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3 /* Copyright 1998-2006 by Ullrich Koethe */
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35
36
37 #ifndef VIGRA_SLANTED_EDGE_MTF_HXX
38 #define VIGRA_SLANTED_EDGE_MTF_HXX
39
40 #include <algorithm>
41 #include "array_vector.hxx"
42 #include "basicgeometry.hxx"
43 #include "edgedetection.hxx"
44 #include "fftw3.hxx"
45 #include "functorexpression.hxx"
46 #include "linear_solve.hxx"
47 #include "mathutil.hxx"
48 #include "numerictraits.hxx"
49 #include "separableconvolution.hxx"
50 #include "static_assert.hxx"
51 #include "stdimage.hxx"
52 #include "transformimage.hxx"
53 #include "utilities.hxx"
54 #include "multi_shape.hxx"
55
56 namespace vigra {
57
58 /** \addtogroup SlantedEdgeMTF Camera MTF Estimation
59 Determine the magnitude transfer function (MTF) of a camera using the slanted edge method.
60 */
61 //@{
62
63 /********************************************************/
64 /* */
65 /* SlantedEdgeMTFOptions */
66 /* */
67 /********************************************************/
68
69 /** \brief Pass options to one of the \ref slantedEdgeMTF() functions.
70
71 <tt>SlantedEdgeMTFOptions</tt> is an argument objects that holds various optional
72 parameters used by the \ref slantedEdgeMTF() functions. If a parameter is not explicitly
73 set, a suitable default will be used. Changing the defaults is only necessary if you can't
74 obtain good input data, but absolutely need an MTF estimate.
75
76 <b> Usage:</b>
77
78 <b>\#include</b> <vigra/slanted_edge_mtf.hxx><br>
79 Namespace: vigra
80
81 \code
82 MultiArray<2, float> src(w,h);
83 std::vector<vigra::TinyVector<double, 2> > mtf;
84
85 ...
86 slantedEdgeMTF(src, mtf,
87 SlantedEdgeMTFOptions().mtfSmoothingScale(1.0));
88
89 // print the frequency / attenuation pairs found
90 for(int k=0; k<result.size(); ++k)
91 std::cout << "frequency: " << mtf[k][0] << ", estimated attenuation: " << mtf[k][1] << std::endl;
92 \endcode
93 */
94
95 class SlantedEdgeMTFOptions
96 {
97 public:
98 /** Initialize all options with default values.
99 */
100 SlantedEdgeMTFOptions()
101 : minimum_number_of_lines(20),
102 desired_edge_width(10),
103 minimum_edge_width(5),
104 mtf_smoothing_scale(2.0)
105 {}
106
107 /** Minimum number of pixels the edge must cross.
108
109 The longer the edge the more accurate the resulting MTF estimate. If you don't have good
110 data, but absolutely have to compute an MTF, you may force a lower value here.<br>
111 Default: 20
112 */
113 SlantedEdgeMTFOptions & minimumNumberOfLines(unsigned int n)
114 {
115 minimum_number_of_lines = n;
116 return *this;
117 }
118
119 /** Desired number of pixels perpendicular to the edge.
120
121 The larger the regions to either side of the edge,
122 the more accurate the resulting MTF estimate. If you don't have good
123 data, but absolutely have to compute an MTF, you may force a lower value here.<br>
124 Default: 10
125 */
126 SlantedEdgeMTFOptions & desiredEdgeWidth(unsigned int n)
127 {
128 desired_edge_width = n;
129 return *this;
130 }
131
132 /** Minimum acceptable number of pixels perpendicular to the edge.
133
134 The larger the regions to either side of the edge,
135 the more accurate the resulting MTF estimate. If you don't have good
136 data, but absolutely have to compute an MTF, you may force a lower value here.<br>
137 Default: 5
138 */
139 SlantedEdgeMTFOptions & minimumEdgeWidth(unsigned int n)
140 {
141 minimum_edge_width = n;
142 return *this;
143 }
144
145 /** Amount of smoothing of the computed MTF.
146
147 If the data is noisy, so will be the MTF. Thus, some smoothing is useful.<br>
148 Default: 2.0
149 */
150 SlantedEdgeMTFOptions & mtfSmoothingScale(double scale)
151 {
152 vigra_precondition(scale >= 0.0,
153 "SlantedEdgeMTFOptions: MTF smoothing scale must not be < 0.");
154 mtf_smoothing_scale = scale;
155 return *this;
156 }
157
158 unsigned int minimum_number_of_lines, desired_edge_width, minimum_edge_width;
159 double mtf_smoothing_scale;
160 };
161
162 //@}
163
164 namespace detail {
165
166 struct SortEdgelsByStrength
167 {
168 bool operator()(Edgel const & l, Edgel const & r) const
169 {
170 return l.strength > r.strength;
171 }
172 };
173
174 /* Make sure that the edge runs vertically, intersects the top and bottom border
175 of the image, and white is on the left.
