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/* */
/* Copyright 1998-2004 by Ullrich Koethe */
/* */
/* This file is part of the VIGRA computer vision library. */
/* The VIGRA Website is */
/* http://hci.iwr.uni-heidelberg.de/vigra/ */
/* Please direct questions, bug reports, and contributions to */
/* ullrich.koethe@iwr.uni-heidelberg.de or */
/* vigra@informatik.uni-hamburg.de */
/* */
/* Permission is hereby granted, free of charge, to any person */
/* obtaining a copy of this software and associated documentation */
/* files (the "Software"), to deal in the Software without */
/* restriction, including without limitation the rights to use, */
/* copy, modify, merge, publish, distribute, sublicense, and/or */
/* sell copies of the Software, and to permit persons to whom the */
/* Software is furnished to do so, subject to the following */
/* conditions: */
/* */
/* The above copyright notice and this permission notice shall be */
/* included in all copies or substantial portions of the */
/* Software. */
/* */
/* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND */
/* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES */
/* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND */
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/* WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING */
/* FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR */
/* OTHER DEALINGS IN THE SOFTWARE. */
/* */
/************************************************************************/
#ifndef VIGRA_FFTW3_HXX
#define VIGRA_FFTW3_HXX
#include <cmath>
#include <functional>
#include "stdimage.hxx"
#include "copyimage.hxx"
#include "transformimage.hxx"
#include "combineimages.hxx"
#include "numerictraits.hxx"
#include "imagecontainer.hxx"
#include <fftw3.h>
namespace vigra {
typedef double fftw_real;
/********************************************************/
/* */
/* FFTWComplex */
/* */
/********************************************************/
/** \brief Wrapper class for the FFTW type '<TT>fftw_complex</TT>'.
This class provides constructors and other member functions
for the C struct '<TT>fftw_complex</TT>'. This struct is the basic
pixel type of the <a href="http://www.fftw.org/">FFTW Fast Fourier Transform</a>
library. It inherits the data members '<TT>re</TT>' and '<TT>im</TT>'
that denote the real and imaginary part of the number. In addition it
defines transformations to polar coordinates,
as well as \ref FFTWComplexOperators "arithmetic operators" and
\ref FFTWComplexAccessors "accessors".
FFTWComplex implements the concepts \ref AlgebraicField and
\ref DivisionAlgebra. The standard image types <tt>FFTWRealImage</tt>
and <tt>FFTWComplexImage</tt> are defined.
<b>See also:</b>
<ul>
<li> \ref FFTWComplexTraits
<li> \ref FFTWComplexOperators
<li> \ref FFTWComplexAccessors
</ul>
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
class FFTWComplex
{
fftw_complex data_;
public:
/** The complex' component type, as defined in '<TT>fftw3.h</TT>'
*/
typedef fftw_real value_type;
/** reference type (result of operator[])
*/
typedef fftw_real & reference;
/** const reference type (result of operator[] const)
*/
typedef fftw_real const & const_reference;
/** iterator type (result of begin() )
*/
typedef fftw_real * iterator;
/** const iterator type (result of begin() const)
*/
typedef fftw_real const * const_iterator;
/** The norm type (result of magnitde())
*/
typedef fftw_real NormType;
/** The squared norm type (result of squaredMagnitde())
*/
typedef fftw_real SquaredNormType;
/** Construct from real and imaginary part.
Default: 0.
*/
FFTWComplex(value_type const & re = 0.0, value_type const & im = 0.0)
{
data_[0] = re;
data_[1] = im;
}
/** Copy constructor.
*/
FFTWComplex(FFTWComplex const & o)
{
data_[0] = o.data_[0];
data_[1] = o.data_[1];
}
/** Construct from plain <TT>fftw_complex</TT>.
*/
FFTWComplex(fftw_complex const & o)
{
data_[0] = o[0];
data_[1] = o[1];
}
/** Construct from TinyVector.
*/
template <class T>
FFTWComplex(TinyVector<T, 2> const & o)
{
data_[0] = o[0];
data_[1] = o[1];
}
/** Assignment.
*/
FFTWComplex& operator=(FFTWComplex const & o)
{
data_[0] = o.data_[0];
data_[1] = o.data_[1];
return *this;
}
/** Assignment.
*/
FFTWComplex& operator=(fftw_complex const & o)
{
data_[0] = o[0];
data_[1] = o[1];
return *this;
}
/** Assignment.
*/
FFTWComplex& operator=(fftw_real const & o)
{
data_[0] = o;
data_[1] = 0.0;
return *this;
}
/** Assignment.
*/
template <class T>
FFTWComplex& operator=(TinyVector<T, 2> const & o)
{
data_[0] = o[0];
data_[1] = o[1];
return *this;
}
reference re()
{ return data_[0]; }
const_reference re() const
{ return data_[0]; }
reference im()
{ return data_[1]; }
const_reference im() const
{ return data_[1]; }
/** Unary negation.
*/
FFTWComplex operator-() const
{ return FFTWComplex(-data_[0], -data_[1]); }
/** Squared magnitude x*conj(x)
*/
SquaredNormType squaredMagnitude() const
{ return data_[0]*data_[0]+data_[1]*data_[1]; }
/** Magnitude (length of radius vector).
*/
NormType magnitude() const
{ return VIGRA_CSTD::sqrt(squaredMagnitude()); }
/** Phase angle.
*/
value_type phase() const
{ return VIGRA_CSTD::atan2(data_[1], data_[0]); }
/** Access components as if number were a vector.
*/
reference operator[](int i)
{ return data_[i]; }
/** Read components as if number were a vector.
*/
const_reference operator[](int i) const
{ return data_[i]; }
/** Length of complex number (always 2).
*/
int size() const
{ return 2; }
iterator begin()
{ return data_; }
iterator end()
{ return data_ + 2; }
const_iterator begin() const
{ return data_; }
const_iterator end() const
{ return data_ + 2; }
};
/********************************************************/
/* */
/* FFTWComplexTraits */
/* */
/********************************************************/
/** \page FFTWComplexTraits Numeric and Promote Traits of FFTWComplex
The numeric and promote traits for fftw_complex and FFTWComplex follow
the general specifications for \ref NumericPromotionTraits and
\ref AlgebraicField. They are explicitly specialized for the types
involved:
\code
template<>
struct NumericTraits<fftw_complex>
{
typedef fftw_complex Promote;
typedef fftw_complex RealPromote;
typedef fftw_complex ComplexPromote;
typedef fftw_real ValueType;
typedef VigraFalseType isIntegral;
typedef VigraFalseType isScalar;
typedef VigraFalseType isOrdered;
typedef VigraTrueType isComplex;
// etc.
};
template<>
struct NumericTraits<FFTWComplex>
{
typedef FFTWComplex Promote;
typedef FFTWComplex RealPromote;
typedef FFTWComplex ComplexPromote;
typedef fftw_real ValueType;
typedef VigraFalseType isIntegral;
typedef VigraFalseType isScalar;
typedef VigraFalseType isOrdered;
typedef VigraTrueType isComplex;
// etc.
