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affine_registration.hxx
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3/* Copyright 2005-2006 by Ullrich Koethe */
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35
36#ifndef VIGRA_AFFINE_REGISTRATION_HXX
37#define VIGRA_AFFINE_REGISTRATION_HXX
38
39#include "mathutil.hxx"
40#include "matrix.hxx"
41#include "linear_solve.hxx"
42#include "tinyvector.hxx"
43#include "splineimageview.hxx"
44#include "imagecontainer.hxx"
45#include "multi_shape.hxx"
46#include "affinegeometry.hxx"
47
48#include <cmath>
49
50 namespace vigra {
51
52/** \addtogroup Registration Image Registration
53
54 Transform different image into a common coordinate system.
55*/
56//@{
57
58/********************************************************/
59/* */
60/* affineMatrix2DFromCorrespondingPoints */
61/* */
62/********************************************************/
63
64/** \brief Create homogeneous matrix that maps corresponding points onto each other.
65
66 For use with \ref affineWarpImage(). When only two corresponding points are given,
67 the matrix will only represent a similarity transform
68 (translation, rotation, and uniform scaling). When only one point pair is given,
69 the result will be a pure translation.
70*/
71 template <class SrcIterator, class DestIterator>
72linalg::TemporaryMatrix<double>
73 affineMatrix2DFromCorrespondingPoints(SrcIterator s, SrcIterator send, DestIterator d)
74{
75 int size = send - s;
76
77 linalg::TemporaryMatrix<double> ret(identityMatrix<double>(3));
78
79 if(size == 1)
80 {
81 ret(0,2) = (*d)[0] - (*s)[0];
82 ret(1,2) = (*d)[1] - (*s)[1];
83 }
84 else if(size == 2)
85 {
86 Matrix<double> m(4,4), r(4,1), so(4,1);
87
88 for(int k=0; k<size; ++k, ++s, ++d)
89 {
90 m(2*k,0) = (*s)[0];
91 m(2*k,1) = -(*s)[1];
92 m(2*k,2) = 1.0;
93 m(2*k,3) = 0.0;
94 r(2*k,0) = (*d)[0];
95
96 m(2*k+1,0) = (*s)[1];
97 m(2*k+1,1) = (*s)[0];
98 m(2*k+1,2) = 0.0;
99 m(2*k+1,3) = 1.0;
100 r(2*k+1,0) = (*d)[1];
101 }
102
103 if(!linearSolve(m, r, so))
104 vigra_fail("affineMatrix2DFromCorrespondingPoints(): singular solution matrix.");
105
106 ret(0,0) = so(0,0);
107 ret(1,1) = so(0,0);
108 ret(0,1) = -so(1,0);
109 ret(1,0) = so(1,0);
110 ret(0,2) = so(2,0);
111 ret(1,2) = so(3,0);
112 }
113 else if(size >= 3)
114 {
115 Matrix<double> m(3,3), rx(3,1), sx(3,1), ry(3,1), sy(3,1), c(3,1);
116 c(2,0) = 1.0;
117 for(int k=0; k<size; ++k, ++s, ++d)
118 {
119 c(0,0) = (*s)[0];
120 c(1,0) = (*s)[1];
121
122 m += outer(c);
123 rx += (*d)[0]*c;
124 ry += (*d)[1]*c;
125 }
126
127 if(!linearSolve(m, rx, sx) || !linearSolve(m, ry, sy))
128 vigra_fail("affineMatrix2DFromCorrespondingPoints(): singular solution matrix.");
129
130 ret(0,0) = sx(0,0);
131 ret(0,1) = sx(1,0);
132 ret(0,2) = sx(2,0);
133 ret(1,0) = sy(0,0);
134 ret(1,1) = sy(1,0);
135 ret(1,2) = sy(2,0);
136 }
137
138 return ret;
139}
140
141 /** \brief Option object for affine registration functions.
142
143 The template parameter <tt>SPLINEORDER</tt> (default: 2) specifies
144 the order of interpolation for the intensities at non-integer image
145 coordinates.
146 */
147 template <int SPLINEORDER = 2>
148 class AffineMotionEstimationOptions
149{
150 public:
151 double burt_filter_strength;
152 int highest_level, iterations_per_level;
153 bool use_laplacian_pyramid;
154
155 AffineMotionEstimationOptions()
156 : burt_filter_strength(0.4),
157 highest_level(4),
158 iterations_per_level(4),
159 use_laplacian_pyramid(false)
160 {}
161
162 template <int ORDER>
163 AffineMotionEstimationOptions(AffineMotionEstimationOptions<ORDER> const & other)
164 : burt_filter_strength(other.burt_filter_strength),
165 highest_level(other.highest_level),
166 iterations_per_level(other.iterations_per_level),
167 use_laplacian_pyramid(other.use_laplacian_pyramid)
168 {}
169
170 /** \brief Change the spline order for intensity interpolation.
