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fftw3.hxx |

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2 /* */
3 /* Copyright 1998-2004 by Ullrich Koethe */
4 /* */
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34 /************************************************************************/
35
36 #ifndef VIGRA_FFTW3_HXX
37 #define VIGRA_FFTW3_HXX
38
39 #include <cmath>
40 #include <functional>
41 #include <complex>
42 #include "stdimage.hxx"
43 #include "copyimage.hxx"
44 #include "transformimage.hxx"
45 #include "combineimages.hxx"
46 #include "numerictraits.hxx"
47 #include "imagecontainer.hxx"
48 #include <fftw3.h>
49
50 namespace vigra {
51
52 typedef double fftw_real;
53
54 template <class T>
55 struct FFTWReal;
56
57 template <>
58 struct FFTWReal<fftw_complex>
59 {
60 typedef double type;
61 };
62
63 template <>
64 struct FFTWReal<fftwf_complex>
65 {
66 typedef float type;
67 };
68
69 template <>
70 struct FFTWReal<fftwl_complex>
71 {
72 typedef long double type;
73 };
74
75 template <class T>
76 struct FFTWReal2Complex;
77
78 template <>
79 struct FFTWReal2Complex<double>
80 {
81 typedef fftw_complex type;
82 typedef fftw_plan plan_type;
83 };
84
85 template <>
86 struct FFTWReal2Complex<float>
87 {
88 typedef fftwf_complex type;
89 typedef fftwf_plan plan_type;
90 };
91
92 template <>
93 struct FFTWReal2Complex<long double>
94 {
95 typedef fftwl_complex type;
96 typedef fftwl_plan plan_type;
97 };
98
99 /********************************************************/
100 /* */
101 /* FFTWComplex */
102 /* */
103 /********************************************************/
104
105 /** \brief Wrapper class for the FFTW complex types '<TT>fftw_complex</TT>'.
106
107 This class encapsulates the low-level complex number types provided by the
108 <a href="http://www.fftw.org/">FFTW Fast Fourier Transform</a> library (i.e.
109 '<TT>fftw_complex</TT>', '<TT>fftwf_complex</TT>', '<TT>fftwl_complex</TT>').
110 In particular, it provides constructors, member functions and
111 \ref FFTWComplexOperators "arithmetic operators" that make FFTW complex numbers
112 compatible with <tt>std::complex</tt>. In addition, the class defines
113 transformations to polar coordinates and \ref FFTWComplexAccessors "accessors".
114
115 FFTWComplex implements the concepts \ref AlgebraicField and
116 \ref DivisionAlgebra. The standard image types <tt>FFTWRealImage</tt>
117 and <tt>FFTWComplexImage</tt> are defined.
118
119 <b>See also:</b>
120 <ul>
121 <li> \ref FFTWComplexTraits
122 <li> \ref FFTWComplexOperators
123 <li> \ref FFTWComplexAccessors
124 </ul>
125
126 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
127 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
128 Namespace: vigra
129 */
130 template <class Real = double>
131 class FFTWComplex
132 {
133 public:
134 /** The wrapped complex type
135 */
136 typedef typename FFTWReal2Complex<Real>::type complex_type;
137
138 /** The complex' component type, as defined in '<TT>fftw3.h</TT>'
139 */
140 typedef Real value_type;
141
142 /** reference type (result of operator[])
143 */
144 typedef value_type & reference;
145
146 /** const reference type (result of operator[] const)
147 */
148 typedef value_type const & const_reference;
149
150 /** iterator type (result of begin() )
151 */
152 typedef value_type * iterator;
153
154 /** const iterator type (result of begin() const)
155 */
156 typedef value_type const * const_iterator;
157
158 /** The norm type (result of magnitude())
159 */
160 typedef value_type NormType;
161
162 /** The squared norm type (result of squaredMagnitde())
163 */
164 typedef value_type SquaredNormType;
165
166 /** Construct from real and imaginary part.
167 Default: 0.
168 */
169 FFTWComplex(value_type const & re = 0.0, value_type const & im = 0.0)
170 {
171 data_[0] = re;
172 data_[1] = im;
173 }
174
175 /** Copy constructor.
176 */
177 FFTWComplex(FFTWComplex const & o)
178 {
179 data_[0] = o.data_[0];
180 data_[1] = o.data_[1];
181 }
182
183 /** Copy constructor.
184 */
185 template <class U>
186 FFTWComplex(FFTWComplex<U> const & o)
187 {
188 data_[0] = (Real)o.real();
189 data_[1] = (Real)o.imag();
190 }
191
192 /** Construct from plain <TT>fftw_complex</TT>.
193 */
194 FFTWComplex(fftw_complex const & o)
195 {
196 data_[0] = (Real)o[0];
197 data_[1] = (Real)o[1];
198 }
199
200 /** Construct from plain <TT>fftwf_complex</TT>.
201 */
202 FFTWComplex(fftwf_complex const & o)
203 {
204 data_[0] = (Real)o[0];
205 data_[1] = (Real)o[1];
206 }
207
208 /** Construct from plain <TT>fftwl_complex</TT>.
209 */
210 FFTWComplex(fftwl_complex const & o)
211 {
212 data_[0] = (Real)o[0];
213 data_[1] = (Real)o[1];
214 }
215
216 /** Construct from std::complex.
217 */
218 template <class T>
219 FFTWComplex(std::complex<T> const & o)
220 {
221 data_[0] = (Real)o.real();
222 data_[1] = (Real)o.imag();
223 }
224
225 /** Construct from TinyVector.
226 */
227 template <class T>
228 FFTWComplex(TinyVector<T, 2> const & o)
229 {
230 data_[0] = (Real)o[0];
231 data_[1] = (Real)o[1];
232 }
233
234 /** Assignment.
235 */
236 FFTWComplex& operator=(FFTWComplex const & o)
237 {
238 data_[0] = o.data_[0];
239 data_[1] = o.data_[1];
240 return *this;
241 }
242
243 /** Assignment.
244 */
245 template <class U>
246 FFTWComplex& operator=(FFTWComplex<U> const & o)
247 {
248 data_[0] = (Real)o.real();
249 data_[1] = (Real)o.imag();
250 return *this;
251 }
252
253 /** Assignment.
254 */
255 FFTWComplex& operator=(fftw_complex const & o)
256 {
257 data_[0] = (Real)o[0];
258 data_[1] = (Real)o[1];
259 return *this;
260 }
261
262 /** Assignment.
263 */
264 FFTWComplex& operator=(fftwf_complex const & o)
265 {
266 data_[0] = (Real)o[0];
267 data_[1] = (Real)o[1];
268 return *this;
269 }
270
271 /** Assignment.
272 */
273 FFTWComplex& operator=(fftwl_complex const & o)
274 {
275 data_[0] = (Real)o[0];
276 data_[1] = (Real)o[1];
277 return *this;
278 }
279
280 /** Assignment.
281 */
282 FFTWComplex& operator=(double o)
283 {
284 data_[0] = (Real)o;
285 data_[1] = 0.0;
286 return *this;
287 }
288
289 /** Assignment.
290 */
291 FFTWComplex& operator=(float o)
292 {
293 data_[0] = (Real)o;
294 data_[1] = 0.0;
295 return *this;
296 }
297
298 /** Assignment.
299 */
300 FFTWComplex& operator=(long double o)
301 {
302 data_[0] = (Real)o;
303 data_[1] = 0.0;
304 return *this;
305 }
306
307 /** Assignment.
308 */
309 template <class T>
310 FFTWComplex& operator=(TinyVector<T, 2> const & o)
311 {
312 data_[0] = (Real)o[0];
313 data_[1] = (Real)o[1];
314 return *this;
315 }
316
317 /** Assignment.
318 */
319 template <class T>
320 FFTWComplex& operator=(std::complex<T> const & o)
321 {
322 data_[0] = (Real)o.real();
323 data_[1] = (Real)o.imag();
324 return *this;
325 }
326
327 reference re()
328 { return data_[0]; }
329
330 const_reference re() const
331 { return data_[0]; }
332
333 reference real()
334 { return data_[0]; }
335
336 const_reference real() const
337 { return data_[0]; }
338
339 reference im()
340 { return data_[1]; }
341
342 const_reference im() const
343 { return data_[1]; }
344
345 reference imag()
346 { return data_[1]; }
347
348 const_reference imag() const
349 { return data_[1]; }
350
351 /** Unary negation.
352 */
353 FFTWComplex operator-() const
354 { return FFTWComplex(-data_[0], -data_[1]); }
355
356 /** Squared magnitude x*conj(x)
357 */
358 SquaredNormType squaredMagnitude() const
359 { return data_[0]*data_[0]+data_[1]*data_[1]; }
360
361 /** Magnitude (length of radius vector).
362 */
363 NormType magnitude() const
364 { return VIGRA_CSTD::sqrt(squaredMagnitude()); }
365
366 /** Phase angle.
367 */
368 value_type phase() const
369 { return VIGRA_CSTD::atan2(data_[1], data_[0]); }
370
371 /** Access components as if number were a vector.
372 */
373 reference operator[](int i)
374 { return data_[i]; }
375
376 /** Read components as if number were a vector.
377 */
378 const_reference operator[](int i) const
379 { return data_[i]; }
380
381 /** Length of complex number (always 2).
382 */
383 int size() const
384 { return 2; }
385
386 iterator begin()
387 { return data_; }
388
389 iterator end()
390 { return data_ + 2; }
391
392 const_iterator begin() const
393 { return data_; }
394
395 const_iterator end() const
396 { return data_ + 2; }
397
398 private:
399 complex_type data_;
400 };
401
402 /********************************************************/
403 /* */
404 /* FFTWComplexTraits */
405 /* */
406 /********************************************************/
407
408 /** \page FFTWComplexTraits Numeric and Promote Traits of FFTWComplex
409
410 The numeric and promote traits for fftw_complex and FFTWComplex follow
411 the general specifications for \ref NumericPromotionTraits and
412 \ref AlgebraicField. They are explicitly specialized for the types
413 involved:
414
415 \code
416
417 template<>
418 struct NumericTraits<fftw_complex>
419 {
420 typedef fftw_complex Promote;
421 typedef fftw_complex RealPromote;
422 typedef fftw_complex ComplexPromote;
423 typedef fftw_real ValueType;
424
425 typedef VigraFalseType isIntegral;
426 typedef VigraFalseType isScalar;
427 typedef VigraFalseType isOrdered;
428 typedef VigraTrueType isComplex;
429
430 // etc.
431 };
432
433 template<class Real>
434 struct NumericTraits<FFTWComplex<Real> >
435 {
436 typedef FFTWComplex<Real> Promote;
437 typedef FFTWComplex<Real> RealPromote;
438 typedef FFTWComplex<Real> ComplexPromote;
439 typedef Real ValueType;
440
441 typedef VigraFalseType isIntegral;
442 typedef VigraFalseType isScalar;
443 typedef VigraFalseType isOrdered;
444 typedef VigraTrueType isComplex;
445
446 // etc.