};
template<>
struct NormTraits<fftw_complex>
{
typedef fftw_complex Type;
typedef fftw_real SquaredNormType;
typedef fftw_real NormType;
};
template<>
struct NormTraits<FFTWComplex>
{
typedef FFTWComplex Type;
typedef fftw_real SquaredNormType;
typedef fftw_real NormType;
};
template <>
struct PromoteTraits<fftw_complex, fftw_complex>
{
typedef fftw_complex Promote;
};
template <>
struct PromoteTraits<fftw_complex, double>
{
typedef fftw_complex Promote;
};
template <>
struct PromoteTraits<double, fftw_complex>
{
typedef fftw_complex Promote;
};
template <>
struct PromoteTraits<FFTWComplex, FFTWComplex>
{
typedef FFTWComplex Promote;
};
template <>
struct PromoteTraits<FFTWComplex, double>
{
typedef FFTWComplex Promote;
};
template <>
struct PromoteTraits<double, FFTWComplex>
{
typedef FFTWComplex Promote;
};
\endcode
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
template<>
struct NumericTraits<fftw_complex>
{
typedef fftw_complex Type;
typedef fftw_complex Promote;
typedef fftw_complex RealPromote;
typedef fftw_complex ComplexPromote;
typedef fftw_real ValueType;
typedef VigraFalseType isIntegral;
typedef VigraFalseType isScalar;
typedef NumericTraits<fftw_real>::isSigned isSigned;
typedef VigraFalseType isOrdered;
typedef VigraTrueType isComplex;
static FFTWComplex zero() { return FFTWComplex(0.0, 0.0); }
static FFTWComplex one() { return FFTWComplex(1.0, 0.0); }
static FFTWComplex nonZero() { return one(); }
static const Promote & toPromote(const Type & v) { return v; }
static const RealPromote & toRealPromote(const Type & v) { return v; }
static const Type & fromPromote(const Promote & v) { return v; }
static const Type & fromRealPromote(const RealPromote & v) { return v; }
};
template<>
struct NumericTraits<FFTWComplex>
{
typedef FFTWComplex Type;
typedef FFTWComplex Promote;
typedef FFTWComplex RealPromote;
typedef FFTWComplex ComplexPromote;
typedef fftw_real ValueType;
typedef VigraFalseType isIntegral;
typedef VigraFalseType isScalar;
typedef NumericTraits<fftw_real>::isSigned isSigned;
typedef VigraFalseType isOrdered;
typedef VigraTrueType isComplex;
static FFTWComplex zero() { return FFTWComplex(0.0, 0.0); }
static FFTWComplex one() { return FFTWComplex(1.0, 0.0); }
static FFTWComplex nonZero() { return one(); }
static const Promote & toPromote(const Type & v) { return v; }
static const RealPromote & toRealPromote(const Type & v) { return v; }
static const Type & fromPromote(const Promote & v) { return v; }
static const Type & fromRealPromote(const RealPromote & v) { return v; }
};
template<>
struct NormTraits<fftw_complex>
{
typedef fftw_complex Type;
typedef fftw_real SquaredNormType;
typedef fftw_real NormType;
};
template<>
struct NormTraits<FFTWComplex>
{
typedef FFTWComplex Type;
typedef fftw_real SquaredNormType;
typedef fftw_real NormType;
};
template <>
struct PromoteTraits<fftw_complex, fftw_complex>
{
typedef fftw_complex Promote;
};
template <>
struct PromoteTraits<fftw_complex, double>
{
typedef fftw_complex Promote;
};
template <>
struct PromoteTraits<double, fftw_complex>
{
typedef fftw_complex Promote;
};
template <>
struct PromoteTraits<FFTWComplex, FFTWComplex>
{
typedef FFTWComplex Promote;
};
template <>
struct PromoteTraits<FFTWComplex, double>
{
typedef FFTWComplex Promote;
};
template <>
struct PromoteTraits<double, FFTWComplex>
{
typedef FFTWComplex Promote;
};
template<class T>
struct CanSkipInitialization<std::complex<T> >
{
typedef typename CanSkipInitialization<T>::type type;
static const bool value = type::asBool;
};
template<>
struct CanSkipInitialization<FFTWComplex>
{
typedef CanSkipInitialization<fftw_real>::type type;
static const bool value = type::asBool;
};
/********************************************************/
/* */
/* FFTWComplex Operations */
/* */
/********************************************************/
/** \addtogroup FFTWComplexOperators Functions for FFTWComplex
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
These functions fulfill the requirements of an Algebraic Field.
Return types are determined according to \ref FFTWComplexTraits.
Namespace: vigra
<p>
*/
//@{
/// equal
inline bool operator ==(FFTWComplex const &a, const FFTWComplex &b) {
return a.re() == b.re() && a.im() == b.im();
}
/// not equal
inline bool operator !=(FFTWComplex const &a, const FFTWComplex &b) {
return a.re() != b.re() || a.im() != b.im();
}
/// add-assignment
inline FFTWComplex &operator +=(FFTWComplex &a, const FFTWComplex &b) {
a.re() += b.re();
a.im() += b.im();
return a;
}
/// subtract-assignment
inline FFTWComplex &operator -=(FFTWComplex &a, const FFTWComplex &b) {
a.re() -= b.re();
a.im() -= b.im();
return a;
}
/// multiply-assignment
inline FFTWComplex &operator *=(FFTWComplex &a, const FFTWComplex &b) {
FFTWComplex::value_type t = a.re()*b.re()-a.im()*b.im();
a.im() = a.re()*b.im()+a.im()*b.re();
a.re() = t;
return a;
}
/// divide-assignment
inline FFTWComplex &operator /=(FFTWComplex &a, const FFTWComplex &b) {
FFTWComplex::value_type sm = b.squaredMagnitude();
FFTWComplex::value_type t = (a.re()*b.re()+a.im()*b.im())/sm;
a.im() = (b.re()*a.im()-a.re()*b.im())/sm;
a.re() = t;
return a;
}
/// multiply-assignment with scalar double
inline FFTWComplex &operator *=(FFTWComplex &a, const double &b) {
a.re() *= b;
a.im() *= b;
return a;
}
/// divide-assignment with scalar double
inline FFTWComplex &operator /=(FFTWComplex &a, const double &b) {
a.re() /= b;
a.im() /= b;
return a;
}
/// addition
inline FFTWComplex operator +(FFTWComplex a, const FFTWComplex &b) {
a += b;
return a;
}
/// subtraction
inline FFTWComplex operator -(FFTWComplex a, const FFTWComplex &b) {
a -= b;
return a;
}
/// multiplication
inline FFTWComplex operator *(FFTWComplex a, const FFTWComplex &b) {
a *= b;
return a;
}
/// right multiplication with scalar double
inline FFTWComplex operator *(FFTWComplex a, const double &b) {
a *= b;
return a;
}
/// left multiplication with scalar double
inline FFTWComplex operator *(const double &a, FFTWComplex b) {
b *= a;
return b;
}
/// division
inline FFTWComplex operator /(FFTWComplex a, const FFTWComplex &b) {
a /= b;
return a;
}
/// right division with scalar double
inline FFTWComplex operator /(FFTWComplex a, const double &b) {
a /= b;
return a;
}
using VIGRA_CSTD::abs;
/// absolute value (= magnitude)
inline FFTWComplex::value_type abs(const FFTWComplex &a)
{
return a.magnitude();
}
/// complex conjugate
inline FFTWComplex conj(const FFTWComplex &a)
{
return FFTWComplex(a.re(), -a.im());
}
/// norm (= magnitude)
inline FFTWComplex::NormType norm(const FFTWComplex &a)
{
return a.magnitude();
}
/// squared norm (= squared magnitude)
inline FFTWComplex::SquaredNormType squaredNorm(const FFTWComplex &a)
{
return a.squaredMagnitude();
}
//@}
/** \addtogroup StandardImageTypes
*/
//@{
/********************************************************/
/* */
/* FFTWRealImage */
/* */
/********************************************************/
/** Float (<tt>fftw_real</tt>) image.