171
172 Usage:
173 \code
174 // use linear interpolation
175 AffineMotionEstimationOptions<>().splineOrder<1>();
176 \endcode
177
178 Default: order = 2 (quadratic interpolation)
179 */
180 template <int NEWORDER>
181 AffineMotionEstimationOptions<NEWORDER> splineOrder() const
182 {
183 return AffineMotionEstimationOptions<NEWORDER>(*this);
184 }
185
186 /** \brief Define amount of smoothing before subsampling to the next pyramid level.
187
188 Pyramids are created with the Burt filter:
189 \code
190 [0.25 - center / 2.0, 0.25, center, 0.25, 0.25 - center / 2.0]
191 \endcode
192 \a center must thus be between 0.25 and 0.5, and the smaller it is,
193 the more smoothing is applied.
194
195 Default: 0.4 (moderate smoothing)
196 */
197 AffineMotionEstimationOptions & burtFilterCenterStrength(double center)
198 {
199 vigra_precondition(0.25 <= center && center <= 0.5,
200 "AffineMotionEstimationOptions::burtFilterCenterStrength(): center must be between 0.25 and 0.5 (inclusive).");
201 burt_filter_strength = center;
202 return *this;
203 }
204
205 /** \brief Define the highest level of the image pyramid.
206
207 The original image is at level 0, and each level downsamples
208 the image by 1/2.
209
210 Default: 4 (16-fold downsampling)
211 */
212 AffineMotionEstimationOptions & highestPyramidLevel(unsigned int level)
213 {
214 highest_level = (int)level;
215 return *this;
216 }
217
218 /** \brief Number of Gauss-Newton iterations per level.
219
220 Default: 4
221 */
222 AffineMotionEstimationOptions & iterationsPerLevel(unsigned int iter)
223 {
224 vigra_precondition(0 < iter,
225 "AffineMotionEstimationOptions::iterationsPerLevel(): must do at least one iteration per level.");
226 iterations_per_level = (int)iter;
227 return *this;
228 }
229
230 /** \brief Base registration on a Gaussian pyramid.
231
232 Images are registered such that the similarity in intensity is
233 maximized.
234
235 Default: true
236 */
237 AffineMotionEstimationOptions & useGaussianPyramid(bool f = true)
238 {
239 use_laplacian_pyramid = !f;
240 return *this;
241 }
242
243 /** \brief Base registration on a Laplacian pyramid.
244
245 Images are registered such that the similarity in second
246 derivatives (=Laplacian operator results) is maximized.
247
248 Default: false
249 */
250 AffineMotionEstimationOptions & useLaplacianPyramid(bool f = true)
251 {
252 use_laplacian_pyramid = f;
253 return *this;
254 }
255};
256
257 namespace detail {
258
259 struct TranslationEstimationFunctor
260{
261 template <class SplineImage, class Image>
262 void operator()(SplineImage const & src, Image const & dest, Matrix<double> & matrix) const
263 {
264 int w = dest.width();
265 int h = dest.height();
266
267 Matrix<double> grad(2,1), m(2,2), r(2,1), s(2,1);
268 double dx = matrix(0,0), dy = matrix(1,0);
269
270 for(int y = 0; y < h; ++y)
271 {
272 double sx = matrix(0,1)*y + matrix(0,2);
273 double sy = matrix(1,1)*y + matrix(1,2);
274 for(int x = 0; x < w; ++x, sx += dx, sy += dy)
275 {
276 if(!src.isInside(sx, sy))
277 continue;
278
279 grad(0,0) = src.dx(sx, sy);
280 grad(1,0) = src.dy(sx, sy);
281 double diff = dest(x, y) - src(sx, sy);
282
283 m += outer(grad);
284 r -= diff*grad;
285 }
286 }
287
288 linearSolve(m, r, s);
289
290 matrix(0,2) -= s(0,0);
291 matrix(1,2) -= s(1,0);
292 }
293};
294
295 struct SimilarityTransformEstimationFunctor
296{
297 template <class SplineImage, class Image>
298 void operator()(SplineImage const & src, Image const & dest, Matrix<double> & matrix) const
299 {
300 int w = dest.width();
301 int h = dest.height();
302
303 Matrix<double> grad(2,1), coord(4, 2), c(4, 1), m(4, 4), r(4,1), s(4,1);
304 coord(0,0) = 1.0;
305 coord(1,1) = 1.0;
306 double dx = matrix(0,0), dy = matrix(1,0);
307
308 for(int y = 0; y < h; ++y)
309 {
310 double sx = matrix(0,1)*y + matrix(0,2);
311 double sy = matrix(1,1)*y + matrix(1,2);
312 for(int x = 0; x < w; ++x, sx += dx, sy += dy)
313 {
