

fwhms	the FWHM of the underlying Gauss 1D filters (in mm)
metz_powers	the powers of the 1D Metz filters
sampling_distances	in each dimensions (in mm)
max_kernel_sizes	maximum number of elements in the kernels. -1 means unrestricted

For each of these parameters, the index range should be from 1 to num_dimensions, with 1 corresponding to the 1st (i.e. slowest) index.

Warning

the fwhms parameter does not give the FWHM of the Metz filter, but of the underlying Gauss.

References stir::Array< num_dimensions, elemT >::fill(), stir::VectorWithOffset< T >::fill(), stir::fourier(), stir::VectorWithOffset< T >::get_length(), stir::VectorWithOffset< T >::get_min_index(), stir::VectorWithOffset< T >::grow(), stir::info(), stir::inverse_fourier(), and stir::sum().

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

• /home/sirfuser/devel/STIRdistrib/STIR/src/include/stir/SeparableMetzArrayFilter.h
• /home/sirfuser/devel/STIRdistrib/STIR/src/buildblock/SeparableMetzArrayFilter.cxx