The type <tt>fftw_real</tt> is defined as <tt>double</tt> (in FFTW 2 it used to be
either <tt>float</tt> or <tt>double</tt>, as specified during compilation of FFTW).
FFTWRealImage uses \ref vigra::BasicImageIterator and \ref vigra::StandardAccessor and
their const counterparts to access the data.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
typedef BasicImage<fftw_real> FFTWRealImage;
/********************************************************/
/* */
/* FFTWComplexImage */
/* */
/********************************************************/
template<>
struct IteratorTraits<
BasicImageIterator<FFTWComplex, FFTWComplex **> >
{
typedef BasicImageIterator<FFTWComplex, FFTWComplex **> Iterator;
typedef Iterator iterator;
typedef BasicImageIterator<FFTWComplex, FFTWComplex **> mutable_iterator;
typedef ConstBasicImageIterator<FFTWComplex, FFTWComplex **> const_iterator;
typedef iterator::iterator_category iterator_category;
typedef iterator::value_type value_type;
typedef iterator::reference reference;
typedef iterator::index_reference index_reference;
typedef iterator::pointer pointer;
typedef iterator::difference_type difference_type;
typedef iterator::row_iterator row_iterator;
typedef iterator::column_iterator column_iterator;
typedef VectorAccessor<FFTWComplex> default_accessor;
typedef VectorAccessor<FFTWComplex> DefaultAccessor;
typedef VigraTrueType hasConstantStrides;
};
template<>
struct IteratorTraits<
ConstBasicImageIterator<FFTWComplex, FFTWComplex **> >
{
typedef ConstBasicImageIterator<FFTWComplex, FFTWComplex **> Iterator;
typedef Iterator iterator;
typedef BasicImageIterator<FFTWComplex, FFTWComplex **> mutable_iterator;
typedef ConstBasicImageIterator<FFTWComplex, FFTWComplex **> const_iterator;
typedef iterator::iterator_category iterator_category;
typedef iterator::value_type value_type;
typedef iterator::reference reference;
typedef iterator::index_reference index_reference;
typedef iterator::pointer pointer;
typedef iterator::difference_type difference_type;
typedef iterator::row_iterator row_iterator;
typedef iterator::column_iterator column_iterator;
typedef VectorAccessor<FFTWComplex> default_accessor;
typedef VectorAccessor<FFTWComplex> DefaultAccessor;
typedef VigraTrueType hasConstantStrides;
};
/** Complex (FFTWComplex) image.
It uses \ref vigra::BasicImageIterator and \ref vigra::StandardAccessor and
their const counterparts to access the data.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
typedef BasicImage<FFTWComplex> FFTWComplexImage;
//@}
/********************************************************/
/* */
/* FFTWComplex-Accessors */
/* */
/********************************************************/
/** \addtogroup DataAccessors
*/
//@{
/** \defgroup FFTWComplexAccessors Accessors for FFTWComplex
Encapsulate access to pixels of type FFTWComplex
*/
//@{
/** Encapsulate access to the the real part of a complex number.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
class FFTWRealAccessor
{
public:
/// The accessor's value type.
typedef fftw_real value_type;
/// Read real part at iterator position.
template <class ITERATOR>
value_type operator()(ITERATOR const & i) const {
return (*i).re();
}
/// Read real part at offset from iterator position.
template <class ITERATOR, class DIFFERENCE>
value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
return i[d].re();
}
/// Write real part at iterator position from a scalar.
template <class ITERATOR>
void set(value_type const & v, ITERATOR const & i) const {
(*i).re()= v;
}
/// Write real part at offset from iterator position from a scalar.
template <class ITERATOR, class DIFFERENCE>
void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
i[d].re()= v;
}
/// Write real part at iterator position into a scalar.
template <class ITERATOR>
void set(FFTWComplex const & v, ITERATOR const & i) const {
*i = v.re();
}
/// Write real part at offset from iterator position into a scalar.
template <class ITERATOR, class DIFFERENCE>
void set(FFTWComplex const & v, ITERATOR const & i, DIFFERENCE d) const {
i[d] = v.re();
}
};
/** Encapsulate access to the the imaginary part of a complex number.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
class FFTWImaginaryAccessor
{
public:
/// The accessor's value type.
typedef fftw_real value_type;
/// Read imaginary part at iterator position.
template <class ITERATOR>
value_type operator()(ITERATOR const & i) const {
return (*i).im();
}
/// Read imaginary part at offset from iterator position.
template <class ITERATOR, class DIFFERENCE>
value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
return i[d].im();
}
/// Write imaginary part at iterator position from a scalar.
template <class ITERATOR>
void set(value_type const & v, ITERATOR const & i) const {
(*i).im()= v;
}
/// Write imaginary part at offset from iterator position from a scalar.
template <class ITERATOR, class DIFFERENCE>
void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
i[d].im()= v;
}
/// Write imaginary part at iterator position into a scalar.
template <class ITERATOR>
void set(FFTWComplex const & v, ITERATOR const & i) const {
*i = v.im();
}
/// Write imaginary part at offset from iterator position into a scalar.
template <class ITERATOR, class DIFFERENCE>
void set(FFTWComplex const & v, ITERATOR const & i, DIFFERENCE d) const {
i[d] = v.im();
}
};
/** Write a real number into a complex one. The imaginary part is set
to 0.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
class FFTWWriteRealAccessor: public FFTWRealAccessor
{
public:
/// The accessor's value type.
typedef fftw_real value_type;
/** Write real number at iterator position. Set imaginary part
to 0.
*/
template <class ITERATOR>
void set(value_type const & v, ITERATOR const & i) const {
(*i).re()= v;
(*i).im()= 0;
}
/** Write real number at offset from iterator position. Set imaginary part
to 0.
*/
template <class ITERATOR, class DIFFERENCE>
void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
i[d].re()= v;
i[d].im()= 0;
}
};
/** Calculate magnitude of complex number on the fly.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
class FFTWMagnitudeAccessor
{
public:
/// The accessor's value type.
typedef fftw_real value_type;
/// Read magnitude at iterator position.
template <class ITERATOR>
value_type operator()(ITERATOR const & i) const {
return (*i).magnitude();
}
/// Read magnitude at offset from iterator position.
template <class ITERATOR, class DIFFERENCE>
value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
return (i[d]).magnitude();
}
};
/** Calculate phase of complex number on the fly.