314 if(!src.isInside(sx, sy))
315 continue;
316
317 grad(0,0) = src.dx(sx, sy);
318 grad(1,0) = src.dy(sx, sy);
319 coord(2,0) = (double)x;
320 coord(3,1) = (double)x;
321 coord(3,0) = -(double)y;
322 coord(2,1) = (double)y;
323 double diff = dest(x, y) - src(sx, sy);
324
325 c = coord * grad;
326 m += outer(c);
327 r -= diff*c;
328 }
329 }
330
331 linearSolve(m, r, s);
332
333 matrix(0,2) -= s(0,0);
334 matrix(1,2) -= s(1,0);
335 matrix(0,0) -= s(2,0);
336 matrix(1,1) -= s(2,0);
337 matrix(0,1) += s(3,0);
338 matrix(1,0) -= s(3,0);
339 }
340};
341
342 struct AffineTransformEstimationFunctor
343{
344 template <class SplineImage, class Image>
345 void operator()(SplineImage const & src, Image const & dest, Matrix<double> & matrix) const
346 {
347 int w = dest.width();
348 int h = dest.height();
349
350 Matrix<double> grad(2,1), coord(6, 2), c(6, 1), m(6,6), r(6,1), s(6,1);
351 coord(0,0) = 1.0;
352 coord(1,1) = 1.0;
353 double dx = matrix(0,0), dy = matrix(1,0);
354
355 for(int y = 0; y < h; ++y)
356 {
357 double sx = matrix(0,1)*y + matrix(0,2);
358 double sy = matrix(1,1)*y + matrix(1,2);
359 for(int x = 0; x < w; ++x, sx += dx, sy += dy)
360 {
361 if(!src.isInside(sx, sy))
362 continue;
363
364 grad(0,0) = src.dx(sx, sy);
365 grad(1,0) = src.dy(sx, sy);
366 coord(2,0) = (double)x;
367 coord(4,1) = (double)x;
368 coord(3,0) = (double)y;
369 coord(5,1) = (double)y;
370 double diff = dest(x, y) - src(sx, sy);
371
372 c = coord * grad;
373 m += outer(c);
374 r -= diff*c;
375 }
376 }
377
378 linearSolve(m, r, s);
379
380 matrix(0,2) -= s(0,0);
381 matrix(1,2) -= s(1,0);
382 matrix(0,0) -= s(2,0);
383 matrix(0,1) -= s(3,0);
384 matrix(1,0) -= s(4,0);
385 matrix(1,1) -= s(5,0);
386 }
387};
388
389 template <class SrcIterator, class SrcAccessor,
390 class DestIterator, class DestAccessor,
391 int SPLINEORDER, class Functor>
392 void
393estimateAffineMotionImpl(SrcIterator sul, SrcIterator slr, SrcAccessor src,
394 DestIterator dul, DestIterator dlr, DestAccessor dest,
395 Matrix<double> & affineMatrix,
396 AffineMotionEstimationOptions<SPLINEORDER> const & options,
397 Functor motionModel)
398{
399 typedef typename NumericTraits<typename SrcAccessor::value_type>::RealPromote STmpType;
400 typedef BasicImage<STmpType> STmpImage;
401 typedef typename NumericTraits<typename DestAccessor::value_type>::RealPromote DTmpType;
402 typedef BasicImage<DTmpType> DTmpImage;
403
404 int toplevel = options.highest_level;
405 ImagePyramid<STmpImage> srcPyramid(0, toplevel, sul, slr, src);
406 ImagePyramid<DTmpImage> destPyramid(0, toplevel, dul, dlr, dest);
407
408 if(options.use_laplacian_pyramid)
409 {
410 pyramidReduceBurtLaplacian(srcPyramid, 0, toplevel, options.burt_filter_strength);
411 pyramidReduceBurtLaplacian(destPyramid, 0, toplevel, options.burt_filter_strength);
412 }
413 else
414 {
415 pyramidReduceBurtFilter(srcPyramid, 0, toplevel, options.burt_filter_strength);
416 pyramidReduceBurtFilter(destPyramid, 0, toplevel, options.burt_filter_strength);
417 }
418
419 Matrix<double> currentMatrix(affineMatrix(2,2) == 0.0
420 ? identityMatrix<double>(3)
421 : affineMatrix);
422 currentMatrix(0,2) /= std::pow(2.0, toplevel);
423 currentMatrix(1,2) /= std::pow(2.0, toplevel);
424
425 for(int level = toplevel; level >= 0; --level)
426 {
427 SplineImageView<SPLINEORDER, STmpType> sp(srcImageRange(srcPyramid[level]));
428
429 for(int iter = 0; iter < options.iterations_per_level; ++iter)
430 {
431 motionModel(sp, destPyramid[level], currentMatrix);
432 }
433
434 if(level > 0)
435 {
436 currentMatrix(0,2) *= 2.0;
437 currentMatrix(1,2) *= 2.0;
438 }
439 }
440
441 affineMatrix = currentMatrix;
442}
443
444} // namespace detail
445
446/********************************************************/
447/* */
448/* estimateTranslation */
449/* */
450/********************************************************/
451
452/** \brief Estimate the optical flow between two images according to a translation model.