447 };
448
449 template<>
450 struct NormTraits<fftw_complex>
451 {
452 typedef fftw_complex Type;
453 typedef fftw_real SquaredNormType;
454 typedef fftw_real NormType;
455 };
456
457 template<class Real>
458 struct NormTraits<FFTWComplex>
459 {
460 typedef FFTWComplex Type;
461 typedef fftw_real SquaredNormType;
462 typedef fftw_real NormType;
463 };
464
465 template <>
466 struct PromoteTraits<fftw_complex, fftw_complex>
467 {
468 typedef fftw_complex Promote;
469 };
470
471 template <>
472 struct PromoteTraits<fftw_complex, double>
473 {
474 typedef fftw_complex Promote;
475 };
476
477 template <>
478 struct PromoteTraits<double, fftw_complex>
479 {
480 typedef fftw_complex Promote;
481 };
482
483 template <class Real>
484 struct PromoteTraits<FFTWComplex<Real>, FFTWComplex<Real> >
485 {
486 typedef FFTWComplex<Real> Promote;
487 };
488
489 template <class Real>
490 struct PromoteTraits<FFTWComplex<Real>, double>
491 {
492 typedef FFTWComplex<Real> Promote;
493 };
494
495 template <class Real>
496 struct PromoteTraits<double, FFTWComplex<Real> >
497 {
498 typedef FFTWComplex<Real> Promote;
499 };
500 \endcode
501
502 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
503 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
504 Namespace: vigra
505
506 */
507 template<>
508 struct NumericTraits<fftw_complex>
509 {
510 typedef fftw_complex Type;
511 typedef fftw_complex Promote;
512 typedef fftw_complex RealPromote;
513 typedef fftw_complex ComplexPromote;
514 typedef fftw_real ValueType;
515
516 typedef VigraFalseType isIntegral;
517 typedef VigraFalseType isScalar;
518 typedef NumericTraits<fftw_real>::isSigned isSigned;
519 typedef VigraFalseType isOrdered;
520 typedef VigraTrueType isComplex;
521
522 static FFTWComplex<> zero() { return FFTWComplex<>(0.0, 0.0); }
523 static FFTWComplex<> one() { return FFTWComplex<>(1.0, 0.0); }
524 static FFTWComplex<> nonZero() { return one(); }
525
526 static const Promote & toPromote(const Type & v) { return v; }
527 static const RealPromote & toRealPromote(const Type & v) { return v; }
528 static const Type & fromPromote(const Promote & v) { return v; }
529 static const Type & fromRealPromote(const RealPromote & v) { return v; }
530 };
531
532 template<class Real>
533 struct NumericTraits<FFTWComplex<Real> >
534 {
535 typedef FFTWComplex<Real> Type;
536 typedef FFTWComplex<Real> Promote;
537 typedef FFTWComplex<Real> RealPromote;
538 typedef FFTWComplex<Real> ComplexPromote;
539 typedef typename Type::value_type ValueType;
540
541 typedef VigraFalseType isIntegral;
542 typedef VigraFalseType isScalar;
543 typedef typename NumericTraits<ValueType>::isSigned isSigned;
544 typedef VigraFalseType isOrdered;
545 typedef VigraTrueType isComplex;
546
547 static Type zero() { return Type(0.0, 0.0); }
548 static Type one() { return Type(1.0, 0.0); }
549 static Type nonZero() { return one(); }
550
551 static const Promote & toPromote(const Type & v) { return v; }
552 static const RealPromote & toRealPromote(const Type & v) { return v; }
553 static const Type & fromPromote(const Promote & v) { return v; }
554 static const Type & fromRealPromote(const RealPromote & v) { return v; }
555 };
556
557 template<>
558 struct NormTraits<fftw_complex>
559 {
560 typedef fftw_complex Type;
561 typedef fftw_real SquaredNormType;
562 typedef fftw_real NormType;
563 };
564
565 template<class Real>
566 struct NormTraits<FFTWComplex<Real> >
567 {
568 typedef FFTWComplex<Real> Type;
569 typedef typename Type::SquaredNormType SquaredNormType;
570 typedef typename Type::NormType NormType;
571 };
572
573 template <>
574 struct PromoteTraits<fftw_complex, fftw_complex>
575 {
576 typedef fftw_complex Promote;
577 };
578
579 template <>
580 struct PromoteTraits<fftw_complex, double>
581 {
582 typedef fftw_complex Promote;
583 };
584
585 template <>
586 struct PromoteTraits<double, fftw_complex>
587 {
588 typedef fftw_complex Promote;
589 };
590
591 template <class Real>
592 struct PromoteTraits<FFTWComplex<Real>, FFTWComplex<Real> >
593 {
594 typedef FFTWComplex<Real> Promote;
595 };
596
597 template <class Real>
598 struct PromoteTraits<FFTWComplex<Real>, double>
599 {
600 typedef FFTWComplex<Real> Promote;
601 };
602
603 template <class Real>
604 struct PromoteTraits<double, FFTWComplex<Real> >
605 {
606 typedef FFTWComplex<Real> Promote;
607 };
608
609 template<class T>
610 struct CanSkipInitialization<std::complex<T> >
611 {
612 typedef typename CanSkipInitialization<T>::type type;
613 static const bool value = type::asBool;
614 };
615
616 template<class Real>
617 struct CanSkipInitialization<FFTWComplex<Real> >
618 {
619 typedef typename CanSkipInitialization<Real>::type type;
620 static const bool value = type::asBool;
621 };
622
623 namespace multi_math {
624
625 template <class ARG>
626 struct MultiMathOperand;
627
628 template <class Real>
629 struct MultiMathOperand<FFTWComplex<Real> >
630 {
631 typedef MultiMathOperand<FFTWComplex<Real> > AllowOverload;
632 typedef FFTWComplex<Real> result_type;
633
634 static const int ndim = 0;
635
636 MultiMathOperand(FFTWComplex<Real> const & v)
637 : v_(v)
638 {}
639
640 template <class SHAPE>
641 bool checkShape(SHAPE const &) const
642 {
643 return true;
644 }
645
646 template <class SHAPE>
647 FFTWComplex<Real> const & operator[](SHAPE const &) const
648 {
649 return v_;
650 }
651
652 void inc(unsigned int /*LEVEL*/) const
653 {}
654
655 void reset(unsigned int /*LEVEL*/) const
656 {}
657
658 FFTWComplex<Real> const & operator*() const
659 {
660 return v_;
661 }
662
663 FFTWComplex<Real> v_;
664 };
665
666 } // namespace multi_math
667
668 template<class Ty>
669 class FFTWAllocator
670 {
671 public:
672 typedef std::size_t size_type;
673 typedef std::ptrdiff_t difference_type;
674 typedef Ty *pointer;
675 typedef const Ty *const_pointer;
676 typedef Ty& reference;
677 typedef const Ty& const_reference;
678 typedef Ty value_type;
679
680 pointer address(reference val) const
681 { return &val; }
682
683 const_pointer address(const_reference val) const
684 { return &val; }
685
686 template<class Other>
687 struct rebind
688 {
689 typedef FFTWAllocator<Other> other;
690 };
691
692 FFTWAllocator() throw()
693 {}
694
695 template<class Other>
696 FFTWAllocator(const FFTWAllocator<Other>& right) throw()
697 {}
698
699 template<class Other>
700 FFTWAllocator& operator=(const FFTWAllocator<Other>& right)
701 {
702 return *this;
703 }
704
705 pointer allocate(size_type count, void * = 0)
706 {
707 return (pointer)fftw_malloc(count * sizeof(Ty));
708 }
709
710 void deallocate(pointer ptr, size_type count)
711 {
712 fftw_free(ptr);
713 }
714
715 void construct(pointer ptr, const Ty& val)
716 {
717 new(ptr) Ty(val);
718
719 }
720
721 void destroy(pointer ptr)
722 {
723 ptr->~Ty();
724 }
725
726 size_type max_size() const throw()
727 {
728 return NumericTraits<std::ptrdiff_t>::max() / sizeof(Ty);
729 }
730 };
731
732 } // namespace vigra
733
734 namespace std {
735
736 template<class Real>
737 class allocator<vigra::FFTWComplex<Real> >
738 {
739 public:
740 typedef vigra::FFTWComplex<Real> value_type;
741 typedef size_t size_type;
742 typedef std::ptrdiff_t difference_type;
743 typedef value_type *pointer;
744 typedef const value_type *const_pointer;
745 typedef value_type& reference;
746 typedef const value_type& const_reference;
747
748 pointer address(reference val) const
749 { return &val; }
750
751 const_pointer address(const_reference val) const
752 { return &val; }
753
754 template<class Other>
755 struct rebind
756 {
757 typedef allocator<Other> other;
758 };
759
760 allocator() throw()
761 {}
762
763 template<class Other>
764 allocator(const allocator<Other>& right) throw()
765 {}
766
767 template<class Other>
768 allocator& operator=(const allocator<Other>& right)
769 {
770 return *this;
771 }
772
773 pointer allocate(size_type count, void * = 0)
774 {
775 return (pointer)fftw_malloc(count * sizeof(value_type));
776 }
777
778 void deallocate(pointer ptr, size_type /*count*/)
779 {
780 fftw_free(ptr);
781 }
782
783 void construct(pointer ptr, const value_type& val)
784 {
785 new(ptr) value_type(val);
786
787 }
788
789 void destroy(pointer ptr)
790 {
791 ptr->~value_type();
792 }
793
794 size_type max_size() const throw()
795 {
796 return vigra::NumericTraits<std::ptrdiff_t>::max() / sizeof(value_type);
797 }
798 };
799
800 } // namespace std
801
802 namespace vigra {
803
804 /********************************************************/
805 /* */
806 /* FFTWComplex Operations */
807 /* */
808 /********************************************************/
809
810 /** \addtogroup FFTWComplexOperators Functions for FFTWComplex
811
812 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
813 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
814
815 These functions fulfill the requirements of an Algebraic Field.
816 Return types are determined according to \ref FFTWComplexTraits.
817
818 Namespace: vigra
819 <p>
820
821 */
822 //@{
823 /// equal
824 template <class R>
825 inline bool operator ==(FFTWComplex<R> const &a, const FFTWComplex<R> &b) {
826 return a.re() == b.re() && a.im() == b.im();
827 }
828
829 template <class R>
830 inline bool operator ==(FFTWComplex<R> const &a, double b) {
831 return a.re() == b && a.im() == 0.0;
832 }
833
834 template <class R>
835 inline bool operator ==(double a, const FFTWComplex<R> &b) {
836 return a == b.re() && 0.0 == b.im();
837 }
838
839 /// not equal
840 template <class R>
841 inline bool operator !=(FFTWComplex<R> const &a, const FFTWComplex<R> &b) {
842 return a.re() != b.re() || a.im() != b.im();
843 }
844
845 /// not equal
846 template <class R>
847 inline bool operator !=(FFTWComplex<R> const &a, double b) {
848 return a.re() != b || a.im() != 0.0;
849 }
850
851 /// not equal
852 template <class R>
853 inline bool operator !=(double a, const FFTWComplex<R> &b) {
854 return a != b.re() || 0.0 != b.im();
855 }
856
857 /// add-assignment
858 template <class R>
859 inline FFTWComplex<R> & operator +=(FFTWComplex<R> &a, const FFTWComplex<R> &b) {
860 a.re() += b.re();
861 a.im() += b.im();
862 return a;
863 }
864
865 /// subtract-assignment
866 template <class R>
867 inline FFTWComplex<R> & operator -=(FFTWComplex<R> &a, const FFTWComplex<R> &b) {
868 a.re() -= b.re();
869 a.im() -= b.im();
870 return a;
871 }
872
873 /// multiply-assignment
874 template <class R>
875 inline FFTWComplex<R> & operator *=(FFTWComplex<R> &a, const FFTWComplex<R> &b) {
876 typename FFTWComplex<R>::value_type t = a.re()*b.re()-a.im()*b.im();
877 a.im() = a.re()*b.im()+a.im()*b.re();
878 a.re() = t;
879 return a;
880 }
881
882 /// divide-assignment
883 template <class R>
884 inline FFTWComplex<R> & operator /=(FFTWComplex<R> &a, const FFTWComplex<R> &b) {
885 typename FFTWComplex<R>::value_type sm = b.squaredMagnitude();
886 typename FFTWComplex<R>::value_type t = (a.re()*b.re()+a.im()*b.im())/sm;
887 a.im() = (b.re()*a.im()-a.re()*b.im())/sm;
888 a.re() = t;
889 return a;
890 }
891
892 /// add-assignment with scalar double
893 template <class R>
894 inline FFTWComplex<R> & operator +=(FFTWComplex<R> &a, double b) {
895 a.re() += (R)b;
896 return a;
897 }
898
899 /// subtract-assignment with scalar double
900 template <class R>
901 inline FFTWComplex<R> & operator -=(FFTWComplex<R> &a, double b) {
902 a.re() -= (R)b;
903 return a;
904 }
905
906 /// multiply-assignment with scalar double
907 template <class R>
908 inline FFTWComplex<R> & operator *=(FFTWComplex<R> &a, double b) {
909 a.re() *= (R)b;
910 a.im() *= (R)b;
911 return a;
912 }
913
914 /// divide-assignment with scalar double
915 template <class R>
916 inline FFTWComplex<R> & operator /=(FFTWComplex<R> &a, double b) {
917 a.re() /= (R)b;
918 a.im() /= (R)b;
919 return a;
920 }
921
922 /// addition
923 template <class R>
924 inline FFTWComplex<R> operator +(FFTWComplex<R> a, const FFTWComplex<R> &b) {
925 a += b;
926 return a;
927 }
928
929 /// right addition with scalar double
930 template <class R>
931 inline FFTWComplex<R> operator +(FFTWComplex<R> a, double b) {
932 a += b;
933 return a;
934 }
935
936 /// left addition with scalar double
937 template <class R>
938 inline FFTWComplex<R> operator +(double a, FFTWComplex<R> b) {
939 b += a;
940 return b;
941 }
942
943 /// subtraction
944 template <class R>
945 inline FFTWComplex<R> operator -(FFTWComplex<R> a, const FFTWComplex<R> &b) {
946 a -= b;
947 return a;
948 }
949
950 /// right subtraction with scalar double
951 template <class R>
952 inline FFTWComplex<R> operator -(FFTWComplex<R> a, double b) {
953 a -= b;
954 return a;
955 }
956
957 /// left subtraction with scalar double
958 template <class R>
959 inline FFTWComplex<R> operator -(double a, FFTWComplex<R> const & b) {
960 return (-b) += a;
961 }
962
963 /// multiplication
964 template <class R>
965 inline FFTWComplex<R> operator *(FFTWComplex<R> a, const FFTWComplex<R> &b) {
966 a *= b;
967 return a;
968 }
969
970 /// right multiplication with scalar double
971 template <class R>
972 inline FFTWComplex<R> operator *(FFTWComplex<R> a, double b) {
973 a *= b;
974 return a;
975 }
976
977 /// left multiplication with scalar double
978 template <class R>
979 inline FFTWComplex<R> operator *(double a, FFTWComplex<R> b) {
980 b *= a;
981 return b;
982 }
983
984 /// division
985 template <class R>
986 inline FFTWComplex<R> operator /(FFTWComplex<R> a, const FFTWComplex<R> &b) {
987 a /= b;
988 return a;
989 }
990
991 /// right division with scalar double
992 template <class R>
993 inline FFTWComplex<R> operator /(FFTWComplex<R> a, double b) {
994 a /= b;
995 return a;
996 }
997
998 using VIGRA_CSTD::abs;
999
1000 /// absolute value (= magnitude)
1001 template <class R>
1002 inline typename FFTWComplex<R>::NormType abs(const FFTWComplex<R> &a)
1003 {
1004 return a.magnitude();
1005 }
1006
1007 /// pahse
1008 template <class R>
1009 inline R arg(const FFTWComplex<R> &a)
1010 {
1011 return a.phase();
1012 }
1013
1014 /// real part
1015 template <class R>
1016 inline R real(const FFTWComplex<R> &a)
1017 {
1018 return a.real();
1019 }
1020
1021 /// imaginary part
1022 template <class R>
1023 inline R imag(const FFTWComplex<R> &a)
1024 {
1025 return a.imag();
1026 }
1027
1028 /// complex conjugate
1029 template <class R>
1030 inline FFTWComplex<R> conj(const FFTWComplex<R> &a)
1031 {
1032 return FFTWComplex<R>(a.re(), -a.im());
1033 }
1034
1035 /// norm (= magnitude)
1036 template <class R>
1037 inline typename FFTWComplex<R>::NormType norm(const FFTWComplex<R> &a)
1038 {
1039 return a.magnitude();
1040 }
1041
1042 /// squared norm (= squared magnitude)
1043 template <class R>
1044 inline typename FFTWComplex<R>::SquaredNormType squaredNorm(const FFTWComplex<R> &a)
1045 {
1046 return a.squaredMagnitude();
1047 }
1048
1049 #define VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(fct) \
1050 template <class R> \
1051 inline FFTWComplex<R> fct(const FFTWComplex<R> &a) \
1052 { \
1053 return std::fct(reinterpret_cast<std::complex<R> const &>(a)); \
1054 }
1055
1056 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(cos)
1057 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(cosh)
1058 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(exp)
1059 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(log)
1060 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(log10)
1061 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(sin)
1062 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(sinh)
1063 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(sqrt)
1064 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(tan)
1065 VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION(tanh)
1066
1067 #undef VIGRA_DEFINE_FFTW_COMPLEX_FUNCTION
1068
1069 template <class R>
1070 inline FFTWComplex<R> pow(const FFTWComplex<R> &a, int e)
1071 {
1072 return std::pow(reinterpret_cast<std::complex<R> const &>(a), e);
1073 }
1074
1075 template <class R>
1076 inline FFTWComplex<R> pow(const FFTWComplex<R> &a, R const & e)
1077 {
1078 return std::pow(reinterpret_cast<std::complex<R> const &>(a), e);
1079 }
1080
1081 template <class R>
1082 inline FFTWComplex<R> pow(const FFTWComplex<R> &a, const FFTWComplex<R> & e)
1083 {
1084 return std::pow(reinterpret_cast<std::complex<R> const &>(a),
1085 reinterpret_cast<std::complex<R> const &>(e));
1086 }
1087
1088 template <class R>
1089 inline FFTWComplex<R> pow(R const & a, const FFTWComplex<R> &e)
1090 {
1091 return std::pow(a, reinterpret_cast<std::complex<R> const &>(e));
1092 }
1093
1094 //@}
1095
1096 } // namespace vigra
1097
1098 namespace std {
1099
1100 template <class Real>
1101 ostream & operator<<(ostream & s, vigra::FFTWComplex<Real> const & v)
1102 {
1103 s << std::complex<Real>(v.re(), v.im());
1104 return s;
1105 }
1106
1107 } // namespace std
1108
1109 namespace vigra {
1110
1111 /** \addtogroup StandardImageTypes
1112 */
1113 //@{
1114
1115 /********************************************************/
1116 /* */
1117 /* FFTWRealImage */
1118 /* */
1119 /********************************************************/
1120
1121 /** Float (<tt>fftw_real</tt>) image.