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\> (for FFTW 3) or<br>
<b>\#include</b> \<<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>\> (for deprecated FFTW 2)<br>
Namespace: vigra
*/
class FFTWPhaseAccessor
{
public:
/// The accessor's value type.
typedef fftw_real value_type;
/// Read phase at iterator position.
template <class ITERATOR>
value_type operator()(ITERATOR const & i) const {
return (*i).phase();
}
/// Read phase at offset from iterator position.
template <class ITERATOR, class DIFFERENCE>
value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
return (i[d]).phase();
}
};
//@}
//@}
/********************************************************/
/* */
/* Fourier Transform */
/* */
/********************************************************/
/** \addtogroup FourierTransform Fast Fourier Transform
This documentation describes the VIGRA interface to FFTW version 3. The interface
to the old FFTW version 2 (file "vigra/fftw.hxx") is deprecated.
VIGRA uses the <a href="http://www.fftw.org/">FFTW Fast Fourier
Transform</a> package to perform Fourier transformations. VIGRA
provides a wrapper for FFTW's complex number type (FFTWComplex),
but FFTW's functions are used verbatim. If the image is stored as
a FFTWComplexImage, the simplest call to an FFT function is like this:
\code
vigra::FFTWComplexImage spatial(width,height), fourier(width,height);
... // fill image with data
// create a plan with estimated performance optimization
fftw_plan forwardPlan = fftw_plan_dft_2d(height, width,
(fftw_complex *)spatial.begin(), (fftw_complex *)fourier.begin(),
FFTW_FORWARD, FFTW_ESTIMATE );
// calculate FFT (this can be repeated as often as needed,
// with fresh data written into the source array)
fftw_execute(forwardPlan);
// release the plan memory
fftw_destroy_plan(forwardPlan);
// likewise for the inverse transform
fftw_plan backwardPlan = fftw_plan_dft_2d(height, width,
(fftw_complex *)fourier.begin(), (fftw_complex *)spatial.begin(),
FFTW_BACKWARD, FFTW_ESTIMATE);
fftw_execute(backwardPlan);
fftw_destroy_plan(backwardPlan);
// do not forget to normalize the result according to the image size
transformImage(srcImageRange(spatial), destImage(spatial),
std::bind1st(std::multiplies<FFTWComplex>(), 1.0 / width / height));
\endcode
Note that in the creation of a plan, the height must be given
first. Note also that <TT>spatial.begin()</TT> may only be passed
to <TT>fftw_plan_dft_2d</TT> if the transform shall be applied to the
entire image. When you want to restrict operation to an ROI, you
can create a copy of the ROI in an image of appropriate size, or
you may use the Guru interface to FFTW.
More information on using FFTW can be found <a href="http://www.fftw.org/doc/">here</a>.
FFTW produces fourier images that have the DC component (the
origin of the Fourier space) in the upper left corner. Often, one
wants the origin in the center of the image, so that frequencies
always increase towards the border of the image. This can be
achieved by calling \ref moveDCToCenter(). The inverse
transformation is done by \ref moveDCToUpperLeft().
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\><br>
Namespace: vigra
*/
/** \addtogroup FourierTransform
*/
//@{
/********************************************************/
/* */
/* moveDCToCenter */
/* */
/********************************************************/
/** \brief Rearrange the quadrants of a Fourier image so that the origin is
in the image center.
FFTW produces fourier images where the DC component (origin of
fourier space) is located in the upper left corner of the
image. The quadrants are placed like this (using a 4x4 image for
example):
\code
DC 4 3 3
4 4 3 3
1 1 2 2
1 1 2 2
\endcode
After applying the function, the quadrants are at their usual places:
\code
2 2 1 1
2 2 1 1
3 3 DC 4
3 3 4 4
\endcode
This transformation can be reversed by \ref moveDCToUpperLeft().
Note that the transformation must not be executed in place - input
and output images must be different.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
void moveDCToCenter(SrcImageIterator src_upperleft,
SrcImageIterator src_lowerright, SrcAccessor sa,
DestImageIterator dest_upperleft, DestAccessor da);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
void moveDCToCenter(
triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<DestImageIterator, DestAccessor> dest);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\><br>
Namespace: vigra
\code
vigra::FFTWComplexImage spatial(width,height), fourier(width,height);
... // fill image with data
// create a plan with estimated performance optimization
fftw_plan forwardPlan = fftw_plan_dft_2d(height, width,
(fftw_complex *)spatial.begin(), (fftw_complex *)fourier.begin(),
FFTW_FORWARD, FFTW_ESTIMATE );
// calculate FFT
fftw_execute(forwardPlan);
vigra::FFTWComplexImage rearrangedFourier(width, height);
moveDCToCenter(srcImageRange(fourier), destImage(rearrangedFourier));
// delete the plan
fftw_destroy_plan(forwardPlan);
\endcode
*/
doxygen_overloaded_function(template <...> void moveDCToCenter)
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
void moveDCToCenter(SrcImageIterator src_upperleft,
SrcImageIterator src_lowerright, SrcAccessor sa,
DestImageIterator dest_upperleft, DestAccessor da)
{
int w = int(src_lowerright.x - src_upperleft.x);
int h = int(src_lowerright.y - src_upperleft.y);
int w1 = w/2;
int h1 = h/2;
int w2 = (w+1)/2;
int h2 = (h+1)/2;
// 2. Quadrant zum 4.
copyImage(srcIterRange(src_upperleft,
src_upperleft + Diff2D(w2, h2), sa),
destIter (dest_upperleft + Diff2D(w1, h1), da));
// 4. Quadrant zum 2.
copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
src_lowerright, sa),
destIter (dest_upperleft, da));
// 1. Quadrant zum 3.
copyImage(srcIterRange(src_upperleft + Diff2D(w2, 0),
src_upperleft + Diff2D(w, h2), sa),
destIter (dest_upperleft + Diff2D(0, h1), da));
// 3. Quadrant zum 1.
copyImage(srcIterRange(src_upperleft + Diff2D(0, h2),
src_upperleft + Diff2D(w2, h), sa),
destIter (dest_upperleft + Diff2D(w1, 0), da));
}
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
inline void moveDCToCenter(
triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<DestImageIterator, DestAccessor> dest)
{
moveDCToCenter(src.first, src.second, src.third,
dest.first, dest.second);
}
/********************************************************/
/* */
/* moveDCToUpperLeft */
/* */
/********************************************************/
/** \brief Rearrange the quadrants of a Fourier image so that the origin is
in the image's upper left.