453
454 This function applies the same algorithm as \ref estimateAffineTransform()
455 with the additional constraint that the motion model must be a translation
456 rather than affine.
457
458 <b> Declarations:</b>
459
460 <b>\#include</b> <vigra/affine_registration.hxx><br>
461 Namespace: vigra
462
463 pass 2D array views:
464 \code
465 namespace vigra {
466 template <class T1, class S1,
467 class T2, class S2,
468 int SPLINEORDER>
469 void
470 estimateTranslation(MultiArrayView<2, T1, S1> const & src,
471 MultiArrayView<2, T2, S2> dest,
472 Matrix<double> & affineMatrix,
473 AffineMotionEstimationOptions<SPLINEORDER> const & options = AffineMotionEstimationOptions<SPLINEORDER>());
474 }
475 \endcode
476
477 \deprecatedAPI{estimateTranslation}
478 pass \ref ImageIterators and \ref DataAccessors :
479 \code
480 namespace vigra {
481 template <class SrcIterator, class SrcAccessor,
482 class DestIterator, class DestAccessor,
483 int SPLINEORDER = 2>
484 void
485 estimateTranslation(SrcIterator sul, SrcIterator slr, SrcAccessor src,
486 DestIterator dul, DestIterator dlr, DestAccessor dest,
487 Matrix<double> & affineMatrix,
488 AffineMotionEstimationOptions<SPLINEORDER> const & options =
489 AffineMotionEstimationOptions<>())
490 }
491 \endcode
492 use argument objects in conjunction with \ref ArgumentObjectFactories :
493 \code
494 namespace vigra {
495 template <class SrcIterator, class SrcAccessor,
496 class DestIterator, class DestAccessor,
497 int SPLINEORDER = 2>
498 void
499 estimateTranslation(triple<SrcIterator, SrcIterator, SrcAccessor> src,
500 triple<DestIterator, DestIterator, DestAccessor> dest,
501 Matrix<double> & affineMatrix,
502 AffineMotionEstimationOptions<SPLINEORDER> const & options =
503 AffineMotionEstimationOptions<>())
504 }
505 \endcode
506 \deprecatedEnd
507*/
508doxygen_overloaded_function(template <...> void estimateTranslation)
509
510 template <class SrcIterator, class SrcAccessor,
511 class DestIterator, class DestAccessor,
512 int SPLINEORDER>
513 inline void
514 estimateTranslation(SrcIterator sul, SrcIterator slr, SrcAccessor src,
515 DestIterator dul, DestIterator dlr, DestAccessor dest,
516 Matrix<double> & affineMatrix,
517 AffineMotionEstimationOptions<SPLINEORDER> const & options)
518{
519 detail::estimateAffineMotionImpl(sul, slr, src, dul, dlr, dest, affineMatrix,
520 options, detail::TranslationEstimationFunctor());
521}
522
523 template <class SrcIterator, class SrcAccessor,
524 class DestIterator, class DestAccessor>
525 inline void
526 estimateTranslation(SrcIterator sul, SrcIterator slr, SrcAccessor src,
527 DestIterator dul, DestIterator dlr, DestAccessor dest,
528 Matrix<double> & affineMatrix)
529{
530 estimateTranslation(sul, slr, src, dul, dlr, dest,
531 affineMatrix, AffineMotionEstimationOptions<>());
532}
533
534 template <class SrcIterator, class SrcAccessor,
535 class DestIterator, class DestAccessor,
536 int SPLINEORDER>
537 inline void
538 estimateTranslation(triple<SrcIterator, SrcIterator, SrcAccessor> src,
539 triple<DestIterator, DestIterator, DestAccessor> dest,
540 Matrix<double> & affineMatrix,
541 AffineMotionEstimationOptions<SPLINEORDER> const & options)
542{
543 estimateTranslation(src.first, src.second, src.third, dest.first, dest.second, dest.third,
544 affineMatrix, options);
545}
546
547 template <class SrcIterator, class SrcAccessor,
548 class DestIterator, class DestAccessor>
549 inline void
550 estimateTranslation(triple<SrcIterator, SrcIterator, SrcAccessor> src,
551 triple<DestIterator, DestIterator, DestAccessor> dest,
552 Matrix<double> & affineMatrix)
553{
554 estimateTranslation(src.first, src.second, src.third, dest.first, dest.second, dest.third,
555 affineMatrix, AffineMotionEstimationOptions<>());
556}
557
558 template <class T1, class S1,
559 class T2, class S2,
560 int SPLINEORDER>
561 inline void
562 estimateTranslation(MultiArrayView<2, T1, S1> const & src,
563 MultiArrayView<2, T2, S2> dest,