1122
1123 The type <tt>fftw_real</tt> is defined as <tt>double</tt> (in FFTW 2 it used to be
1124 either <tt>float</tt> or <tt>double</tt>, as specified during compilation of FFTW).
1125 FFTWRealImage uses \ref vigra::BasicImageIterator and \ref vigra::StandardAccessor and
1126 their const counterparts to access the data.
1127
1128 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1129 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1130 Namespace: vigra
1131 */
1132 typedef BasicImage<fftw_real> FFTWRealImage;
1133
1134 /********************************************************/
1135 /* */
1136 /* FFTWComplexImage */
1137 /* */
1138 /********************************************************/
1139
1140 template<class R>
1141 struct IteratorTraits<
1142 BasicImageIterator<FFTWComplex<R>, FFTWComplex<R> **> >
1143 {
1144 typedef FFTWComplex<R> Type;
1145 typedef BasicImageIterator<Type, Type **> Iterator;
1146 typedef Iterator iterator;
1147 typedef BasicImageIterator<Type, Type **> mutable_iterator;
1148 typedef ConstBasicImageIterator<Type, Type **> const_iterator;
1149 typedef typename iterator::iterator_category iterator_category;
1150 typedef typename iterator::value_type value_type;
1151 typedef typename iterator::reference reference;
1152 typedef typename iterator::index_reference index_reference;
1153 typedef typename iterator::pointer pointer;
1154 typedef typename iterator::difference_type difference_type;
1155 typedef typename iterator::row_iterator row_iterator;
1156 typedef typename iterator::column_iterator column_iterator;
1157 typedef VectorAccessor<Type> default_accessor;
1158 typedef VectorAccessor<Type> DefaultAccessor;
1159 typedef VigraTrueType hasConstantStrides;
1160 };
1161
1162 template<class R>
1163 struct IteratorTraits<
1164 ConstBasicImageIterator<FFTWComplex<R>, FFTWComplex<R> **> >
1165 {
1166 typedef FFTWComplex<R> Type;
1167 typedef ConstBasicImageIterator<Type, Type **> Iterator;
1168 typedef Iterator iterator;
1169 typedef BasicImageIterator<Type, Type **> mutable_iterator;
1170 typedef ConstBasicImageIterator<Type, Type **> const_iterator;
1171 typedef typename iterator::iterator_category iterator_category;
1172 typedef typename iterator::value_type value_type;
1173 typedef typename iterator::reference reference;
1174 typedef typename iterator::index_reference index_reference;
1175 typedef typename iterator::pointer pointer;
1176 typedef typename iterator::difference_type difference_type;
1177 typedef typename iterator::row_iterator row_iterator;
1178 typedef typename iterator::column_iterator column_iterator;
1179 typedef VectorAccessor<Type> default_accessor;
1180 typedef VectorAccessor<Type> DefaultAccessor;
1181 typedef VigraTrueType hasConstantStrides;
1182 };
1183
1184 /** Complex (FFTWComplex) image.
1185 It uses \ref vigra::BasicImageIterator and \ref vigra::StandardAccessor and
1186 their const counterparts to access the data.
1187
1188 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1189 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1190 Namespace: vigra
1191 */
1192 typedef BasicImage<FFTWComplex<> > FFTWComplexImage;
1193
1194 //@}
1195
1196 /********************************************************/
1197 /* */
1198 /* FFTWComplex-Accessors */
1199 /* */
1200 /********************************************************/
1201
1202 /** \addtogroup DataAccessors
1203 */
1204 //@{
1205 /** \defgroup FFTWComplexAccessors Accessors for FFTWComplex
1206
1207 Encapsulate access to pixels of type FFTWComplex
1208 */
1209 //@{
1210 /** Encapsulate access to the the real part of a complex number.
1211
1212 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1213 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1214 Namespace: vigra
1215 */
1216 template <class Real = double>
1217 class FFTWRealAccessor
1218 {
1219 public:
1220
1221 /// The accessor's value type.
1222 typedef Real value_type;
1223
1224 /// Read real part at iterator position.
1225 template <class ITERATOR>
1226 value_type operator()(ITERATOR const & i) const {
1227 return (*i).re();
1228 }
1229
1230 /// Read real part at offset from iterator position.
1231 template <class ITERATOR, class DIFFERENCE>
1232 value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
1233 return i[d].re();
1234 }
1235
1236 /// Write real part at iterator position from a scalar.
1237 template <class ITERATOR>
1238 void set(value_type const & v, ITERATOR const & i) const {
1239 (*i).re()= v;
1240 }
1241
1242 /// Write real part at offset from iterator position from a scalar.
1243 template <class ITERATOR, class DIFFERENCE>
1244 void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
1245 i[d].re()= v;
1246 }
1247
1248 /// Write real part at iterator position into a scalar.
1249 template <class R, class ITERATOR>
1250 void set(FFTWComplex<R> const & v, ITERATOR const & i) const {
1251 *i = v.re();
1252 }
1253
1254 /// Write real part at offset from iterator position into a scalar.
1255 template <class R, class ITERATOR, class DIFFERENCE>
1256 void set(FFTWComplex<R> const & v, ITERATOR const & i, DIFFERENCE d) const {
1257 i[d] = v.re();
1258 }
1259 };
1260
1261 /** Encapsulate access to the the imaginary part of a complex number.
1262
1263 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1264 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1265 Namespace: vigra
1266 */
1267 template <class Real = double>
1268 class FFTWImaginaryAccessor
1269 {
1270 public:
1271 /// The accessor's value type.
1272 typedef Real value_type;
1273
1274 /// Read imaginary part at iterator position.
1275 template <class ITERATOR>
1276 value_type operator()(ITERATOR const & i) const {
1277 return (*i).im();
1278 }
1279
1280 /// Read imaginary part at offset from iterator position.
1281 template <class ITERATOR, class DIFFERENCE>
1282 value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
1283 return i[d].im();
1284 }
1285
1286 /// Write imaginary part at iterator position from a scalar.
1287 template <class ITERATOR>
1288 void set(value_type const & v, ITERATOR const & i) const {
1289 (*i).im()= v;
1290 }
1291
1292 /// Write imaginary part at offset from iterator position from a scalar.
1293 template <class ITERATOR, class DIFFERENCE>
1294 void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
1295 i[d].im()= v;
1296 }
1297
1298 /// Write imaginary part at iterator position into a scalar.
1299 template <class R, class ITERATOR>
1300 void set(FFTWComplex<R> const & v, ITERATOR const & i) const {
1301 *i = v.im();
1302 }
1303
1304 /// Write imaginary part at offset from iterator position into a scalar.
1305 template <class R, class ITERATOR, class DIFFERENCE>
1306 void set(FFTWComplex<R> const & v, ITERATOR const & i, DIFFERENCE d) const {
1307 i[d] = v.im();
1308 }
1309 };
1310
1311 /** Write a real number into a complex one. The imaginary part is set
1312 to 0.
1313
1314 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1315 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1316 Namespace: vigra
1317 */
1318 template <class Real = double>
1319 class FFTWWriteRealAccessor
1320 : public FFTWRealAccessor<Real>
1321 {
1322 public:
1323 /// The accessor's value type.
1324 typedef Real value_type;
1325
1326 /** Write real number at iterator position. Set imaginary part
1327 to 0.
1328 */
1329 template <class ITERATOR>
1330 void set(value_type const & v, ITERATOR const & i) const {
1331 (*i).re()= v;
1332 (*i).im()= 0;
1333 }
1334
1335 /** Write real number at offset from iterator position. Set imaginary part
1336 to 0.
1337 */
1338 template <class ITERATOR, class DIFFERENCE>
1339 void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
1340 i[d].re()= v;
1341 i[d].im()= 0;
1342 }
1343 };
1344
1345 /** Calculate squared magnitude of complex number on the fly.
1346
1347 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1348 Namespace: vigra
1349 */
1350 template <class Real = double>
1351 class FFTWSquaredMagnitudeAccessor
1352 {
1353 public:
1354 /// The accessor's value type.
1355 typedef Real value_type;
1356
1357 /// Read squared magnitude at iterator position.
1358 template <class ITERATOR>
1359 value_type operator()(ITERATOR const & i) const {
1360 return (*i).squaredMagnitude();
1361 }
1362
1363 /// Read squared magnitude at offset from iterator position.
1364 template <class ITERATOR, class DIFFERENCE>
1365 value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
1366 return (i[d]).squaredMagnitude();
1367 }
1368 };
1369
1370 /** Calculate magnitude of complex number on the fly.
1371
1372 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1373 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1374 Namespace: vigra
1375 */
1376 template <class Real = double>
1377 class FFTWMagnitudeAccessor
1378 {
1379 public:
1380 /// The accessor's value type.
1381 typedef Real value_type;
1382
1383 /// Read magnitude at iterator position.
1384 template <class ITERATOR>
1385 value_type operator()(ITERATOR const & i) const {
1386 return (*i).magnitude();
1387 }
1388
1389 /// Read magnitude at offset from iterator position.
1390 template <class ITERATOR, class DIFFERENCE>
1391 value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
1392 return (i[d]).magnitude();
1393 }
1394 };
1395
1396 /** Calculate phase of complex number on the fly.
1397
1398 <b>\#include</b> <vigra/fftw3.hxx> (for FFTW 3) or<br>
1399 <b>\#include</b> <vigra/fftw.hxx> (for deprecated FFTW 2)<br>
1400 Namespace: vigra
1401 */
1402 template <class Real = double>
1403 class FFTWPhaseAccessor
1404 {
1405 public:
1406 /// The accessor's value type.
1407 typedef Real value_type;
1408
1409 /// Read phase at iterator position.
1410 template <class ITERATOR>
1411 value_type operator()(ITERATOR const & i) const {
1412 return (*i).phase();
1413 }
1414
1415 /// Read phase at offset from iterator position.
1416 template <class ITERATOR, class DIFFERENCE>
1417 value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
1418 return (i[d]).phase();
1419 }
1420 };
1421
1422 //@}
1423 //@}
1424
1425 /********************************************************/
1426 /* */
1427 /* Fourier Transform */
1428 /* */
1429 /********************************************************/
1430
1431 /* \addtogroup FourierTransform Fast Fourier Transform
1432
1433 This documentation describes the VIGRA interface to FFTW version 3. The interface
1434 to the old FFTW version 2 (file "vigra/fftw.hxx") is deprecated.