This function is the inversion of \ref moveDCToCenter(). See there
for declarations and a usage example.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
void moveDCToUpperLeft(SrcImageIterator src_upperleft,
SrcImageIterator src_lowerright, SrcAccessor sa,
DestImageIterator dest_upperleft, DestAccessor da);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
void moveDCToUpperLeft(
triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<DestImageIterator, DestAccessor> dest);
}
\endcode
*/
doxygen_overloaded_function(template <...> void moveDCToUpperLeft)
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
void moveDCToUpperLeft(SrcImageIterator src_upperleft,
SrcImageIterator src_lowerright, SrcAccessor sa,
DestImageIterator dest_upperleft, DestAccessor da)
{
int w = int(src_lowerright.x - src_upperleft.x);
int h = int(src_lowerright.y - src_upperleft.y);
int w2 = w/2;
int h2 = h/2;
int w1 = (w+1)/2;
int h1 = (h+1)/2;
// 2. Quadrant zum 4.
copyImage(srcIterRange(src_upperleft,
src_upperleft + Diff2D(w2, h2), sa),
destIter (dest_upperleft + Diff2D(w1, h1), da));
// 4. Quadrant zum 2.
copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
src_lowerright, sa),
destIter (dest_upperleft, da));
// 1. Quadrant zum 3.
copyImage(srcIterRange(src_upperleft + Diff2D(w2, 0),
src_upperleft + Diff2D(w, h2), sa),
destIter (dest_upperleft + Diff2D(0, h1), da));
// 3. Quadrant zum 1.
copyImage(srcIterRange(src_upperleft + Diff2D(0, h2),
src_upperleft + Diff2D(w2, h), sa),
destIter (dest_upperleft + Diff2D(w1, 0), da));
}
template <class SrcImageIterator, class SrcAccessor,
class DestImageIterator, class DestAccessor>
inline void moveDCToUpperLeft(
triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<DestImageIterator, DestAccessor> dest)
{
moveDCToUpperLeft(src.first, src.second, src.third,
dest.first, dest.second);
}
template <class DestImageIterator, class DestAccessor>
void fftShift(DestImageIterator upperleft,
DestImageIterator lowerright, DestAccessor da)
{
int w = int(lowerright.x - upperleft.x);
int h = int(lowerright.y - upperleft.y);
int w2 = w/2;
int h2 = h/2;
int w1 = (w+1)/2;
int h1 = (h+1)/2;
// 2. Quadrant zum 4.
swapImageData(destIterRange(upperleft,
upperleft + Diff2D(w2, h2), da),
destIter (upperleft + Diff2D(w1, h1), da));
// 1. Quadrant zum 3.
swapImageData(destIterRange(upperleft + Diff2D(w2, 0),
upperleft + Diff2D(w, h2), da),
destIter (upperleft + Diff2D(0, h1), da));
}
template <class DestImageIterator, class DestAccessor>
inline void fftShift(
triple<DestImageIterator, DestImageIterator, DestAccessor> dest)
{
fftShift(dest.first, dest.second, dest.third);
}
namespace detail {
template <class T>
void
fourierTransformImpl(FFTWComplexImage::const_traverser sul,
FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest, T sign)
{
int w = int(slr.x - sul.x);
int h = int(slr.y - sul.y);
FFTWComplexImage sworkImage, dworkImage;
fftw_complex * srcPtr = (fftw_complex *)(&*sul);
fftw_complex * destPtr = (fftw_complex *)(&*dul);
// test for right memory layout (fftw expects a 2*width*height floats array)
if (h > 1 && &(*(sul + Diff2D(w, 0))) != &(*(sul + Diff2D(0, 1))))
{
sworkImage.resize(w, h);
copyImage(srcIterRange(sul, slr, src), destImage(sworkImage));
srcPtr = (fftw_complex *)(&(*sworkImage.upperLeft()));
}
if (h > 1 && &(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
{
dworkImage.resize(w, h);
destPtr = (fftw_complex *)(&(*dworkImage.upperLeft()));
}
fftw_plan plan = fftw_plan_dft_2d(h, w, srcPtr, destPtr, sign, FFTW_ESTIMATE );
fftw_execute(plan);
fftw_destroy_plan(plan);
if (h > 1 && &(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
{
copyImage(srcImageRange(dworkImage), destIter(dul, dest));
}
}
} // namespace detail
/********************************************************/
/* */
/* fourierTransform */
/* */
/********************************************************/
/** \brief Compute forward and inverse Fourier transforms.
In the forward direction, the input image may be scalar or complex, and the output image
is always complex. In the inverse direction, both input and output must be complex.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor>
void fourierTransform(SrcImageIterator srcUpperLeft,
SrcImageIterator srcLowerRight, SrcAccessor src,
FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor dest);
void
fourierTransformInverse(FFTWComplexImage::const_traverser sul,
FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor>
void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
void
fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\><br>
Namespace: vigra
\code
// compute complex Fourier transform of a real image
vigra::DImage src(w, h);
vigra::FFTWComplexImage fourier(w, h);
fourierTransform(srcImageRange(src), destImage(fourier));
// compute inverse Fourier transform
// note that both source and destination image must be of type vigra::FFTWComplexImage
vigra::FFTWComplexImage inverseFourier(w, h);
fourierTransform(srcImageRange(fourier), destImage(inverseFourier));
\endcode
*/
doxygen_overloaded_function(template <...> void fourierTransform)
inline void
fourierTransform(FFTWComplexImage::const_traverser sul,
FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
{
detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_FORWARD);
}
template <class SrcImageIterator, class SrcAccessor>
void fourierTransform(SrcImageIterator srcUpperLeft,
SrcImageIterator srcLowerRight, SrcAccessor sa,
FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor da)
{
// copy real input images into a complex one...
int w= srcLowerRight.x - srcUpperLeft.x;
int h= srcLowerRight.y - srcUpperLeft.y;
FFTWComplexImage workImage(w, h);
copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
destImage(workImage, FFTWWriteRealAccessor()));
// ...and call the complex -> complex version of the algorithm
FFTWComplexImage const & cworkImage = workImage;
fourierTransform(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
destUpperLeft, da);
}
template <class SrcImageIterator, class SrcAccessor>
inline
void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest)
{
fourierTransform(src.first, src.second, src.third, dest.first, dest.second);
}
/** \brief Compute inverse Fourier transforms.
See \ref fourierTransform() for details.
*/
inline void
fourierTransformInverse(FFTWComplexImage::const_traverser sul,
FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
{
detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_BACKWARD);
}
template <class DestImageIterator, class DestAccessor>
void fourierTransformInverse(FFTWComplexImage::const_traverser sul,
FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
DestImageIterator dul, DestAccessor dest)
{
int w = slr.x - sul.x;
int h = slr.y - sul.y;
FFTWComplexImage workImage(w, h);
fourierTransformInverse(sul, slr, src, workImage.upperLeft(), workImage.accessor());
copyImage(srcImageRange(workImage), destIter(dul, dest));
}
template <class DestImageIterator, class DestAccessor>
inline void
fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
pair<DestImageIterator, DestAccessor> dest)
{
fourierTransformInverse(src.first, src.second, src.third, dest.first, dest.second);
}
/********************************************************/
/* */
/* applyFourierFilter */
/* */
/********************************************************/
/** \brief Apply a filter (defined in the frequency domain) to an image.