564 Matrix<double> & affineMatrix,
565 AffineMotionEstimationOptions<SPLINEORDER> const & options)
566{
567 estimateTranslation(srcImageRange(src), destImageRange(dest),
568 affineMatrix, options);
569}
570
571 template <class T1, class S1,
572 class T2, class S2>
573 inline void
574 estimateTranslation(MultiArrayView<2, T1, S1> const & src,
575 MultiArrayView<2, T2, S2> dest,
576 Matrix<double> & affineMatrix)
577{
578 estimateTranslation(srcImageRange(src), destImageRange(dest),
579 affineMatrix, AffineMotionEstimationOptions<>());
580}
581
582/********************************************************/
583/* */
584/* estimateSimilarityTransform */
585/* */
586/********************************************************/
587
588/** \brief Estimate the optical flow between two images according to a similarity transform model
589 (e.g. translation, rotation, and uniform scaling).
590
591 This function applies the same algorithm as \ref estimateAffineTransform()
592 with the additional constraint that the motion model must be a similarity
593 transform rather than affine.
594
595 <b> Declarations:</b>
596
597 <b>\#include</b> <vigra/affine_registration.hxx><br>
598 Namespace: vigra
599
600 pass 2D array views:
601 \code
602 namespace vigra {
603 template <class T1, class S1,
604 class T2, class S2,
605 int SPLINEORDER>
606 void
607 estimateSimilarityTransform(MultiArrayView<2, T1, S1> const & src,
608 MultiArrayView<2, T2, S2> dest,
609 Matrix<double> & affineMatrix,
610 AffineMotionEstimationOptions<SPLINEORDER> const & options =
611 AffineMotionEstimationOptions<SPLINEORDER>());
612 }
613 \endcode
614
615 \deprecatedAPI{estimateSimilarityTransform}
616 pass \ref ImageIterators and \ref DataAccessors :
617 \code
618 namespace vigra {
619 template <class SrcIterator, class SrcAccessor,
620 class DestIterator, class DestAccessor,
621 int SPLINEORDER = 2>
622 void
623 estimateSimilarityTransform(SrcIterator sul, SrcIterator slr, SrcAccessor src,
624 DestIterator dul, DestIterator dlr, DestAccessor dest,
625 Matrix<double> & affineMatrix,
626 AffineMotionEstimationOptions<SPLINEORDER> const & options =
627 AffineMotionEstimationOptions<>())
628 }
629 \endcode
630 use argument objects in conjunction with \ref ArgumentObjectFactories :
631 \code
632 namespace vigra {
633 template <class SrcIterator, class SrcAccessor,
634 class DestIterator, class DestAccessor,
635 int SPLINEORDER = 2>
636 void
637 estimateSimilarityTransform(triple<SrcIterator, SrcIterator, SrcAccessor> src,
638 triple<DestIterator, DestIterator, DestAccessor> dest,
639 Matrix<double> & affineMatrix,
640 AffineMotionEstimationOptions<SPLINEORDER> const & options =
641 AffineMotionEstimationOptions<>())
642 }
643 \endcode
644 \deprecatedEnd
645*/
646doxygen_overloaded_function(template <...> void estimateSimilarityTransform)
647
648 template <class SrcIterator, class SrcAccessor,
649 class DestIterator, class DestAccessor,
650 int SPLINEORDER>
651 inline void
652 estimateSimilarityTransform(SrcIterator sul, SrcIterator slr, SrcAccessor src,
653 DestIterator dul, DestIterator dlr, DestAccessor dest,
654 Matrix<double> & affineMatrix,
655 AffineMotionEstimationOptions<SPLINEORDER> const & options)
656{
657 detail::estimateAffineMotionImpl(sul, slr, src, dul, dlr, dest, affineMatrix,
658 options, detail::SimilarityTransformEstimationFunctor());
659}
660
661 template <class SrcIterator, class SrcAccessor,
662 class DestIterator, class DestAccessor>
663 inline void
664 estimateSimilarityTransform(SrcIterator sul, SrcIterator slr, SrcAccessor src,
665 DestIterator dul, DestIterator dlr, DestAccessor dest,
666 Matrix<double> & affineMatrix)
667{
668 estimateSimilarityTransform(sul, slr, src, dul, dlr, dest,
669 affineMatrix, AffineMotionEstimationOptions<>());
670}
671
672 template <class SrcIterator, class SrcAccessor,
673 class DestIterator, class DestAccessor,
674 int SPLINEORDER>
675 inline void