1435
1436 VIGRA uses the <a href="http://www.fftw.org/">FFTW Fast Fourier
1437 Transform</a> package to perform Fourier transformations. VIGRA
1438 provides a wrapper for FFTW's complex number type (FFTWComplex),
1439 but FFTW's functions are used verbatim. If the image is stored as
1440 a FFTWComplexImage, the simplest call to an FFT function is like this:
1441
1442 \code
1443 vigra::FFTWComplexImage spatial(width,height), fourier(width,height);
1444 ... // fill image with data
1445
1446 // create a plan with estimated performance optimization
1447 fftw_plan forwardPlan = fftw_plan_dft_2d(height, width,
1448 (fftw_complex *)spatial.begin(), (fftw_complex *)fourier.begin(),
1449 FFTW_FORWARD, FFTW_ESTIMATE );
1450 // calculate FFT (this can be repeated as often as needed,
1451 // with fresh data written into the source array)
1452 fftw_execute(forwardPlan);
1453
1454 // release the plan memory
1455 fftw_destroy_plan(forwardPlan);
1456
1457 // likewise for the inverse transform
1458 fftw_plan backwardPlan = fftw_plan_dft_2d(height, width,
1459 (fftw_complex *)fourier.begin(), (fftw_complex *)spatial.begin(),
1460 FFTW_BACKWARD, FFTW_ESTIMATE);
1461 fftw_execute(backwardPlan);
1462 fftw_destroy_plan(backwardPlan);
1463
1464 // do not forget to normalize the result according to the image size
1465 transformImage(srcImageRange(spatial), destImage(spatial),
1466 std::bind1st(std::multiplies<FFTWComplex>(), 1.0 / width / height));
1467 \endcode
1468
1469 Note that in the creation of a plan, the height must be given
1470 first. Note also that <TT>spatial.begin()</TT> may only be passed
1471 to <TT>fftw_plan_dft_2d</TT> if the transform shall be applied to the
1472 entire image. When you want to restrict operation to an ROI, you
1473 can create a copy of the ROI in an image of appropriate size, or
1474 you may use the Guru interface to FFTW.
1475
1476 More information on using FFTW can be found <a href="http://www.fftw.org/doc/">here</a>.
1477
1478 FFTW produces fourier images that have the DC component (the
1479 origin of the Fourier space) in the upper left corner. Often, one
1480 wants the origin in the center of the image, so that frequencies
1481 always increase towards the border of the image. This can be
1482 achieved by calling \ref moveDCToCenter(). The inverse
1483 transformation is done by \ref moveDCToUpperLeft().
1484
1485 <b>\#include</b> <vigra/fftw3.hxx><br>
1486 Namespace: vigra
1487 */
1488
1489 /** \addtogroup FourierTransform Fast Fourier Transform
1490
1491 VIGRA provides a powerful C++ API for the popular <a href="http://www.fftw.org/">FFTW library</a>
1492 for fast Fourier transforms. There are two versions of the API: an older one based on image
1493 iterators (and therefore restricted to 2D) and a new one based on \ref MultiArrayView that
1494 works for arbitrary dimensions. In addition, the functions \ref convolveFFT() and
1495 \ref applyFourierFilter() provide an easy-to-use interface for FFT-based convolution,
1496 a major application of Fourier transforms.
1497 */
1498 //@{
1499
1500 /********************************************************/
1501 /* */
1502 /* moveDCToCenter */
1503 /* */
1504 /********************************************************/
1505
1506 /** \brief Rearrange the quadrants of a Fourier image so that the origin is
1507 in the image center.
1508
1509 FFTW produces fourier images where the DC component (origin of
1510 fourier space) is located in the upper left corner of the
1511 image. The quadrants are placed like this (using a 4x4 image for
1512 example):
1513
1514 \code
1515 DC 4 3 3
1516 4 4 3 3
1517 1 1 2 2
1518 1 1 2 2
1519 \endcode
1520
1521 After applying the function, the quadrants are at their usual places:
1522
1523 \code
1524 2 2 1 1
1525 2 2 1 1
1526 3 3 DC 4
1527 3 3 4 4
1528 \endcode
1529
1530 This transformation can be reversed by \ref moveDCToUpperLeft().
1531 Note that the 2D versions of this transformation must not be executed in place - input
1532 and output images must be different. In contrast, the nD version (with MultiArrayView
1533 argument) always works in-place.
1534
1535 <b> Declarations:</b>
1536
1537 use MultiArrayView (this works in-place, with arbitrary dimension N):
1538 \code
1539 namespace vigra {
1540 template <unsigned int N, class T, class Stride>
1541 void moveDCToCenter(MultiArrayView<N, T, Stride> a);
1542 }
1543 \endcode
1544
1545 pass iterators explicitly (2D only, not in-place):
1546 \code
1547 namespace vigra {
1548 template <class SrcImageIterator, class SrcAccessor,
1549 class DestImageIterator, class DestAccessor>
1550 void moveDCToCenter(SrcImageIterator src_upperleft,
1551 SrcImageIterator src_lowerright, SrcAccessor sa,
1552 DestImageIterator dest_upperleft, DestAccessor da);
1553 }
1554 \endcode
1555
1556
1557 use argument objects in conjunction with \ref ArgumentObjectFactories (2D only, not in-place):
1558 \code
1559 namespace vigra {
1560 template <class SrcImageIterator, class SrcAccessor,
1561 class DestImageIterator, class DestAccessor>
1562 void moveDCToCenter(
1563 triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
1564 pair<DestImageIterator, DestAccessor> dest);
1565 }
1566 \endcode
1567
1568 <b> Usage:</b>
1569
1570 <b>\#include</b> <vigra/fftw3.hxx> (for 2D variants) <br>
1571 <b>\#include</b> <vigra/multi_fft.hxx> (for nD variants) <br>
1572 Namespace: vigra
1573
1574 \code
1575 vigra::FFTWComplexImage spatial(width,height), fourier(width,height);
1576 ... // fill image with data
1577
1578 // create a plan with estimated performance optimization
1579 fftw_plan forwardPlan = fftw_plan_dft_2d(height, width,
1580 (fftw_complex *)spatial.begin(), (fftw_complex *)fourier.begin(),
1581 FFTW_FORWARD, FFTW_ESTIMATE );
1582 // calculate FFT
1583 fftw_execute(forwardPlan);
1584
1585 vigra::FFTWComplexImage rearrangedFourier(width, height);
1586 moveDCToCenter(srcImageRange(fourier), destImage(rearrangedFourier));
1587
1588 // delete the plan
1589 fftw_destroy_plan(forwardPlan);
1590 \endcode
1591 */
1592 doxygen_overloaded_function(template <...> void moveDCToCenter)
1593
1594 template <class SrcImageIterator, class SrcAccessor,
1595 class DestImageIterator, class DestAccessor>
1596 void moveDCToCenter(SrcImageIterator src_upperleft,
1597 SrcImageIterator src_lowerright, SrcAccessor sa,
1598 DestImageIterator dest_upperleft, DestAccessor da)
1599 {
1600 int w = int(src_lowerright.x - src_upperleft.x);
1601 int h = int(src_lowerright.y - src_upperleft.y);
1602 int w1 = w/2;
1603 int h1 = h/2;
1604 int w2 = (w+1)/2;
1605 int h2 = (h+1)/2;
1606
1607 // 2. Quadrant zum 4.
1608 copyImage(srcIterRange(src_upperleft,
1609 src_upperleft + Diff2D(w2, h2), sa),
1610 destIter (dest_upperleft + Diff2D(w1, h1), da));
1611
1612 // 4. Quadrant zum 2.
1613 copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
1614 src_lowerright, sa),
1615 destIter (dest_upperleft, da));
1616
1617 // 1. Quadrant zum 3.
1618 copyImage(srcIterRange(src_upperleft + Diff2D(w2, 0),
1619 src_upperleft + Diff2D(w, h2), sa),
1620 destIter (dest_upperleft + Diff2D(0, h1), da));
1621
1622 // 3. Quadrant zum 1.
1623 copyImage(srcIterRange(src_upperleft + Diff2D(0, h2),
1624 src_upperleft + Diff2D(w2, h), sa),
1625 destIter (dest_upperleft + Diff2D(w1, 0), da));
1626 }
1627
1628 template <class SrcImageIterator, class SrcAccessor,
1629 class DestImageIterator, class DestAccessor>
1630 inline void moveDCToCenter(
1631 triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
1632 pair<DestImageIterator, DestAccessor> dest)
1633 {
1634 moveDCToCenter(src.first, src.second, src.third,
1635 dest.first, dest.second);
1636 }
1637
1638 /********************************************************/
1639 /* */
1640 /* moveDCToUpperLeft */
1641 /* */
1642 /********************************************************/
1643
1644 /** \brief Rearrange the quadrants of a Fourier image so that the origin is
1645 in the image's upper left.
1646
1647 This function is the inversion of \ref moveDCToCenter(). See there
1648 for a detailed description and usage examples.
1649
1650 <b> Declarations:</b>
1651
1652 use MultiArrayView (this works in-place, with arbitrary dimension N):
1653 \code
1654 namespace vigra {
1655 template <unsigned int N, class T, class Stride>
1656 void moveDCToUpperLeft(MultiArrayView<N, T, Stride> a);
1657 }
1658 \endcode
1659
1660 pass iterators explicitly (2D only, not in-place):
1661 \code
1662 namespace vigra {
1663 template <class SrcImageIterator, class SrcAccessor,
1664 class DestImageIterator, class DestAccessor>
1665 void moveDCToUpperLeft(SrcImageIterator src_upperleft,
1666 SrcImageIterator src_lowerright, SrcAccessor sa,
1667 DestImageIterator dest_upperleft, DestAccessor da);
1668 }
1669 \endcode
1670
1671
1672 use argument objects in conjunction with \ref ArgumentObjectFactories (2D only, not in-place):
1673 \code
1674 namespace vigra {
1675 template <class SrcImageIterator, class SrcAccessor,
1676 class DestImageIterator, class DestAccessor>
1677 void moveDCToUpperLeft(
1678 triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
1679 pair<DestImageIterator, DestAccessor> dest);
1680 }
1681 \endcode
1682 */
1683 doxygen_overloaded_function(template <...> void moveDCToUpperLeft)
1684
1685 template <class SrcImageIterator, class SrcAccessor,
1686 class DestImageIterator, class DestAccessor>
1687 void moveDCToUpperLeft(SrcImageIterator src_upperleft,
1688 SrcImageIterator src_lowerright, SrcAccessor sa,
1689 DestImageIterator dest_upperleft, DestAccessor da)
1690 {
1691 int w = int(src_lowerright.x - src_upperleft.x);
1692 int h = int(src_lowerright.y - src_upperleft.y);
1693 int w2 = w/2;
1694 int h2 = h/2;
1695 int w1 = (w+1)/2;
1696 int h1 = (h+1)/2;
1697
1698 // 2. Quadrant zum 4.
1699 copyImage(srcIterRange(src_upperleft,
1700 src_upperleft + Diff2D(w2, h2), sa),
1701 destIter (dest_upperleft + Diff2D(w1, h1), da));
1702
1703 // 4. Quadrant zum 2.
1704 copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
1705 src_lowerright, sa),
1706 destIter (dest_upperleft, da));
1707
1708 // 1. Quadrant zum 3.
1709 copyImage(srcIterRange(src_upperleft + Diff2D(w2, 0),
1710 src_upperleft + Diff2D(w, h2), sa),
1711 destIter (dest_upperleft + Diff2D(0, h1), da));
1712
1713 // 3. Quadrant zum 1.
1714 copyImage(srcIterRange(src_upperleft + Diff2D(0, h2),
1715 src_upperleft + Diff2D(w2, h), sa),
1716 destIter (dest_upperleft + Diff2D(w1, 0), da));
1717 }
1718
1719 template <class SrcImageIterator, class SrcAccessor,
1720 class DestImageIterator, class DestAccessor>
1721 inline void moveDCToUpperLeft(
1722 triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
1723 pair<DestImageIterator, DestAccessor> dest)
1724 {
1725 moveDCToUpperLeft(src.first, src.second, src.third,
1726 dest.first, dest.second);
1727 }
1728
1729 namespace detail {
1730
1731 template <class T>
1732 void
1733 fourierTransformImpl(FFTWComplexImage::const_traverser sul,
1734 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
1735 FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest, T sign)
1736 {
1737 int w = int(slr.x - sul.x);
1738 int h = int(slr.y - sul.y);
1739
1740 FFTWComplexImage sworkImage, dworkImage;
1741
1742 fftw_complex * srcPtr = (fftw_complex *)(&*sul);
1743 fftw_complex * destPtr = (fftw_complex *)(&*dul);
1744
1745 // test for right memory layout (fftw expects a 2*width*height floats array)
1746 if (h > 1 && &(*(sul + Diff2D(w, 0))) != &(*(sul + Diff2D(0, 1))))
1747 {
1748 sworkImage.resize(w, h);
1749 copyImage(srcIterRange(sul, slr, src), destImage(sworkImage));
1750 srcPtr = (fftw_complex *)(&(*sworkImage.upperLeft()));
1751 }
1752 if (h > 1 && &(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
1753 {
1754 dworkImage.resize(w, h);
1755 destPtr = (fftw_complex *)(&(*dworkImage.upperLeft()));
1756 }
1757
1758 fftw_plan plan = fftw_plan_dft_2d(h, w, srcPtr, destPtr, sign, FFTW_ESTIMATE );
1759 fftw_execute(plan);
1760 fftw_destroy_plan(plan);
1761
1762 if (h > 1 && &(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
1763 {
1764 copyImage(srcImageRange(dworkImage), destIter(dul, dest));
1765 }
1766 }
1767
1768 } // namespace detail
1769
1770 /********************************************************/
1771 /* */
1772 /* fourierTransform */
1773 /* */
1774 /********************************************************/
1775
1776 /** \brief Compute forward and inverse Fourier transforms.