After transferring the image into the frequency domain, it is
multiplied pixel-wise with the filter and transformed back. The
result is put into the given destination image which must have the right size.
The result will be normalized to compensate for the two FFTs.
If the destination image is scalar, only the real part of the result image is
retained. In this case, you are responsible for choosing a filter image
which ensures a zero imaginary part of the result (e.g. use a real, even symmetric
filter image, or a purely imaginary, odd symmetric on).
The DC entry of the filter must be in the upper left, which is the
position where FFTW expects it (see \ref moveDCToUpperLeft()).
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor,
class FilterImageIterator, class FilterAccessor,
class DestImageIterator, class DestAccessor>
void applyFourierFilter(SrcImageIterator srcUpperLeft,
SrcImageIterator srcLowerRight, SrcAccessor sa,
FilterImageIterator filterUpperLeft, FilterAccessor fa,
DestImageIterator destUpperLeft, DestAccessor da);
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor,
class FilterImageIterator, class FilterAccessor,
class DestImageIterator, class DestAccessor>
void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<FilterImageIterator, FilterAccessor> filter,
pair<DestImageIterator, DestAccessor> dest);
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\><br>
Namespace: vigra
\code
// create a Gaussian filter in Fourier space
vigra::FImage gaussFilter(w, h), filter(w, h);
for(int y=0; y<h; ++y)
for(int x=0; x<w; ++x)
{
xx = float(x - w / 2) / w;
yy = float(y - h / 2) / h;
gaussFilter(x,y) = std::exp(-(xx*xx + yy*yy) / 2.0 * scale);
}
// applyFourierFilter() expects the filter's DC in the upper left
moveDCToUpperLeft(srcImageRange(gaussFilter), destImage(filter));
vigra::FFTWComplexImage result(w, h);
vigra::applyFourierFilter(srcImageRange(image), srcImage(filter), result);
\endcode
For inspection of the result, \ref FFTWMagnitudeAccessor might be
useful. If you want to apply the same filter repeatedly, it may be more
efficient to use the FFTW functions directly with FFTW plans optimized
for good performance.
*/
doxygen_overloaded_function(template <...> void applyFourierFilter)
template <class SrcImageIterator, class SrcAccessor,
class FilterImageIterator, class FilterAccessor,
class DestImageIterator, class DestAccessor>
void applyFourierFilter(SrcImageIterator srcUpperLeft,
SrcImageIterator srcLowerRight, SrcAccessor sa,
FilterImageIterator filterUpperLeft, FilterAccessor fa,
DestImageIterator destUpperLeft, DestAccessor da)
{
// copy real input images into a complex one...
int w = int(srcLowerRight.x - srcUpperLeft.x);
int h = int(srcLowerRight.y - srcUpperLeft.y);
FFTWComplexImage workImage(w, h);
copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
destImage(workImage, FFTWWriteRealAccessor()));
// ...and call the impl
FFTWComplexImage const & cworkImage = workImage;
applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
filterUpperLeft, fa,
destUpperLeft, da);
}
template <class FilterImageIterator, class FilterAccessor,
class DestImageIterator, class DestAccessor>
inline
void applyFourierFilter(
FFTWComplexImage::const_traverser srcUpperLeft,
FFTWComplexImage::const_traverser srcLowerRight,
FFTWComplexImage::ConstAccessor sa,
FilterImageIterator filterUpperLeft, FilterAccessor fa,
DestImageIterator destUpperLeft, DestAccessor da)
{
int w = srcLowerRight.x - srcUpperLeft.x;
int h = srcLowerRight.y - srcUpperLeft.y;
// test for right memory layout (fftw expects a 2*width*height floats array)
if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
applyFourierFilterImpl(srcUpperLeft, srcLowerRight, sa,
filterUpperLeft, fa,
destUpperLeft, da);
else
{
FFTWComplexImage workImage(w, h);
copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
destImage(workImage));
FFTWComplexImage const & cworkImage = workImage;
applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
filterUpperLeft, fa,
destUpperLeft, da);
}
}
template <class SrcImageIterator, class SrcAccessor,
class FilterImageIterator, class FilterAccessor,
class DestImageIterator, class DestAccessor>
inline
void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
pair<FilterImageIterator, FilterAccessor> filter,
pair<DestImageIterator, DestAccessor> dest)
{
applyFourierFilter(src.first, src.second, src.third,
filter.first, filter.second,
dest.first, dest.second);
}
template <class FilterImageIterator, class FilterAccessor,
class DestImageIterator, class DestAccessor>
void applyFourierFilterImpl(
FFTWComplexImage::const_traverser srcUpperLeft,
FFTWComplexImage::const_traverser srcLowerRight,
FFTWComplexImage::ConstAccessor,
FilterImageIterator filterUpperLeft, FilterAccessor fa,
DestImageIterator destUpperLeft, DestAccessor da)
{
int w = int(srcLowerRight.x - srcUpperLeft.x);
int h = int(srcLowerRight.y - srcUpperLeft.y);
FFTWComplexImage complexResultImg(srcLowerRight - srcUpperLeft);
// FFT from srcImage to complexResultImg
fftw_plan forwardPlan=
fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
(fftw_complex *)complexResultImg.begin(),
FFTW_FORWARD, FFTW_ESTIMATE );
fftw_execute(forwardPlan);
fftw_destroy_plan(forwardPlan);
// convolve in freq. domain (in complexResultImg)
combineTwoImages(srcImageRange(complexResultImg), srcIter(filterUpperLeft, fa),
destImage(complexResultImg), std::multiplies<FFTWComplex>());
// FFT back into spatial domain (inplace in complexResultImg)
fftw_plan backwardPlan=
fftw_plan_dft_2d(h, w, (fftw_complex *)complexResultImg.begin(),
(fftw_complex *)complexResultImg.begin(),
FFTW_BACKWARD, FFTW_ESTIMATE);
fftw_execute(backwardPlan);
fftw_destroy_plan(backwardPlan);
typedef typename
NumericTraits<typename DestAccessor::value_type>::isScalar
isScalarResult;
// normalization (after FFTs), maybe stripping imaginary part
applyFourierFilterImplNormalization(complexResultImg, destUpperLeft, da,
isScalarResult());
}
template <class DestImageIterator, class DestAccessor>
void applyFourierFilterImplNormalization(FFTWComplexImage const &srcImage,
DestImageIterator destUpperLeft,
DestAccessor da,
VigraFalseType)
{
double normFactor= 1.0/(srcImage.width() * srcImage.height());
for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
{
DestImageIterator dIt= destUpperLeft;
for(int x= 0; x< srcImage.width(); x++, dIt.x++)
{
da.setComponent(srcImage(x, y).re()*normFactor, dIt, 0);
da.setComponent(srcImage(x, y).im()*normFactor, dIt, 1);
}
}
}
inline
void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
FFTWComplexImage::traverser destUpperLeft,
FFTWComplexImage::Accessor da,
VigraFalseType)
{
transformImage(srcImageRange(srcImage), destIter(destUpperLeft, da),
linearIntensityTransform<FFTWComplex>(1.0/(srcImage.width() * srcImage.height())));
}
template <class DestImageIterator, class DestAccessor>
void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
DestImageIterator destUpperLeft,
DestAccessor da,
VigraTrueType)
{
double normFactor= 1.0/(srcImage.width() * srcImage.height());
for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
{
DestImageIterator dIt= destUpperLeft;
for(int x= 0; x< srcImage.width(); x++, dIt.x++)
da.set(srcImage(x, y).re()*normFactor, dIt);
}
}
/**********************************************************/
/* */
/* applyFourierFilterFamily */
/* */
/**********************************************************/
/** \brief Apply an array of filters (defined in the frequency domain) to an image.