676 estimateSimilarityTransform(triple<SrcIterator, SrcIterator, SrcAccessor> src,
677 triple<DestIterator, DestIterator, DestAccessor> dest,
678 Matrix<double> & affineMatrix,
679 AffineMotionEstimationOptions<SPLINEORDER> const & options)
680{
681 estimateSimilarityTransform(src.first, src.second, src.third, dest.first, dest.second, dest.third,
682 affineMatrix, options);
683}
684
685 template <class SrcIterator, class SrcAccessor,
686 class DestIterator, class DestAccessor>
687 inline void
688 estimateSimilarityTransform(triple<SrcIterator, SrcIterator, SrcAccessor> src,
689 triple<DestIterator, DestIterator, DestAccessor> dest,
690 Matrix<double> & affineMatrix)
691{
692 estimateSimilarityTransform(src.first, src.second, src.third, dest.first, dest.second, dest.third,
693 affineMatrix, AffineMotionEstimationOptions<>());
694}
695
696 template <class T1, class S1,
697 class T2, class S2,
698 int SPLINEORDER>
699 inline void
700 estimateSimilarityTransform(MultiArrayView<2, T1, S1> const & src,
701 MultiArrayView<2, T2, S2> dest,
702 Matrix<double> & affineMatrix,
703 AffineMotionEstimationOptions<SPLINEORDER> const & options)
704{
705 estimateSimilarityTransform(srcImageRange(src), destImageRange(dest),
706 affineMatrix, options);
707}
708
709 template <class T1, class S1,
710 class T2, class S2>
711 inline void
712 estimateSimilarityTransform(MultiArrayView<2, T1, S1> const & src,
713 MultiArrayView<2, T2, S2> dest,
714 Matrix<double> & affineMatrix)
715{
716 estimateSimilarityTransform(srcImageRange(src), destImageRange(dest),
717 affineMatrix, AffineMotionEstimationOptions<>());
718}
719
720/********************************************************/
721/* */
722/* estimateAffineTransform */
723/* */
724/********************************************************/
725
726/** \brief Estimate the optical flow between two images according to an affine transform model
727 (e.g. translation, rotation, non-uniform scaling, and shearing).
728
729 This function implements the algorithm described in
730
731 J.R. Bergen, P. Anandan, K.J. Hanna, R. Hingorani: <i>"Hierarchical model-based motion estimation"</i>, ECCV 1992
732
733 Specifically, it minimizes the squared loss between the images I at two consecutive time
734 points t-1 and t:
735 \f[ \min_{\theta} \sum_{\mathbf{x}} \left(I(\mathbf{x}, t) - I(\mathbf{x} - \mathbf{u}_{\theta}(\mathbf{x}), t-1)\right)^2
736 \f]
737 where \f$\mathbf{x}\f$ are the pixel coordinates and \f$\mathbf{u}_{\theta}(\mathbf{x})\f$
738 is an affine motion model parameterized by \f$\theta\f$. Since the objective is
739 non-linear, it is linearized by first-order Taylor expansion w.r.t. \f$\theta\f$,
740 and a local optimum is determined iteratively by the Gauss-Newton method. To handle
741 larger displacements, the algorithm employs a coarse-to-fine strategy, where the
742 motion is first estimated on downsampled versions of the images and then refined at
743 consecutively higher resolutions.
744
745 The algorithm's parameters can be controlled by the option object
746 \ref vigra::AffineMotionEstimationOptions. In particular, one can determine if
747 <ul>
748 <li> I in the objective refers to the original images (default) or their second
749 derivatives (<tt>options.useLaplacianPyramid()</tt> -- makes motion
750 estimation invariant against additive intensity offsets);</li>
751 <li> the highest pyramid level to be used
752 (<tt>options.highestPyramidLevel(h)</tt> -- images are downsampled to 2<sup>-h</sup> times their original size, default: h=4);</li>
753 <li> the number of Gauss-Newton iterations per resolution level
754 (<tt>options.iterationsPerLevel(i)</tt>, default: i=4);</li>
755 <li> the interpolation order to compute subpixel intensities \f$I(\mathbf{x} - \mathbf{u}_{\theta}(\mathbf{x}), t-1)\f$ (default: 2)
756 </ul>
757
758 The resulting affine model is stored in parameter <tt>affineMatrix</tt>, which
759 can be used by \ref affineWarpImage() to apply the transformation to time frame t-1.