1777
1778 The array referring to the spatial domain (i.e. the input in a forward transform,
1779 and the output in an inverse transform) may be scalar or complex. The array representing
1780 the frequency domain (i.e. output for forward transform, input for inverse transform)
1781 must always be complex.
1782
1783 The new implementations (those using MultiArrayView arguments) perform a normalized transform,
1784 whereas the old ones (using 2D iterators or argument objects) perform an un-normalized
1785 transform (i.e. the result of the inverse transform is scaled by the number of pixels).
1786
1787 In general, input and output arrays must have the same shape, with the exception of the
1788 special <a href="http://www.fftw.org/doc/Multi_002dDimensional-DFTs-of-Real-Data.html">R2C
1789 and C2R modes</a> defined by FFTW.
1790
1791 The R2C transform reduces the redundancy in the Fourier representation of a real-valued signal:
1792 Since the Fourier representation of a real signal is symmetric, about half of the Fourier coefficients
1793 can simply be dropped. By convention, this reduction is applied to the first (innermost) dimension,
1794 such that <tt>fourier.shape(0) == spatial.shape(0)/2 + 1</tt> holds. The correct frequency domain
1795 shape can be conveniently computed by means of the function \ref fftwCorrespondingShapeR2C().
1796
1797 Note that your program must always link against <tt>libfftw3</tt>. If you want to compute Fourier
1798 transforms for <tt>float</tt> or <tt>long double</tt> arrays, you must <i>additionally</i> link against <tt>libfftw3f</tt> and <tt>libfftw3l</tt> respectively. (Old-style functions only support <tt>double</tt>).
1799
1800 The Fourier transform functions internally create <a href="http://www.fftw.org/doc/Using-Plans.html">FFTW plans</a>
1801 which control the algorithm details. The plans are creates with the flag <tt>FFTW_ESTIMATE</tt>, i.e.
1802 optimal settings are guessed or read from saved "wisdom" files. If you need more control over planning,
1803 you can use the class \ref FFTWPlan.
1804
1805 <b> Declarations:</b>
1806
1807 use complex-valued MultiArrayView arguments (this works for arbitrary dimension N):
1808 \code
1809 namespace vigra {
1810 template <unsigned int N, class Real, class C1, class C2>
1811 void
1812 fourierTransform(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1813 MultiArrayView<N, FFTWComplex<Real>, C2> out);
1814
1815 template <unsigned int N, class Real, class C1, class C2>
1816 void
1817 fourierTransformInverse(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1818 MultiArrayView<N, FFTWComplex<Real>, C2> out);
1819 }
1820 \endcode
1821
1822 use real-valued MultiArrayView in the spatial domain, complex-valued MultiArrayView
1823 in the frequency domain (this works for arbitrary dimension N, and also supports
1824 the R2C and C2R transform, depending on the array shape in the frequency domain):
1825 \code
1826 namespace vigra {
1827 template <unsigned int N, class Real, class C1, class C2>
1828 void
1829 fourierTransform(MultiArrayView<N, Real, C1> in,
1830 MultiArrayView<N, FFTWComplex<Real>, C2> out);
1831
1832 template <unsigned int N, class Real, class C1, class C2>
1833 void
1834 fourierTransformInverse(MultiArrayView<N, FFTWComplex<Real>, C1> in,
1835 MultiArrayView<N, Real, C2> out);
1836 }
1837 \endcode
1838
1839 pass iterators explicitly (2D only, double only):
1840 \code
1841 namespace vigra {
1842 template <class SrcImageIterator, class SrcAccessor>
1843 void fourierTransform(SrcImageIterator srcUpperLeft,
1844 SrcImageIterator srcLowerRight, SrcAccessor src,
1845 FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor dest);
1846
1847 void
1848 fourierTransformInverse(FFTWComplexImage::const_traverser sul,
1849 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
1850 FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
1851 }
1852 \endcode
1853
1854 use argument objects in conjunction with \ref ArgumentObjectFactories (2D only, double only):
1855 \code
1856 namespace vigra {
1857 template <class SrcImageIterator, class SrcAccessor>
1858 void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
1859 pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
1860
1861 void
1862 fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
1863 FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
1864 pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
1865 }
1866 \endcode
1867
1868 <b> Usage:</b>
1869
1870 <b>\#include</b> <vigra/fftw3.hxx> (old-style 2D variants)<br>
1871 <b>\#include</b> <vigra/multi_fft.hxx> (new-style nD variants)<br>
1872 Namespace: vigra
1873
1874 old-style example (using FFTWComplexImage):
1875 \code
1876 // compute complex Fourier transform of a real image, old-style implementation
1877 vigra::DImage src(w, h);
1878 vigra::FFTWComplexImage fourier(w, h);
1879
1880 fourierTransform(srcImageRange(src), destImage(fourier));
1881
1882 // compute inverse Fourier transform
1883 // note that both source and destination image must be of type vigra::FFTWComplexImage
1884 vigra::FFTWComplexImage inverseFourier(w, h);
1885
1886 fourierTransformInverse(srcImageRange(fourier), destImage(inverseFourier));
1887 \endcode
1888
1889 new-style examples (using MultiArray):
1890 \code
1891 // compute Fourier transform of a real array, using the R2C algorithm
1892 MultiArray<2, double> src(Shape2(w, h));
1893 MultiArray<2, FFTWComplex<double> > fourier(fftwCorrespondingShapeR2C(src.shape()));
1894
1895 fourierTransform(src, fourier);
1896
1897 // compute inverse Fourier transform, using the C2R algorithm
1898 MultiArray<2, double> dest(src.shape());
1899 fourierTransformInverse(fourier, dest);
1900 \endcode
1901
1902 \code
1903 // compute Fourier transform of a real array with standard algorithm
1904 MultiArray<2, double> src(Shape2(w, h));
1905 MultiArray<2, FFTWComplex<double> > fourier(src.shape());
1906
1907 fourierTransform(src, fourier);
1908
1909 // compute inverse Fourier transform, using the C2R algorithm
1910 MultiArray<2, double> dest(src.shape());
1911 fourierTransformInverse(fourier, dest);
1912 \endcode
1913 Complex input arrays are handled in the same way.
1914
1915 */
1916 doxygen_overloaded_function(template <...> void fourierTransform)
1917
1918 inline void
1919 fourierTransform(FFTWComplexImage::const_traverser sul,
1920 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
1921 FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
1922 {
1923 detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_FORWARD);
1924 }
1925
1926 template <class SrcImageIterator, class SrcAccessor>
1927 void fourierTransform(SrcImageIterator srcUpperLeft,
1928 SrcImageIterator srcLowerRight, SrcAccessor sa,
1929 FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor da)
1930 {
1931 // copy real input images into a complex one...
1932 int w= srcLowerRight.x - srcUpperLeft.x;
1933 int h= srcLowerRight.y - srcUpperLeft.y;
1934
1935 FFTWComplexImage workImage(w, h);
1936 copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
1937 destImage(workImage, FFTWWriteRealAccessor<>()));
1938
1939 // ...and call the complex -> complex version of the algorithm
1940 FFTWComplexImage const & cworkImage = workImage;
1941 fourierTransform(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
1942 destUpperLeft, da);
1943 }
1944
1945 template <class SrcImageIterator, class SrcAccessor>
1946 inline
1947 void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
1948 pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest)
1949 {
1950 fourierTransform(src.first, src.second, src.third, dest.first, dest.second);
1951 }
1952
1953 /** \brief Compute inverse Fourier transforms.
1954
1955 See \ref fourierTransform() for details.
1956 */
1957 doxygen_overloaded_function(template <...> void fourierTransformInverse)
1958
1959 inline void
1960 fourierTransformInverse(FFTWComplexImage::const_traverser sul,
1961 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
1962 FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
1963 {
1964 detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_BACKWARD);
1965 }
1966
1967 template <class DestImageIterator, class DestAccessor>
1968 void fourierTransformInverse(FFTWComplexImage::const_traverser sul,
1969 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
1970 DestImageIterator dul, DestAccessor dest)
1971 {
1972 int w = slr.x - sul.x;
1973 int h = slr.y - sul.y;
1974
1975 FFTWComplexImage workImage(w, h);
1976 fourierTransformInverse(sul, slr, src, workImage.upperLeft(), workImage.accessor());
1977 copyImage(srcImageRange(workImage), destIter(dul, dest));
1978 }
1979
1980
1981 template <class DestImageIterator, class DestAccessor>
1982 inline void
1983 fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
1984 FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
1985 pair<DestImageIterator, DestAccessor> dest)
1986 {
1987 fourierTransformInverse(src.first, src.second, src.third, dest.first, dest.second);
1988 }
1989
1990
1991
1992 /********************************************************/
1993 /* */
1994 /* applyFourierFilter */
1995 /* */
1996 /********************************************************/
1997
1998 /** \brief Apply a filter (defined in the frequency domain) to an image.
1999
2000 After transferring the image into the frequency domain, it is
2001 multiplied pixel-wise with the filter and transformed back. The
2002 result is put into the given destination image which must have the right size.
2003 The result will be normalized to compensate for the two FFTs.
2004
2005 If the destination image is scalar, only the real part of the result image is
2006 retained. In this case, you are responsible for choosing a filter image
2007 which ensures a zero imaginary part of the result (e.g. use a real, even symmetric
2008 filter image, or a purely imaginary, odd symmetric one).
2009
2010 The DC entry of the filter must be in the upper left, which is the
2011 position where FFTW expects it (see \ref moveDCToUpperLeft()).
2012
2013 See also \ref convolveFFT() for corresponding functionality on the basis of the
2014 \ref MultiArrayView interface.
2015
2016 <b> Declarations:</b>
2017
2018 pass 2D array views:
2019 \code
2020 namespace vigra {
2021 template <class SrcImageIterator, class SrcAccessor,
2022 class FilterImageIterator, class FilterAccessor,
2023 class DestImageIterator, class DestAccessor>
2024 void applyFourierFilter(SrcImageIterator srcUpperLeft,
2025 SrcImageIterator srcLowerRight, SrcAccessor sa,
2026 FilterImageIterator filterUpperLeft, FilterAccessor fa,
2027 DestImageIterator destUpperLeft, DestAccessor da);
2028 }
2029 \endcode
2030
2031 pass \ref ImageIterators and \ref DataAccessors :
2032 \code
2033 namespace vigra {
2034 template <class SrcImageIterator, class SrcAccessor,
2035 class FilterImageIterator, class FilterAccessor,
2036 class DestImageIterator, class DestAccessor>
2037 void applyFourierFilter(SrcImageIterator srcUpperLeft,
2038 SrcImageIterator srcLowerRight, SrcAccessor sa,
2039 FilterImageIterator filterUpperLeft, FilterAccessor fa,
2040 DestImageIterator destUpperLeft, DestAccessor da);
2041 }
2042 \endcode
2043
2044 use argument objects in conjunction with \ref ArgumentObjectFactories :
2045 \code
2046 namespace vigra {
2047 template <class SrcImageIterator, class SrcAccessor,
2048 class FilterImageIterator, class FilterAccessor,
2049 class DestImageIterator, class DestAccessor>
2050 void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
2051 pair<FilterImageIterator, FilterAccessor> filter,
2052 pair<DestImageIterator, DestAccessor> dest);
2053 }
2054 \endcode
2055
2056 <b> Usage:</b>
2057
2058 <b>\#include</b> <vigra/fftw3.hxx><br>
2059 Namespace: vigra
2060
2061 \code
2062 // create a Gaussian filter in Fourier space
2063 vigra::FImage gaussFilter(w, h), filter(w, h);
2064 for(int y=0; y<h; ++y)
2065 for(int x=0; x<w; ++x)
2066 {
2067 xx = float(x - w / 2) / w;
2068 yy = float(y - h / 2) / h;
2069
2070 gaussFilter(x,y) = std::exp(-(xx*xx + yy*yy) / 2.0 * scale);
2071 }
2072
2073 // applyFourierFilter() expects the filter's DC in the upper left
2074 moveDCToUpperLeft(srcImageRange(gaussFilter), destImage(filter));
2075
2076 vigra::FFTWComplexImage result(w, h);
2077
2078 vigra::applyFourierFilter(srcImageRange(image), srcImage(filter), result);
2079 \endcode
2080
2081 For inspection of the result, \ref FFTWMagnitudeAccessor might be
2082 useful. If you want to apply the same filter repeatedly, it may be more
2083 efficient to use the FFTW functions directly with FFTW plans optimized
2084 for good performance.
2085 */
2086 doxygen_overloaded_function(template <...> void applyFourierFilter)
2087
2088 template <class SrcImageIterator, class SrcAccessor,
2089 class FilterImageIterator, class FilterAccessor,
2090 class DestImageIterator, class DestAccessor>
2091 void applyFourierFilter(SrcImageIterator srcUpperLeft,
2092 SrcImageIterator srcLowerRight, SrcAccessor sa,
2093 FilterImageIterator filterUpperLeft, FilterAccessor fa,
2094 DestImageIterator destUpperLeft, DestAccessor da)
2095 {
2096 // copy real input images into a complex one...