This provides the same functionality as \ref applyFourierFilter(),
but applying several filters at once allows to avoid
repeated Fourier transforms of the source image.
Filters and result images must be stored in \ref vigra::ImageArray data
structures. In contrast to \ref applyFourierFilter(), this function adjusts
the size of the result images and the the length of the array.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor, class FilterType>
void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
SrcImageIterator srcLowerRight, SrcAccessor sa,
const ImageArray<FilterType> &filters,
ImageArray<FFTWComplexImage> &results)
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcImageIterator, class SrcAccessor, class FilterType>
void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
const ImageArray<FilterType> &filters,
ImageArray<FFTWComplexImage> &results)
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\><br>
Namespace: vigra
\code
// assuming the presence of a real-valued image named "image" to
// be filtered in this example
vigra::ImageArray<vigra::FImage> filters(16, image.size());
for (int i=0; i<filters.size(); i++)
// create some meaningful filters here
createMyFilterOfScale(i, destImage(filters[i]));
vigra::ImageArray<vigra::FFTWComplexImage> results();
vigra::applyFourierFilterFamily(srcImageRange(image), filters, results);
\endcode
*/
doxygen_overloaded_function(template <...> void applyFourierFilterFamily)
template <class SrcImageIterator, class SrcAccessor,
class FilterType, class DestImage>
inline
void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
const ImageArray<FilterType> &filters,
ImageArray<DestImage> &results)
{
applyFourierFilterFamily(src.first, src.second, src.third,
filters, results);
}
template <class SrcImageIterator, class SrcAccessor,
class FilterType, class DestImage>
void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
SrcImageIterator srcLowerRight, SrcAccessor sa,
const ImageArray<FilterType> &filters,
ImageArray<DestImage> &results)
{
int w = int(srcLowerRight.x - srcUpperLeft.x);
int h = int(srcLowerRight.y - srcUpperLeft.y);
FFTWComplexImage workImage(w, h);
copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
destImage(workImage, FFTWWriteRealAccessor()));
FFTWComplexImage const & cworkImage = workImage;
applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
filters, results);
}
template <class FilterType, class DestImage>
inline
void applyFourierFilterFamily(
FFTWComplexImage::const_traverser srcUpperLeft,
FFTWComplexImage::const_traverser srcLowerRight,
FFTWComplexImage::ConstAccessor sa,
const ImageArray<FilterType> &filters,
ImageArray<DestImage> &results)
{
int w= srcLowerRight.x - srcUpperLeft.x;
// test for right memory layout (fftw expects a 2*width*height floats array)
if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
applyFourierFilterFamilyImpl(srcUpperLeft, srcLowerRight, sa,
filters, results);
else
{
int h = srcLowerRight.y - srcUpperLeft.y;
FFTWComplexImage workImage(w, h);
copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
destImage(workImage));
FFTWComplexImage const & cworkImage = workImage;
applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
filters, results);
}
}
template <class FilterType, class DestImage>
void applyFourierFilterFamilyImpl(
FFTWComplexImage::const_traverser srcUpperLeft,
FFTWComplexImage::const_traverser srcLowerRight,
FFTWComplexImage::ConstAccessor sa,
const ImageArray<FilterType> &filters,
ImageArray<DestImage> &results)
{
// FIXME: sa is not used
// (maybe check if StandardAccessor, else copy?)
// make sure the filter images have the right dimensions
vigra_precondition((srcLowerRight - srcUpperLeft) == filters.imageSize(),
"applyFourierFilterFamily called with src image size != filters.imageSize()!");
// make sure the result image array has the right dimensions
results.resize(filters.size());
results.resizeImages(filters.imageSize());
// FFT from srcImage to freqImage
int w = int(srcLowerRight.x - srcUpperLeft.x);
int h = int(srcLowerRight.y - srcUpperLeft.y);
FFTWComplexImage freqImage(w, h);
FFTWComplexImage result(w, h);
fftw_plan forwardPlan=
fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
(fftw_complex *)freqImage.begin(),
FFTW_FORWARD, FFTW_ESTIMATE );
fftw_execute(forwardPlan);
fftw_destroy_plan(forwardPlan);
fftw_plan backwardPlan=
fftw_plan_dft_2d(h, w, (fftw_complex *)result.begin(),
(fftw_complex *)result.begin(),
FFTW_BACKWARD, FFTW_ESTIMATE );
typedef typename
NumericTraits<typename DestImage::Accessor::value_type>::isScalar
isScalarResult;
// convolve with filters in freq. domain
for (unsigned int i= 0; i < filters.size(); i++)
{
combineTwoImages(srcImageRange(freqImage), srcImage(filters[i]),
destImage(result), std::multiplies<FFTWComplex>());
// FFT back into spatial domain (inplace in destImage)
fftw_execute(backwardPlan);
// normalization (after FFTs), maybe stripping imaginary part
applyFourierFilterImplNormalization(result,
results[i].upperLeft(), results[i].accessor(),
isScalarResult());
}
fftw_destroy_plan(backwardPlan);
}
/********************************************************/
/* */
/* fourierTransformReal */
/* */
/********************************************************/
/** \brief Real Fourier transforms for even and odd boundary conditions
(aka. cosine and sine transforms).
If the image is real and has even symmetry, its Fourier transform
is also real and has even symmetry. The Fourier transform of a real image with odd
symmetry is imaginary and has odd symmetry. In either case, only about a quarter
of the pixels need to be stored because the rest can be calculated from the symmetry
properties. This is especially useful, if the original image is implicitly assumed
to have reflective or anti-reflective boundary conditions. Then the "negative"
pixel locations are defined as
\code
even (reflective boundary conditions): f[-x] = f[x] (x = 1,...,N-1)
odd (anti-reflective boundary conditions): f[-1] = 0
f[-x] = -f[x-2] (x = 2,...,N-1)
\endcode
end similar at the other boundary (see the FFTW documentation for details).
This has the advantage that more efficient Fourier transforms that use only
real numbers can be implemented. These are also known as cosine and sine transforms
respectively.
If you use the odd transform it is important to note that in the Fourier domain,
the DC component is always zero and is therefore dropped from the data structure.
This means that index 0 in an odd symmetric Fourier domain image refers to
the <i>first</i> harmonic. This is especially important if an image is first
cosine transformed (even symmetry), then in the Fourier domain multiplied
with an odd symmetric filter (e.g. a first derivative) and finally transformed
back to the spatial domain with a sine transform (odd symmetric). For this to work
properly the image must be shifted left or up by one pixel (depending on whether
the x- or y-axis is odd symmetric) before the inverse transform can be applied.