760 See documentation there for the precise meaning of the matrix elements.
761
762 <b> Declarations:</b>
763
764 <b>\#include</b> <vigra/affine_registration.hxx><br>
765 Namespace: vigra
766
767 pass 2D array views:
768 \code
769 namespace vigra {
770 template <class T1, class S1,
771 class T2, class S2,
772 int SPLINEORDER>
773 void
774 estimateAffineTransform(MultiArrayView<2, T1, S1> const & src,
775 MultiArrayView<2, T2, S2> dest,
776 Matrix<double> & affineMatrix,
777 AffineMotionEstimationOptions<SPLINEORDER> const & options =
778 AffineMotionEstimationOptions<SPLINEORDER>());
779 }
780 \endcode
781
782 \deprecatedAPI{estimateAffineTransform}
783 pass \ref ImageIterators and \ref DataAccessors :
784 \code
785 namespace vigra {
786 template <class SrcIterator, class SrcAccessor,
787 class DestIterator, class DestAccessor,
788 int SPLINEORDER = 2>
789 void
790 estimateAffineTransform(SrcIterator sul, SrcIterator slr, SrcAccessor src,
791 DestIterator dul, DestIterator dlr, DestAccessor dest,
792 Matrix<double> & affineMatrix,
793 AffineMotionEstimationOptions<SPLINEORDER> const & options =
794 AffineMotionEstimationOptions<>())
795 }
796 \endcode
797 use argument objects in conjunction with \ref ArgumentObjectFactories :
798 \code
799 namespace vigra {
800 template <class SrcIterator, class SrcAccessor,
801 class DestIterator, class DestAccessor,
802 int SPLINEORDER = 2>
803 void
804 estimateAffineTransform(triple<SrcIterator, SrcIterator, SrcAccessor> src,
805 triple<DestIterator, DestIterator, DestAccessor> dest,
806 Matrix<double> & affineMatrix,
807 AffineMotionEstimationOptions<SPLINEORDER> const & options =
808 AffineMotionEstimationOptions<>())
809 }
810 \endcode
811 \deprecatedEnd
812*/
813doxygen_overloaded_function(template <...> void estimateAffineTransform)
814
815 template <class SrcIterator, class SrcAccessor,
816 class DestIterator, class DestAccessor,
817 int SPLINEORDER>
818 inline void
819 estimateAffineTransform(SrcIterator sul, SrcIterator slr, SrcAccessor src,
820 DestIterator dul, DestIterator dlr, DestAccessor dest,
821 Matrix<double> & affineMatrix,
822 AffineMotionEstimationOptions<SPLINEORDER> const & options)
823{
824 detail::estimateAffineMotionImpl(sul, slr, src, dul, dlr, dest, affineMatrix,
825 options, detail::AffineTransformEstimationFunctor());
826}
827
828 template <class SrcIterator, class SrcAccessor,
829 class DestIterator, class DestAccessor>
830 inline void
831 estimateAffineTransform(SrcIterator sul, SrcIterator slr, SrcAccessor src,
832 DestIterator dul, DestIterator dlr, DestAccessor dest,
833 Matrix<double> & affineMatrix)
834{
835 estimateAffineTransform(sul, slr, src, dul, dlr, dest,
836 affineMatrix, AffineMotionEstimationOptions<>());
837}
838
839 template <class SrcIterator, class SrcAccessor,
840 class DestIterator, class DestAccessor,
841 int SPLINEORDER>
842 inline void
843 estimateAffineTransform(triple<SrcIterator, SrcIterator, SrcAccessor> src,
844 triple<DestIterator, DestIterator, DestAccessor> dest,
845 Matrix<double> & affineMatrix,
846 AffineMotionEstimationOptions<SPLINEORDER> const & options)
847{
848 estimateAffineTransform(src.first, src.second, src.third, dest.first, dest.second, dest.third,
849 affineMatrix, options);
850}
851
852 template <class SrcIterator, class SrcAccessor,
853 class DestIterator, class DestAccessor>
854 inline void
855 estimateAffineTransform(triple<SrcIterator, SrcIterator, SrcAccessor> src,
856 triple<DestIterator, DestIterator, DestAccessor> dest,
857 Matrix<double> & affineMatrix)
858{
859 estimateAffineTransform(src.first, src.second, src.third, dest.first, dest.second, dest.third,
860 affineMatrix, AffineMotionEstimationOptions<>());
861}
862
863 template <class T1, class S1,
864 class T2, class S2,
865 int SPLINEORDER>
866 inline void
867 estimateAffineTransform(MultiArrayView<2, T1, S1> const & src,
868 MultiArrayView<2, T2, S2> dest,
869 Matrix<double> & affineMatrix,