2097 int w = int(srcLowerRight.x - srcUpperLeft.x);
2098 int h = int(srcLowerRight.y - srcUpperLeft.y);
2099
2100 FFTWComplexImage workImage(w, h);
2101 copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
2102 destImage(workImage, FFTWWriteRealAccessor<>()));
2103
2104 // ...and call the impl
2105 FFTWComplexImage const & cworkImage = workImage;
2106 applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
2107 filterUpperLeft, fa,
2108 destUpperLeft, da);
2109 }
2110
2111 template <class FilterImageIterator, class FilterAccessor,
2112 class DestImageIterator, class DestAccessor>
2113 inline
2114 void applyFourierFilter(
2115 FFTWComplexImage::const_traverser srcUpperLeft,
2116 FFTWComplexImage::const_traverser srcLowerRight,
2117 FFTWComplexImage::ConstAccessor sa,
2118 FilterImageIterator filterUpperLeft, FilterAccessor fa,
2119 DestImageIterator destUpperLeft, DestAccessor da)
2120 {
2121 int w = srcLowerRight.x - srcUpperLeft.x;
2122 int h = srcLowerRight.y - srcUpperLeft.y;
2123
2124 // test for right memory layout (fftw expects a 2*width*height floats array)
2125 if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
2126 applyFourierFilterImpl(srcUpperLeft, srcLowerRight, sa,
2127 filterUpperLeft, fa,
2128 destUpperLeft, da);
2129 else
2130 {
2131 FFTWComplexImage workImage(w, h);
2132 copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
2133 destImage(workImage));
2134
2135 FFTWComplexImage const & cworkImage = workImage;
2136 applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
2137 filterUpperLeft, fa,
2138 destUpperLeft, da);
2139 }
2140 }
2141
2142 template <class SrcImageIterator, class SrcAccessor,
2143 class FilterImageIterator, class FilterAccessor,
2144 class DestImageIterator, class DestAccessor>
2145 inline
2146 void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
2147 pair<FilterImageIterator, FilterAccessor> filter,
2148 pair<DestImageIterator, DestAccessor> dest)
2149 {
2150 applyFourierFilter(src.first, src.second, src.third,
2151 filter.first, filter.second,
2152 dest.first, dest.second);
2153 }
2154
2155 template <class FilterImageIterator, class FilterAccessor,
2156 class DestImageIterator, class DestAccessor>
2157 void applyFourierFilterImpl(
2158 FFTWComplexImage::const_traverser srcUpperLeft,
2159 FFTWComplexImage::const_traverser srcLowerRight,
2160 FFTWComplexImage::ConstAccessor,
2161 FilterImageIterator filterUpperLeft, FilterAccessor fa,
2162 DestImageIterator destUpperLeft, DestAccessor da)
2163 {
2164 int w = int(srcLowerRight.x - srcUpperLeft.x);
2165 int h = int(srcLowerRight.y - srcUpperLeft.y);
2166
2167 FFTWComplexImage complexResultImg(srcLowerRight - srcUpperLeft);
2168
2169 // FFT from srcImage to complexResultImg
2170 fftw_plan forwardPlan=
2171 fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
2172 (fftw_complex *)complexResultImg.begin(),
2173 FFTW_FORWARD, FFTW_ESTIMATE );
2174 fftw_execute(forwardPlan);
2175 fftw_destroy_plan(forwardPlan);
2176
2177 // convolve in freq. domain (in complexResultImg)
2178 combineTwoImages(srcImageRange(complexResultImg), srcIter(filterUpperLeft, fa),
2179 destImage(complexResultImg), std::multiplies<FFTWComplex<> >());
2180
2181 // FFT back into spatial domain (inplace in complexResultImg)
2182 fftw_plan backwardPlan=
2183 fftw_plan_dft_2d(h, w, (fftw_complex *)complexResultImg.begin(),
2184 (fftw_complex *)complexResultImg.begin(),
2185 FFTW_BACKWARD, FFTW_ESTIMATE);
2186 fftw_execute(backwardPlan);
2187 fftw_destroy_plan(backwardPlan);
2188
2189 typedef typename
2190 NumericTraits<typename DestAccessor::value_type>::isScalar
2191 isScalarResult;
2192
2193 // normalization (after FFTs), maybe stripping imaginary part
2194 applyFourierFilterImplNormalization(complexResultImg, destUpperLeft, da,
2195 isScalarResult());
2196 }
2197
2198 template <class DestImageIterator, class DestAccessor>
2199 void applyFourierFilterImplNormalization(FFTWComplexImage const &srcImage,
2200 DestImageIterator destUpperLeft,
2201 DestAccessor da,
2202 VigraFalseType)
2203 {
2204 double normFactor= 1.0/(srcImage.width() * srcImage.height());
2205
2206 for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
2207 {
2208 DestImageIterator dIt= destUpperLeft;
2209 for(int x= 0; x< srcImage.width(); x++, dIt.x++)
2210 {
2211 da.setComponent(srcImage(x, y).re()*normFactor, dIt, 0);
2212 da.setComponent(srcImage(x, y).im()*normFactor, dIt, 1);
2213 }
2214 }
2215 }
2216
2217 inline
2218 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
2219 FFTWComplexImage::traverser destUpperLeft,
2220 FFTWComplexImage::Accessor da,
2221 VigraFalseType)
2222 {
2223 transformImage(srcImageRange(srcImage), destIter(destUpperLeft, da),
2224 linearIntensityTransform<FFTWComplex<> >(1.0/(srcImage.width() * srcImage.height())));
2225 }
2226
2227 template <class DestImageIterator, class DestAccessor>
2228 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
2229 DestImageIterator destUpperLeft,
2230 DestAccessor da,
2231 VigraTrueType)
2232 {
2233 double normFactor= 1.0/(srcImage.width() * srcImage.height());
2234
2235 for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
2236 {
2237 DestImageIterator dIt= destUpperLeft;
2238 for(int x= 0; x< srcImage.width(); x++, dIt.x++)
2239 da.set(srcImage(x, y).re()*normFactor, dIt);
2240 }
2241 }
2242
2243 /**********************************************************/
2244 /* */
2245 /* applyFourierFilterFamily */
2246 /* */
2247 /**********************************************************/
2248
2249 /** \brief Apply an array of filters (defined in the frequency domain) to an image.
2250
2251 This provides the same functionality as \ref applyFourierFilter(),
2252 but applying several filters at once allows to avoid
2253 repeated Fourier transforms of the source image.
2254
2255 Filters and result images must be stored in \ref vigra::ImageArray data
2256 structures. In contrast to \ref applyFourierFilter(), this function adjusts
2257 the size of the result images and the the length of the array.
2258
2259 <b> Declarations:</b>
2260
2261 pass 2D array views:
2262 \code
2263 namespace vigra {
2264 template <class SrcImageIterator, class SrcAccessor, class FilterType>
2265 void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
2266 SrcImageIterator srcLowerRight, SrcAccessor sa,
2267 const ImageArray<FilterType> &filters,
2268 ImageArray<FFTWComplexImage> &results)
2269 }
2270 \endcode
2271
2272 pass \ref ImageIterators and \ref DataAccessors :
2273 \code
2274 namespace vigra {
2275 template <class SrcImageIterator, class SrcAccessor, class FilterType>
2276 void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
2277 SrcImageIterator srcLowerRight, SrcAccessor sa,
2278 const ImageArray<FilterType> &filters,
2279 ImageArray<FFTWComplexImage> &results)
2280 }
2281 \endcode
2282
2283 use argument objects in conjunction with \ref ArgumentObjectFactories :
2284 \code
2285 namespace vigra {
2286 template <class SrcImageIterator, class SrcAccessor, class FilterType>
2287 void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
2288 const ImageArray<FilterType> &filters,
2289 ImageArray<FFTWComplexImage> &results)
2290 }
2291 \endcode
2292
2293 <b> Usage:</b>
2294
2295 <b>\#include</b> <vigra/fftw3.hxx><br>
2296 Namespace: vigra
2297
2298 \code
2299 // assuming the presence of a real-valued image named "image" to
2300 // be filtered in this example
2301
2302 vigra::ImageArray<vigra::FImage> filters(16, image.size());
2303
2304 for (int i=0; i<filters.size(); i++)
2305 // create some meaningful filters here
2306 createMyFilterOfScale(i, destImage(filters[i]));
2307
2308 vigra::ImageArray<vigra::FFTWComplexImage> results();
2309
2310 vigra::applyFourierFilterFamily(srcImageRange(image), filters, results);
2311 \endcode
2312 */
2313 doxygen_overloaded_function(template <...> void applyFourierFilterFamily)
2314
2315 template <class SrcImageIterator, class SrcAccessor,
2316 class FilterType, class DestImage>
2317 inline
2318 void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
2319 const ImageArray<FilterType> &filters,
2320 ImageArray<DestImage> &results)
2321 {
2322 applyFourierFilterFamily(src.first, src.second, src.third,
2323 filters, results);
2324 }
2325
2326 template <class SrcImageIterator, class SrcAccessor,
2327 class FilterType, class DestImage>
2328 void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
2329 SrcImageIterator srcLowerRight, SrcAccessor sa,
2330 const ImageArray<FilterType> &filters,
2331 ImageArray<DestImage> &results)
2332 {
2333 int w = int(srcLowerRight.x - srcUpperLeft.x);
2334 int h = int(srcLowerRight.y - srcUpperLeft.y);
2335
2336 FFTWComplexImage workImage(w, h);
2337 copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
2338 destImage(workImage, FFTWWriteRealAccessor<>()));
2339
2340 FFTWComplexImage const & cworkImage = workImage;
2341 applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
2342 filters, results);
2343 }
2344
2345 template <class FilterType, class DestImage>
2346 inline
2347 void applyFourierFilterFamily(
2348 FFTWComplexImage::const_traverser srcUpperLeft,
2349 FFTWComplexImage::const_traverser srcLowerRight,
2350 FFTWComplexImage::ConstAccessor sa,
2351 const ImageArray<FilterType> &filters,
2352 ImageArray<DestImage> &results)
2353 {
2354 int w= srcLowerRight.x - srcUpperLeft.x;
2355
2356 // test for right memory layout (fftw expects a 2*width*height floats array)
2357 if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
2358 applyFourierFilterFamilyImpl(srcUpperLeft, srcLowerRight, sa,
2359 filters, results);
2360 else
2361 {
2362 int h = srcLowerRight.y - srcUpperLeft.y;
2363 FFTWComplexImage workImage(w, h);
2364 copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
2365 destImage(workImage));
2366
2367 FFTWComplexImage const & cworkImage = workImage;
2368 applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
2369 filters, results);
2370 }
2371 }
2372
2373 template <class FilterType, class DestImage>
2374 void applyFourierFilterFamilyImpl(
2375 FFTWComplexImage::const_traverser srcUpperLeft,
2376 FFTWComplexImage::const_traverser srcLowerRight,
2377 FFTWComplexImage::ConstAccessor sa,
2378 const ImageArray<FilterType> &filters,
2379 ImageArray<DestImage> &results)
2380 {
2381 // FIXME: sa is not used
2382 // (maybe check if StandardAccessor, else copy?)
2383
2384 // make sure the filter images have the right dimensions
2385 vigra_precondition((srcLowerRight - srcUpperLeft) == filters.imageSize(),
2386 "applyFourierFilterFamily called with src image size != filters.imageSize()!");
2387
2388 // make sure the result image array has the right dimensions
2389 results.resize(filters.size());
2390 results.resizeImages(filters.imageSize());
2391
2392 // FFT from srcImage to freqImage
2393 int w = int(srcLowerRight.x - srcUpperLeft.x);
2394 int h = int(srcLowerRight.y - srcUpperLeft.y);
2395
2396 FFTWComplexImage freqImage(w, h);
2397 FFTWComplexImage result(w, h);
2398
2399 fftw_plan forwardPlan=
2400 fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
2401 (fftw_complex *)freqImage.begin(),
2402 FFTW_FORWARD, FFTW_ESTIMATE );
2403 fftw_execute(forwardPlan);
2404 fftw_destroy_plan(forwardPlan);
2405
2406 fftw_plan backwardPlan=
2407 fftw_plan_dft_2d(h, w, (fftw_complex *)result.begin(),
2408 (fftw_complex *)result.begin(),
2409 FFTW_BACKWARD, FFTW_ESTIMATE );
2410 typedef typename
2411 NumericTraits<typename DestImage::Accessor::value_type>::isScalar
2412 isScalarResult;
2413
2414 // convolve with filters in freq. domain
2415 for (unsigned int i= 0; i < filters.size(); i++)
2416 {
2417 combineTwoImages(srcImageRange(freqImage), srcImage(filters[i]),
2418 destImage(result), std::multiplies<FFTWComplex<> >());
2419
2420 // FFT back into spatial domain (inplace in destImage)
2421 fftw_execute(backwardPlan);
2422
2423 // normalization (after FFTs), maybe stripping imaginary part
2424 applyFourierFilterImplNormalization(result,
2425 results[i].upperLeft(), results[i].accessor(),
2426 isScalarResult());
2427 }
2428 fftw_destroy_plan(backwardPlan);
2429 }
2430
2431 /********************************************************/
2432 /* */
2433 /* fourierTransformReal */
2434 /* */
2435 /********************************************************/
2436
2437 /** \brief Real Fourier transforms for even and odd boundary conditions
2438 (aka. cosine and sine transforms).
2439
2440
2441 If the image is real and has even symmetry, its Fourier transform
2442 is also real and has even symmetry. The Fourier transform of a real image with odd
2443 symmetry is imaginary and has odd symmetry. In either case, only about a quarter
2444 of the pixels need to be stored because the rest can be calculated from the symmetry
2445 properties. This is especially useful, if the original image is implicitly assumed
2446 to have reflective or anti-reflective boundary conditions. Then the "negative"
2447 pixel locations are defined as
2448
2449 \code
2450 even (reflective boundary conditions): f[-x] = f[x] (x = 1,...,N-1)
2451 odd (anti-reflective boundary conditions): f[-1] = 0
2452 f[-x] = -f[x-2] (x = 2,...,N-1)
2453 \endcode
2454
2455 end similar at the other boundary (see the FFTW documentation for details).