176 */
177 template <class SrcIterator, class SrcAccessor, class DestImage>
178 unsigned int
179 prepareSlantedEdgeInput(SrcIterator sul, SrcIterator slr, SrcAccessor src, DestImage & res,
180 SlantedEdgeMTFOptions const & options)
181 {
182 unsigned int w = slr.x - sul.x;
183 unsigned int h = slr.y - sul.y;
184
185 // find rough estimate of the edge
186 ArrayVector<Edgel> edgels;
187 cannyEdgelList(sul, slr, src, edgels, 2.0);
188 std::sort(edgels.begin(), edgels.end(), SortEdgelsByStrength());
189
190 double x = 0.0, y = 0.0, x2 = 0.0, y2 = 0.0, xy = 0.0;
191 unsigned int c = std::min(w, h);
192
193 for(unsigned int k = 0; k < c; ++k)
194 {
195 x += edgels[k].x;
196 y += edgels[k].y;
197 x2 += sq(edgels[k].x);
198 xy += edgels[k].x*edgels[k].y;
199 y2 += sq(edgels[k].y);
200 }
201 double xc = x / c, yc = y / c;
202 x2 = x2 / c - sq(xc);
203 xy = xy / c - xc*yc;
204 y2 = y2 / c - sq(yc);
205 double angle = 0.5*VIGRA_CSTD::atan2(2*xy, x2 - y2);
206
207 DestImage tmp;
208 // rotate image when slope is less than +-45 degrees
209 if(VIGRA_CSTD::fabs(angle) < M_PI / 4.0)
210 {
211 xc = yc;
212 yc = w - xc - 1;
213 std::swap(w, h);
214 tmp.resize(w, h);
215 rotateImage(srcIterRange(sul, slr, src), destImage(tmp), 90);
216 angle += M_PI / 2.0;
217 }
218 else
219 {
220 tmp.resize(w, h);
221 copyImage(srcIterRange(sul, slr, src), destImage(tmp));
222 if(angle < 0.0)
223 angle += M_PI;
224 }
225 // angle is now between pi/4 and 3*pi/4
226 double slope = VIGRA_CSTD::tan(M_PI/2.0 - angle);
227 vigra_precondition(slope != 0.0,
228 "slantedEdgeMTF(): Input edge is not slanted");
229
230 // trim image so that the edge only intersects the top and bottom border
231 unsigned int minimumNumberOfLines = options.minimum_number_of_lines, //20,
232 edgeWidth = options.desired_edge_width, // 10
233 minimumEdgeWidth = options.minimum_edge_width; // 5
234
235 int y0 = 0, y1 = h;
236 for(; edgeWidth >= minimumEdgeWidth; --edgeWidth)
237 {
238 y0 = int(VIGRA_CSTD::floor((edgeWidth - xc) / slope + yc + 0.5));
239 y1 = int(VIGRA_CSTD::floor((w - edgeWidth - 1 - xc) / slope + yc + 0.5));
240 if(slope < 0.0)
241 std::swap(y0, y1);
242 if(y1 - y0 >= (int)minimumNumberOfLines)
243 break;
244 }
245
246 vigra_precondition(edgeWidth >= minimumEdgeWidth,
247 "slantedEdgeMTF(): Input edge is too slanted or image is too small");
248
249 y0 = std::max(y0, 0);
250 y1 = std::min(y1+1, (int)h);
251
252 res.resize(w, y1-y0);
253
254 // ensure that white is on the left
255 if(tmp(0,0) < tmp(w-1, h-1))
256 {
257 rotateImage(srcIterRange(tmp.upperLeft() + Diff2D(0, y0), tmp.upperLeft() + Diff2D(w, y1), tmp.accessor()),
258 destImage(res), 180);
259 }
260 else
261 {
262 copyImage(srcImageRange(tmp), destImage(res));
263 }
264 return edgeWidth;
265 }
266
267 template <class Image>
268 void slantedEdgeShadingCorrection(Image & i, unsigned int edgeWidth)
269 {
270 using namespace functor;
271
272 // after prepareSlantedEdgeInput(), the white region is on the left
273 // find a plane that approximates the logarithm of the white ROI
274
275 transformImage(srcImageRange(i), destImage(i), log(Arg1() + Param(1.0)));
276
277 unsigned int w = i.width(),
278 h = i.height();
279
280 Matrix<double> m(3,3), r(3, 1), l(3, 1);
281 for(unsigned int y = 0; y < h; ++y)
282 {
283 for(unsigned int x = 0; x < edgeWidth; ++x)
284 {
285 l(0,0) = x;
286 l(1,0) = y;
287 l(2,0) = 1.0;
288 m += outer(l);
289 r += i(x,y)*l;
290 }
291 }
292
293 linearSolve(m, r, l);
294 double a = l(0,0),
295 b = l(1,0),
296 c = l(2,0);
297
298 // subtract the plane and go back to the non-logarithmic representation