870 AffineMotionEstimationOptions<SPLINEORDER> const & options)
871{
872 vigra_precondition(src.shape() == dest.shape(),
873 "estimateAffineTransform(): shape mismatch between input and output.");
874 estimateAffineTransform(srcImageRange(src), destImageRange(dest),
875 affineMatrix, options);
876}
877
878 template <class T1, class S1,
879 class T2, class S2>
880 inline void
881 estimateAffineTransform(MultiArrayView<2, T1, S1> const & src,
882 MultiArrayView<2, T2, S2> dest,
883 Matrix<double> & affineMatrix)
884{
885 vigra_precondition(src.shape() == dest.shape(),
886 "estimateAffineTransform(): shape mismatch between input and output.");
887 estimateAffineTransform(srcImageRange(src), destImageRange(dest),
888 affineMatrix, AffineMotionEstimationOptions<>());
889}
890
891//@}
892
893} // namespace vigra
894
895
896#endif /* VIGRA_AFFINE_REGISTRATION_HXX */
vigra::AffineMotionEstimationOptions
Option object for affine registration functions.
Definition affine_registration.hxx:149
vigra::AffineMotionEstimationOptions::useLaplacianPyramid
AffineMotionEstimationOptions & useLaplacianPyramid(bool f=true)
Base registration on a Laplacian pyramid.
Definition affine_registration.hxx:250
vigra::AffineMotionEstimationOptions::splineOrder
AffineMotionEstimationOptions< NEWORDER > splineOrder() const
Change the spline order for intensity interpolation.
Definition affine_registration.hxx:181
vigra::AffineMotionEstimationOptions::useGaussianPyramid
AffineMotionEstimationOptions & useGaussianPyramid(bool f=true)
Base registration on a Gaussian pyramid.
Definition affine_registration.hxx:237
vigra::AffineMotionEstimationOptions::burtFilterCenterStrength
AffineMotionEstimationOptions & burtFilterCenterStrength(double center)
Define amount of smoothing before subsampling to the next pyramid level.
Definition affine_registration.hxx:197
vigra::AffineMotionEstimationOptions::iterationsPerLevel
AffineMotionEstimationOptions & iterationsPerLevel(unsigned int iter)
Number of Gauss-Newton iterations per level.
Definition affine_registration.hxx:222
vigra::AffineMotionEstimationOptions::highestPyramidLevel
AffineMotionEstimationOptions & highestPyramidLevel(unsigned int level)
Define the highest level of the image pyramid.
Definition affine_registration.hxx:212
vigra::MultiArrayView
Base class for, and view to, MultiArray.
Definition multi_array.hxx:705
vigra::linalg::Matrix
Definition matrix.hxx:125
vigra
vigra::identityMatrix
void identityMatrix(MultiArrayView< 2, T, C > &r)
Definition matrix.hxx:845
vigra::pyramidReduceBurtLaplacian
void pyramidReduceBurtLaplacian(ImagePyramid< Image, Alloc > &pyramid, int fromLevel, int toLevel, double centerValue=0.4)
Create a Laplacian pyramid.
Definition resampling_convolution.hxx:1197
vigra::outer
void outer(const MultiArrayView< 2, T, C1 > &x, const MultiArrayView< 2, T, C2 > &y, MultiArrayView< 2, T, C3 > &r)
Definition matrix.hxx:1459
vigra::estimateTranslation
void estimateTranslation(...)
Estimate the optical flow between two images according to a translation model.
vigra::pyramidReduceBurtFilter
void pyramidReduceBurtFilter(...)
Two-fold down-sampling for image pyramid construction.
vigra::linearSolve
bool linearSolve(...)
vigra::estimateSimilarityTransform
void estimateSimilarityTransform(...)
Estimate the optical flow between two images according to a similarity transform model (e....
vigra::estimateAffineTransform
void estimateAffineTransform(...)
Estimate the optical flow between two images according to an affine transform model (e....
vigra::affineMatrix2DFromCorrespondingPoints
linalg::TemporaryMatrix< double > affineMatrix2DFromCorrespondingPoints(SrcIterator s, SrcIterator send, DestIterator d)
Create homogeneous matrix that maps corresponding points onto each other.
Definition affine_registration.hxx:73

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de) Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany | html generated using doxygen and Python vigra 1.12.4