2456 This has the advantage that more efficient Fourier transforms that use only
2457 real numbers can be implemented. These are also known as cosine and sine transforms
2458 respectively.
2459
2460 If you use the odd transform it is important to note that in the Fourier domain,
2461 the DC component is always zero and is therefore dropped from the data structure.
2462 This means that index 0 in an odd symmetric Fourier domain image refers to
2463 the <i>first</i> harmonic. This is especially important if an image is first
2464 cosine transformed (even symmetry), then in the Fourier domain multiplied
2465 with an odd symmetric filter (e.g. a first derivative) and finally transformed
2466 back to the spatial domain with a sine transform (odd symmetric). For this to work
2467 properly the image must be shifted left or up by one pixel (depending on whether
2468 the x- or y-axis is odd symmetric) before the inverse transform can be applied.
2469 (see example below).
2470
2471 The real Fourier transform functions are named <tt>fourierTransformReal??</tt>
2472 where the questions marks stand for either <tt>E</tt> or <tt>O</tt> indicating
2473 whether the x- and y-axis is to be transformed using even or odd symmetry.
2474 The same functions can be used for both the forward and inverse transforms,
2475 only the normalization changes. For signal processing, the following
2476 normalization factors are most appropriate:
2477
2478 \code
2479 forward inverse
2480 ------------------------------------------------------------
2481 X even, Y even 1.0 4.0 * (w-1) * (h-1)
2482 X even, Y odd -1.0 -4.0 * (w-1) * (h+1)
2483 X odd, Y even -1.0 -4.0 * (w+1) * (h-1)
2484 X odd, Y odd 1.0 4.0 * (w+1) * (h+1)
2485 \endcode
2486
2487 where <tt>w</tt> and <tt>h</tt> denote the image width and height.
2488
2489 <b> Declarations:</b>
2490
2491 pass 2D array views:
2492 \code
2493 namespace vigra {
2494 template <class SrcTraverser, class SrcAccessor,
2495 class DestTraverser, class DestAccessor>
2496 void
2497 fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2498 DestTraverser dul, DestAccessor dest, fftw_real norm);
2499
2500 fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
2501 }
2502 \endcode
2503
2504 pass \ref ImageIterators and \ref DataAccessors :
2505 \code
2506 namespace vigra {
2507 template <class SrcTraverser, class SrcAccessor,
2508 class DestTraverser, class DestAccessor>
2509 void
2510 fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2511 DestTraverser dul, DestAccessor dest, fftw_real norm);
2512
2513 fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
2514 }
2515 \endcode
2516
2517
2518 use argument objects in conjunction with \ref ArgumentObjectFactories :
2519 \code
2520 namespace vigra {
2521 template <class SrcTraverser, class SrcAccessor,
2522 class DestTraverser, class DestAccessor>
2523 void
2524 fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
2525 pair<DestTraverser, DestAccessor> dest, fftw_real norm);
2526
2527 fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
2528 }
2529 \endcode
2530
2531 <b> Usage:</b>
2532
2533 <b>\#include</b> <vigra/fftw3.hxx><br>
2534 Namespace: vigra
2535
2536 \code
2537 vigra::FImage spatial(width,height), fourier(width,height);
2538 ... // fill image with data
2539
2540 // forward cosine transform == reflective boundary conditions
2541 fourierTransformRealEE(srcImageRange(spatial), destImage(fourier), (fftw_real)1.0);
2542
2543 // multiply with a first derivative of Gaussian in x-direction
2544 for(int y = 0; y < height; ++y)
2545 {
2546 for(int x = 1; x < width; ++x)
2547 {
2548 double dx = x * M_PI / (width - 1);
2549 double dy = y * M_PI / (height - 1);
2550 fourier(x-1, y) = fourier(x, y) * dx * std::exp(-(dx*dx + dy*dy) * scale*scale / 2.0);
2551 }
2552 fourier(width-1, y) = 0.0;
2553 }
2554
2555 // inverse transform -- odd symmetry in x-direction, even in y,
2556 // due to symmetry of the filter
2557 fourierTransformRealOE(srcImageRange(fourier), destImage(spatial),
2558 (fftw_real)-4.0 * (width+1) * (height-1));
2559 \endcode
2560 */
2561 doxygen_overloaded_function(template <...> void fourierTransformReal)
2562
2563 template <class SrcTraverser, class SrcAccessor,
2564 class DestTraverser, class DestAccessor>
2565 inline void
2566 fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
2567 pair<DestTraverser, DestAccessor> dest, fftw_real norm)
2568 {
2569 fourierTransformRealEE(src.first, src.second, src.third,
2570 dest.first, dest.second, norm);
2571 }
2572
2573 template <class SrcTraverser, class SrcAccessor,
2574 class DestTraverser, class DestAccessor>
2575 inline void
2576 fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2577 DestTraverser dul, DestAccessor dest, fftw_real norm)
2578 {
2579 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2580 norm, FFTW_REDFT00, FFTW_REDFT00);
2581 }
2582
2583 template <class DestTraverser, class DestAccessor>
2584 inline void
2585 fourierTransformRealEE(
2586 FFTWRealImage::const_traverser sul,
2587 FFTWRealImage::const_traverser slr,
2588 FFTWRealImage::Accessor src,
2589 DestTraverser dul, DestAccessor dest, fftw_real norm)
2590 {
2591 int w = slr.x - sul.x;
2592
2593 // test for right memory layout (fftw expects a width*height fftw_real array)
2594 if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
2595 fourierTransformRealImpl(sul, slr, dul, dest,
2596 norm, FFTW_REDFT00, FFTW_REDFT00);
2597 else
2598 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2599 norm, FFTW_REDFT00, FFTW_REDFT00);
2600 }
2601
2602 /********************************************************************/
2603
2604 template <class SrcTraverser, class SrcAccessor,
2605 class DestTraverser, class DestAccessor>
2606 inline void
2607 fourierTransformRealOE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
2608 pair<DestTraverser, DestAccessor> dest, fftw_real norm)
2609 {
2610 fourierTransformRealOE(src.first, src.second, src.third,
2611 dest.first, dest.second, norm);
2612 }
2613
2614 template <class SrcTraverser, class SrcAccessor,
2615 class DestTraverser, class DestAccessor>
2616 inline void
2617 fourierTransformRealOE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2618 DestTraverser dul, DestAccessor dest, fftw_real norm)
2619 {
2620 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2621 norm, FFTW_RODFT00, FFTW_REDFT00);
2622 }
2623
2624 template <class DestTraverser, class DestAccessor>
2625 inline void
2626 fourierTransformRealOE(
2627 FFTWRealImage::const_traverser sul,
2628 FFTWRealImage::const_traverser slr,
2629 FFTWRealImage::Accessor src,
2630 DestTraverser dul, DestAccessor dest, fftw_real norm)
2631 {
2632 int w = slr.x - sul.x;
2633
2634 // test for right memory layout (fftw expects a width*height fftw_real array)
2635 if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
2636 fourierTransformRealImpl(sul, slr, dul, dest,
2637 norm, FFTW_RODFT00, FFTW_REDFT00);
2638 else
2639 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2640 norm, FFTW_RODFT00, FFTW_REDFT00);
2641 }
2642
2643 /********************************************************************/
2644
2645 template <class SrcTraverser, class SrcAccessor,
2646 class DestTraverser, class DestAccessor>
2647 inline void
2648 fourierTransformRealEO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
2649 pair<DestTraverser, DestAccessor> dest, fftw_real norm)
2650 {
2651 fourierTransformRealEO(src.first, src.second, src.third,
2652 dest.first, dest.second, norm);
2653 }
2654
2655 template <class SrcTraverser, class SrcAccessor,
2656 class DestTraverser, class DestAccessor>
2657 inline void
2658 fourierTransformRealEO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2659 DestTraverser dul, DestAccessor dest, fftw_real norm)
2660 {
2661 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2662 norm, FFTW_REDFT00, FFTW_RODFT00);
2663 }
2664
2665 template <class DestTraverser, class DestAccessor>
2666 inline void
2667 fourierTransformRealEO(
2668 FFTWRealImage::const_traverser sul,
2669 FFTWRealImage::const_traverser slr,
2670 FFTWRealImage::Accessor src,
2671 DestTraverser dul, DestAccessor dest, fftw_real norm)
2672 {
2673 int w = slr.x - sul.x;
2674
2675 // test for right memory layout (fftw expects a width*height fftw_real array)
2676 if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
2677 fourierTransformRealImpl(sul, slr, dul, dest,
2678 norm, FFTW_REDFT00, FFTW_RODFT00);
2679 else
2680 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2681 norm, FFTW_REDFT00, FFTW_RODFT00);
2682 }
2683
2684 /********************************************************************/
2685
2686 template <class SrcTraverser, class SrcAccessor,
2687 class DestTraverser, class DestAccessor>
2688 inline void
2689 fourierTransformRealOO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
2690 pair<DestTraverser, DestAccessor> dest, fftw_real norm)
2691 {
2692 fourierTransformRealOO(src.first, src.second, src.third,
2693 dest.first, dest.second, norm);
2694 }
2695
2696 template <class SrcTraverser, class SrcAccessor,
2697 class DestTraverser, class DestAccessor>
2698 inline void
2699 fourierTransformRealOO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2700 DestTraverser dul, DestAccessor dest, fftw_real norm)
2701 {
2702 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2703 norm, FFTW_RODFT00, FFTW_RODFT00);
2704 }
2705
2706 template <class DestTraverser, class DestAccessor>
2707 inline void
2708 fourierTransformRealOO(
2709 FFTWRealImage::const_traverser sul,
2710 FFTWRealImage::const_traverser slr,
2711 FFTWRealImage::Accessor src,
2712 DestTraverser dul, DestAccessor dest, fftw_real norm)
2713 {
2714 int w = slr.x - sul.x;
2715
2716 // test for right memory layout (fftw expects a width*height fftw_real array)
2717 if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
2718 fourierTransformRealImpl(sul, slr, dul, dest,
2719 norm, FFTW_RODFT00, FFTW_RODFT00);
2720 else
2721 fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
2722 norm, FFTW_RODFT00, FFTW_RODFT00);
2723 }
2724
2725 /*******************************************************************/
2726
2727 template <class SrcTraverser, class SrcAccessor,
2728 class DestTraverser, class DestAccessor>
2729 void
2730 fourierTransformRealWorkImageImpl(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
2731 DestTraverser dul, DestAccessor dest,
2732 fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
2733 {
2734 FFTWRealImage workImage(slr - sul);
2735 copyImage(srcIterRange(sul, slr, src), destImage(workImage));
2736 FFTWRealImage const & cworkImage = workImage;
2737 fourierTransformRealImpl(cworkImage.upperLeft(), cworkImage.lowerRight(),
2738 dul, dest, norm, kindx, kindy);
2739 }
2740
2741
2742 template <class DestTraverser, class DestAccessor>
2743 void
2744 fourierTransformRealImpl(
2745 FFTWRealImage::const_traverser sul,
2746 FFTWRealImage::const_traverser slr,
2747 DestTraverser dul, DestAccessor dest,
2748 fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
2749 {
2750 int w = slr.x - sul.x;
2751 int h = slr.y - sul.y;
2752 BasicImage<fftw_real> res(w, h);
2753
2754 fftw_plan plan = fftw_plan_r2r_2d(h, w,
2755 (fftw_real *)&(*sul), (fftw_real *)res.begin(),
2756 kindy, kindx, FFTW_ESTIMATE);
2757 fftw_execute(plan);
2758 fftw_destroy_plan(plan);
2759
2760 if(norm != 1.0)
2761 transformImage(srcImageRange(res), destIter(dul, dest),
2762 std::bind1st(std::multiplies<fftw_real>(), 1.0 / norm));
2763 else
2764 copyImage(srcImageRange(res), destIter(dul, dest));
2765 }
2766
2767
2768 //@}
2769
2770 } // namespace vigra
2771
2772 #endif // VIGRA_FFTW3_HXX
vigra::FFTWComplex::FFTWComplex
FFTWComplex(fftwf_complex const &o)
Definition: fftw3.hxx:202
vigra::ImageArray::imageSize
Size2D imageSize() const
Definition: imagecontainer.hxx:411
vigra::BasicImage::begin
iterator begin()
Definition: basicimage.hxx:963
vigra::FFTWRealAccessor
Definition: fftw3.hxx:1217
vigra::fourierTransformInverse
void fourierTransformInverse(...)
Compute inverse Fourier transforms.
vigra::moveDCToCenter
void moveDCToCenter(...)
Rearrange the quadrants of a Fourier image so that the origin is in the image center.
vigra::moveDCToUpperLeft
void moveDCToUpperLeft(...)
Rearrange the quadrants of a Fourier image so that the origin is in the image&#39;s upper left...
vigra::operator*=
FFTWComplex< R > & operator*=(FFTWComplex< R > &a, double b)
multiply-assignment with scalar double
Definition: fftw3.hxx:908
vigra::operator/=
FFTWComplex< R > & operator/=(FFTWComplex< R > &a, double b)
divide-assignment with scalar double
Definition: fftw3.hxx:916
vigra::atan2
FixedPoint16< 2, OverflowHandling > atan2(FixedPoint16< IntBits, OverflowHandling > y, FixedPoint16< IntBits, OverflowHandling > x)
Arctangent. Accuracy better than 1/3 degree (9 significant bits).