(see example below).
The real Fourier transform functions are named <tt>fourierTransformReal??</tt>
where the questions marks stand for either <tt>E</tt> or <tt>O</tt> indicating
whether the x- and y-axis is to be transformed using even or odd symmetry.
The same functions can be used for both the forward and inverse transforms,
only the normalization changes. For signal processing, the following
normalization factors are most appropriate:
\code
forward inverse
------------------------------------------------------------
X even, Y even 1.0 4.0 * (w-1) * (h-1)
X even, Y odd -1.0 -4.0 * (w-1) * (h+1)
X odd, Y even -1.0 -4.0 * (w+1) * (h-1)
X odd, Y odd 1.0 4.0 * (w+1) * (h+1)
\endcode
where <tt>w</tt> and <tt>h</tt> denote the image width and height.
<b> Declarations:</b>
pass arguments explicitly:
\code
namespace vigra {
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
void
fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm);
fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
}
\endcode
use argument objects in conjunction with \ref ArgumentObjectFactories :
\code
namespace vigra {
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
void
fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
pair<DestTraverser, DestAccessor> dest, fftw_real norm);
fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
}
\endcode
<b> Usage:</b>
<b>\#include</b> \<<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>\><br>
Namespace: vigra
\code
vigra::FImage spatial(width,height), fourier(width,height);
... // fill image with data
// forward cosine transform == reflective boundary conditions
fourierTransformRealEE(srcImageRange(spatial), destImage(fourier), (fftw_real)1.0);
// multiply with a first derivative of Gaussian in x-direction
for(int y = 0; y < height; ++y)
{
for(int x = 1; x < width; ++x)
{
double dx = x * M_PI / (width - 1);
double dy = y * M_PI / (height - 1);
fourier(x-1, y) = fourier(x, y) * dx * std::exp(-(dx*dx + dy*dy) * scale*scale / 2.0);
}
fourier(width-1, y) = 0.0;
}
// inverse transform -- odd symmetry in x-direction, even in y,
// due to symmetry of the filter
fourierTransformRealOE(srcImageRange(fourier), destImage(spatial),
(fftw_real)-4.0 * (width+1) * (height-1));
\endcode
*/
doxygen_overloaded_function(template <...> void fourierTransformReal)
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
pair<DestTraverser, DestAccessor> dest, fftw_real norm)
{
fourierTransformRealEE(src.first, src.second, src.third,
dest.first, dest.second, norm);
}
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_REDFT00, FFTW_REDFT00);
}
template <class DestTraverser, class DestAccessor>
inline void
fourierTransformRealEE(
FFTWRealImage::const_traverser sul,
FFTWRealImage::const_traverser slr,
FFTWRealImage::Accessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
int w = slr.x - sul.x;
// test for right memory layout (fftw expects a width*height fftw_real array)
if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
fourierTransformRealImpl(sul, slr, dul, dest,
norm, FFTW_REDFT00, FFTW_REDFT00);
else
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_REDFT00, FFTW_REDFT00);
}
/********************************************************************/
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealOE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
pair<DestTraverser, DestAccessor> dest, fftw_real norm)
{
fourierTransformRealOE(src.first, src.second, src.third,
dest.first, dest.second, norm);
}
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealOE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_RODFT00, FFTW_REDFT00);
}
template <class DestTraverser, class DestAccessor>
inline void
fourierTransformRealOE(
FFTWRealImage::const_traverser sul,
FFTWRealImage::const_traverser slr,
FFTWRealImage::Accessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
int w = slr.x - sul.x;
// test for right memory layout (fftw expects a width*height fftw_real array)
if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
fourierTransformRealImpl(sul, slr, dul, dest,
norm, FFTW_RODFT00, FFTW_REDFT00);
else
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_RODFT00, FFTW_REDFT00);
}
/********************************************************************/
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealEO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
pair<DestTraverser, DestAccessor> dest, fftw_real norm)
{
fourierTransformRealEO(src.first, src.second, src.third,
dest.first, dest.second, norm);
}
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealEO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_REDFT00, FFTW_RODFT00);
}
template <class DestTraverser, class DestAccessor>
inline void
fourierTransformRealEO(
FFTWRealImage::const_traverser sul,
FFTWRealImage::const_traverser slr,
FFTWRealImage::Accessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
int w = slr.x - sul.x;
// test for right memory layout (fftw expects a width*height fftw_real array)
if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
fourierTransformRealImpl(sul, slr, dul, dest,
norm, FFTW_REDFT00, FFTW_RODFT00);
else
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_REDFT00, FFTW_RODFT00);
}
/********************************************************************/
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealOO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
pair<DestTraverser, DestAccessor> dest, fftw_real norm)
{
fourierTransformRealOO(src.first, src.second, src.third,
dest.first, dest.second, norm);
}
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
inline void
fourierTransformRealOO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_RODFT00, FFTW_RODFT00);
}
template <class DestTraverser, class DestAccessor>
inline void
fourierTransformRealOO(
FFTWRealImage::const_traverser sul,
FFTWRealImage::const_traverser slr,
FFTWRealImage::Accessor src,
DestTraverser dul, DestAccessor dest, fftw_real norm)
{
int w = slr.x - sul.x;
// test for right memory layout (fftw expects a width*height fftw_real array)
if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
fourierTransformRealImpl(sul, slr, dul, dest,
norm, FFTW_RODFT00, FFTW_RODFT00);
else
fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
norm, FFTW_RODFT00, FFTW_RODFT00);
}
/*******************************************************************/
template <class SrcTraverser, class SrcAccessor,
class DestTraverser, class DestAccessor>
void
fourierTransformRealWorkImageImpl(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
DestTraverser dul, DestAccessor dest,
fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
{
FFTWRealImage workImage(slr - sul);
copyImage(srcIterRange(sul, slr, src), destImage(workImage));
FFTWRealImage const & cworkImage = workImage;
fourierTransformRealImpl(cworkImage.upperLeft(), cworkImage.lowerRight(),
dul, dest, norm, kindx, kindy);
}
template <class DestTraverser, class DestAccessor>
void
fourierTransformRealImpl(
FFTWRealImage::const_traverser sul,
FFTWRealImage::const_traverser slr,
DestTraverser dul, DestAccessor dest,
fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
{
int w = slr.x - sul.x;
int h = slr.y - sul.y;
BasicImage<fftw_real> res(w, h);
fftw_plan plan = fftw_plan_r2r_2d(h, w,
(fftw_real *)&(*sul), (fftw_real *)res.begin(),
kindy, kindx, FFTW_ESTIMATE);
fftw_execute(plan);
fftw_destroy_plan(plan);
if(norm != 1.0)
transformImage(srcImageRange(res), destIter(dul, dest),
std::bind1st(std::multiplies<fftw_real>(), 1.0 / norm));
else
copyImage(srcImageRange(res), destIter(dul, dest));
}
//@}
} // namespace vigra
#endif // VIGRA_FFTW3_HXX
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