Definition: fixedpoint.hxx:1654
vigra::FFTWRealImage
BasicImage< fftw_real > FFTWRealImage
Definition: fftw3.hxx:1132
vigra::ImageArray
Fundamental class template for arrays of equal-sized images.
Definition: imagecontainer.hxx:72
vigra::FFTWComplex::value_type
Real value_type
Definition: fftw3.hxx:140
vigra::FFTWPhaseAccessor::operator()
value_type operator()(ITERATOR const &i, DIFFERENCE d) const
Read phase at offset from iterator position.
Definition: fftw3.hxx:1417
vigra::IteratorTraits
Export associated information for each image iterator.
Definition: iteratortraits.hxx:109
vigra::conj
FFTWComplex< R > conj(const FFTWComplex< R > &a)
complex conjugate
Definition: fftw3.hxx:1030
vigra::imag
R imag(const FFTWComplex< R > &a)
imaginary part
Definition: fftw3.hxx:1023
vigra::FFTWComplex::FFTWComplex
FFTWComplex(value_type const &re=0.0, value_type const &im=0.0)
Definition: fftw3.hxx:169
vigra::FFTWComplex::SquaredNormType
value_type SquaredNormType
Definition: fftw3.hxx:164
vigra::BasicImage::accessor
Accessor accessor()
Definition: basicimage.hxx:1064
vigra::arg
R arg(const FFTWComplex< R > &a)
pahse
Definition: fftw3.hxx:1009
vigra::FFTWComplex::complex_type
FFTWReal2Complex< Real >::type complex_type
Definition: fftw3.hxx:136
vigra::applyFourierFilter
void applyFourierFilter(...)
Apply a filter (defined in the frequency domain) to an image.
vigra::FFTWSquaredMagnitudeAccessor
Definition: fftw3.hxx:1351
vigra::FFTWComplex::squaredMagnitude
SquaredNormType squaredMagnitude() const
Definition: fftw3.hxx:358
vigra::FFTWMagnitudeAccessor::value_type
Real value_type
The accessor&#39;s value type.
Definition: fftw3.hxx:1381
vigra::linalg::sin
linalg::TemporaryMatrix< T > sin(MultiArrayView< 2, T, C > const &v)
vigra::FFTWWriteRealAccessor::value_type
Real value_type
The accessor&#39;s value type.
Definition: fftw3.hxx:1324
vigra::FFTWWriteRealAccessor
Definition: fftw3.hxx:1319
vigra::FFTWComplex::phase
value_type phase() const
Definition: fftw3.hxx:368
vigra::linalg::exp
linalg::TemporaryMatrix< T > exp(MultiArrayView< 2, T, C > const &v)
vigra::applyFourierFilterFamily
void applyFourierFilterFamily(...)
Apply an array of filters (defined in the frequency domain) to an image.
vigra::FFTWComplex::operator=
FFTWComplex & operator=(fftw_complex const &o)
Definition: fftw3.hxx:255
vigra::FFTWComplex::operator=
FFTWComplex & operator=(TinyVector< T, 2 > const &o)
Definition: fftw3.hxx:310
vigra::FFTWComplex::const_iterator
value_type const * const_iterator
Definition: fftw3.hxx:156
vigra::transformImage
void transformImage(...)
Apply unary point transformation to each pixel.
vigra::BasicImage::width
int width() const
Definition: basicimage.hxx:838
vigra::FFTWSquaredMagnitudeAccessor::value_type
Real value_type
The accessor&#39;s value type.
Definition: fftw3.hxx:1355
std
Definition: array_vector.hxx:903
vigra::squaredNorm
FFTWComplex< R >::SquaredNormType squaredNorm(const FFTWComplex< R > &a)
squared norm (= squared magnitude)
Definition: fftw3.hxx:1044
vigra::FFTWComplex::operator=
FFTWComplex & operator=(fftwl_complex const &o)
Definition: fftw3.hxx:273
vigra::FFTWComplex::size
int size() const
Definition: fftw3.hxx:383
vigra::real
R real(const FFTWComplex< R > &a)
real part
Definition: fftw3.hxx:1016
vigra::operator+=
FFTWComplex< R > & operator+=(FFTWComplex< R > &a, double b)
add-assignment with scalar double
Definition: fftw3.hxx:894
vigra::Diff2D
Two dimensional difference vector.
Definition: diff2d.hxx:185
vigra::FFTWRealAccessor::value_type
Real value_type
The accessor&#39;s value type.
Definition: fftw3.hxx:1222
vigra::FFTWComplex::operator=
FFTWComplex & operator=(std::complex< T > const &o)
Definition: fftw3.hxx:320
vigra::FFTWImaginaryAccessor::value_type
Real value_type
The accessor&#39;s value type.
Definition: fftw3.hxx:1272
vigra::FFTWComplex::operator=
FFTWComplex & operator=(FFTWComplex const &o)
Definition: fftw3.hxx:236
vigra
Definition: accessor.hxx:43
vigra::FFTWSquaredMagnitudeAccessor::operator()
value_type operator()(ITERATOR const &i) const
Read squared magnitude at iterator position.
Definition: fftw3.hxx:1359
vigra::FFTWSquaredMagnitudeAccessor::operator()
value_type operator()(ITERATOR const &i, DIFFERENCE d) const
Read squared magnitude at offset from iterator position.
Definition: fftw3.hxx:1365
vigra::FFTWPhaseAccessor
Definition: fftw3.hxx:1403
vigra::BasicImage::height
int height() const
Definition: basicimage.hxx:845
vigra::VectorAccessor
Accessor for items that are STL compatible vectors.
Definition: accessor.hxx:771
vigra::norm
FFTWComplex< R >::NormType norm(const FFTWComplex< R > &a)
norm (= magnitude)
Definition: fftw3.hxx:1037
vigra::operator-=
FFTWComplex< R > & operator-=(FFTWComplex< R > &a, double b)
subtract-assignment with scalar double
Definition: fftw3.hxx:901
vigra::FFTWComplex::operator=
FFTWComplex & operator=(float o)
Definition: fftw3.hxx:291
vigra::BasicImageIterator
Definition: basicimage.hxx:262
vigra::operator!=
bool operator!=(double a, const FFTWComplex< R > &b)
not equal
Definition: fftw3.hxx:853
vigra::FFTWRealAccessor::operator()
value_type operator()(ITERATOR const &i, DIFFERENCE d) const
Read real part at offset from iterator position.
Definition: fftw3.hxx:1232
vigra::linalg::log10
linalg::TemporaryMatrix< T > log10(MultiArrayView< 2, T, C > const &v)
vigra::FFTWComplex::FFTWComplex
FFTWComplex(FFTWComplex const &o)
Definition: fftw3.hxx:177
vigra::FFTWComplex::operator[]
reference operator[](int i)
Definition: fftw3.hxx:373
vigra::FFTWImaginaryAccessor::operator()
value_type operator()(ITERATOR const &i) const
Read imaginary part at iterator position.
Definition: fftw3.hxx:1276
vigra::FFTWComplex::const_reference
value_type const & const_reference
Definition: fftw3.hxx:148
vigra::FFTWImaginaryAccessor::operator()
value_type operator()(ITERATOR const &i, DIFFERENCE d) const
Read imaginary part at offset from iterator position.
Definition: fftw3.hxx:1282
vigra::FFTWComplex::FFTWComplex
FFTWComplex(FFTWComplex< U > const &o)
Definition: fftw3.hxx:186
vigra::FFTWPhaseAccessor::operator()
value_type operator()(ITERATOR const &i) const
Read phase at iterator position.
Definition: fftw3.hxx:1411
vigra::FFTWComplex::operator=
FFTWComplex & operator=(long double o)
Definition: fftw3.hxx:300
vigra::BasicImage::resize
void resize(int width, int height)
Definition: basicimage.hxx:776
vigra::FFTWComplex::operator=
FFTWComplex & operator=(FFTWComplex< U > const &o)
Definition: fftw3.hxx:246
vigra::combineTwoImages
void combineTwoImages(...)
Combine two source images into destination image.
vigra::FFTWComplex::FFTWComplex
FFTWComplex(fftw_complex const &o)
Definition: fftw3.hxx:194
vigra::ImageArray::size
size_type size() const
Definition: imagecontainer.hxx:228
vigra::copyImage
void copyImage(...)
Copy source image into destination image.
vigra::FFTWComplex::FFTWComplex
FFTWComplex(fftwl_complex const &o)
Definition: fftw3.hxx:210
vigra::FFTWRealAccessor::operator()
value_type operator()(ITERATOR const &i) const
Read real part at iterator position.
Definition: fftw3.hxx:1226
vigra::operator*
FFTWComplex< R > operator*(double a, FFTWComplex< R > b)
left multiplication with scalar double
Definition: fftw3.hxx:979
vigra::TinyVector
Class for fixed size vectors.This class contains an array of size SIZE of the specified VALUETYPE...
Definition: accessor.hxx:940
vigra::FFTWMagnitudeAccessor::operator()
value_type operator()(ITERATOR const &i) const
Read magnitude at iterator position.
Definition: fftw3.hxx:1385
vigra::FFTWComplex::NormType
value_type NormType
Definition: fftw3.hxx:160
vigra::FFTWImaginaryAccessor
Definition: fftw3.hxx:1268
vigra::BasicImage::lowerRight
traverser lowerRight()
Definition: basicimage.hxx:934
vigra::FFTWMagnitudeAccessor
Definition: fftw3.hxx:1377
vigra::linalg::log
linalg::TemporaryMatrix< T > log(MultiArrayView< 2, T, C > const &v)
vigra::BasicImage
Fundamental class template for images.
Definition: basicimage.hxx:473
vigra::FFTWComplex::operator-
FFTWComplex operator-() const
Definition: fftw3.hxx:353
vigra::fourierTransformReal
void fourierTransformReal(...)
Real Fourier transforms for even and odd boundary conditions (aka. cosine and sine transforms)...
vigra::ConstBasicImageIterator
Definition: basicimage.hxx:294
vigra::operator-
FFTWComplex< R > operator-(double a, FFTWComplex< R > const &b)
left subtraction with scalar double
Definition: fftw3.hxx:959
vigra::abs
FFTWComplex< R >::NormType abs(const FFTWComplex< R > &a)
absolute value (= magnitude)
Definition: fftw3.hxx:1002
vigra::ImageArray::resize
void resize(size_type newSize)
Definition: imagecontainer.hxx:310
vigra::linalg::tan
linalg::TemporaryMatrix< T > tan(MultiArrayView< 2, T, C > const &v)
vigra::FFTWComplex::iterator
value_type * iterator
Definition: fftw3.hxx:152
vigra::FFTWComplex::operator[]
const_reference operator[](int i) const
Definition: fftw3.hxx:378
vigra::FFTWComplex::magnitude
NormType magnitude() const
Definition: fftw3.hxx:363
vigra::linearIntensityTransform
LinearIntensityTransform< DestValueType, Multiplier > linearIntensityTransform(Multiplier scale, DestValueType offset)
Apply a linear transform to the source pixel values.
Definition: transformimage.hxx:800
vigra::StandardAccessor
Encapsulate access to the values an iterator points to.
Definition: accessor.hxx:133
vigra::linalg::cos
linalg::TemporaryMatrix< T > cos(MultiArrayView< 2, T, C > const &v)
vigra::sign
T sign(T t)
The sign function.
Definition: mathutil.hxx:553
vigra::ImageArray::resizeImages
virtual void resizeImages(const Diff2D &newSize)
Definition: imagecontainer.hxx:418
vigra::FFTWPhaseAccessor::value_type
Real value_type
The accessor&#39;s value type.
Definition: fftw3.hxx:1407
vigra::FFTWMagnitudeAccessor::operator()
value_type operator()(ITERATOR const &i, DIFFERENCE d) const
Read magnitude at offset from iterator position.
Definition: fftw3.hxx:1391
vigra::FFTWComplex
Wrapper class for the FFTW complex types &#39;fftw_complex&#39;.
Definition: fftw3.hxx:131
vigra::sqrt
SquareRootTraits< FixedPoint< IntBits, FracBits > >::SquareRootResult sqrt(FixedPoint< IntBits, FracBits > v)
square root.
Definition: fixedpoint.hxx:616
vigra::FFTWComplex::reference
value_type & reference
Definition: fftw3.hxx:144
vigra::operator/
FFTWComplex< R > operator/(FFTWComplex< R > a, double b)
right division with scalar double
Definition: fftw3.hxx:993
vigra::FFTWComplex::FFTWComplex
FFTWComplex(std::complex< T > const &o)
Definition: fftw3.hxx:219
vigra::FFTWComplexImage
BasicImage< FFTWComplex<> > FFTWComplexImage
Definition: fftw3.hxx:1192
vigra::FFTWComplex::FFTWComplex
FFTWComplex(TinyVector< T, 2 > const &o)
Definition: fftw3.hxx:228
vigra::FFTWComplex::operator=
FFTWComplex & operator=(double o)
Definition: fftw3.hxx:282
vigra::BasicImage::upperLeft
traverser upperLeft()
Definition: basicimage.hxx:923
vigra::operator+
FFTWComplex< R > operator+(double a, FFTWComplex< R > b)
left addition with scalar double
Definition: fftw3.hxx:938
vigra::FFTWComplex::operator=
FFTWComplex & operator=(fftwf_complex const &o)
Definition: fftw3.hxx:264
vigra::fourierTransform
void fourierTransform(...)
Compute forward and inverse Fourier transforms.

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.10.0