299 for(unsigned int y = 0; y < h; ++y)
300 {
301 for(unsigned int x = 0; x < w; ++x)
302 {
303 i(x, y) = VIGRA_CSTD::exp(i(x,y) - a*x - b*y - c);
304 }
305 }
306 }
307
308 template <class Image, class BackInsertable>
309 void slantedEdgeSubpixelShift(Image const & img, BackInsertable & centers, double & angle,
310 SlantedEdgeMTFOptions const & options)
311 {
312 unsigned int w = img.width();
313 unsigned int h = img.height();
314
315 Image grad(w, h);
316 Kernel1D<double> kgrad;
317 kgrad.initGaussianDerivative(1.0, 1);
318
319 separableConvolveX(srcImageRange(img), destImage(grad), kernel1d(kgrad));
320
321 int desiredEdgeWidth = (int)options.desired_edge_width;
322 double sy = 0.0, sx = 0.0, syy = 0.0, sxy = 0.0;
323 for(unsigned int y = 0; y < h; ++y)
324 {
325 double a = 0.0,
326 b = 0.0;
327 for(unsigned int x = 0; x < w; ++x)
328 {
329 a += x*grad(x,y);
330 b += grad(x,y);
331 }
332 int c = int(a / b);
333 // c is biased because the numbers of black and white pixels differ
334 // repeat the analysis with a symmetric window around the edge
335 a = 0.0;
336 b = 0.0;
337 int ew = desiredEdgeWidth;
338 if(c-desiredEdgeWidth < 0)
339 ew = c;
340 if(c + ew + 1 >= (int)w)
341 ew = w - c - 1;
342 for(int x = c-ew; x < c+ew+1; ++x)
343 {
344 a += x*grad(x,y);
345 b += grad(x,y);
346 }
347 double sc = a / b;
348 sy += y;
349 sx += sc;
350 syy += sq(y);
351 sxy += sc*y;
352 }
353 // fit a line to the subpixel locations
354 double a = (h * sxy - sx * sy) / (h * syy - sq(sy));
355 double b = (sx * syy - sxy * sy) / (h * syy - sq(sy));
356
357 // compute the regularized subpixel values of the edge location
358 angle = VIGRA_CSTD::atan(a);
359 for(unsigned int y = 0; y < h; ++y)
360 {
361 centers.push_back(a * y + b);
362 }
363 }
364
365 template <class Image, class Vector>
366 void slantedEdgeCreateOversampledLine(Image const & img, Vector const & centers,
367 Image & result)
368 {
369 unsigned int w = img.width();
370 unsigned int h = img.height();
371 unsigned int w2 = std::min(std::min(int(centers[0]), int(centers[h-1])),
372 std::min(int(w - centers[0]) - 1, int(w - centers[h-1]) - 1));
373 unsigned int ww = 8*w2;
374
375 Image r(ww, 1), s(ww, 1);
376 for(unsigned int y = 0; y < h; ++y)
377 {
378 int x0 = int(centers[y]) - w2;
379 int x1 = int((VIGRA_CSTD::ceil(centers[y]) - centers[y])*4);
380 for(; x1 < (int)ww; x1 += 4)
381 {
382 r(x1, 0) += img(x0, y);
383 ++s(x1, 0);
384 ++x0;
385 }
386 }
387
388 for(unsigned int x = 0; x < ww; ++x)
389 {
390 vigra_precondition(s(x,0) > 0.0,
391 "slantedEdgeMTF(): Input edge is not slanted enough");
392 r(x,0) /= s(x,0);
393 }
394
395 result.resize(ww-1, 1);
396 for(unsigned int x = 0; x < ww-1; ++x)
397 {
398 result(x,0) = r(x+1,0) - r(x,0);
399 }
400 }
401
402 template <class Image, class BackInsertable>
403 void slantedEdgeMTFImpl(Image const & i, BackInsertable & mtf, double angle,
404 SlantedEdgeMTFOptions const & options)
405 {
406 unsigned int w = i.width();
407 unsigned int h = i.height();
408
409 double slantCorrection = VIGRA_CSTD::cos(angle);
410 int desiredEdgeWidth = 4*options.desired_edge_width;
411
412 Image magnitude;
413
414 if(w - 2*desiredEdgeWidth < 64)
415 {
416 FFTWComplexImage otf(w, h);
417 fourierTransform(srcImageRange(i), destImage(otf));
418
419 magnitude.resize(w, h);
420 for(unsigned int y = 0; y < h; ++y)
421 {
422 for(unsigned int x = 0; x < w; ++x)
423 {
424 magnitude(x, y) = norm(otf(x, y));
425 }
426 }
427 }
428 else
429 {
430 w -= 2*desiredEdgeWidth;
431 FFTWComplexImage otf(w, h);
432 fourierTransform(srcImageRange(i, Rect2D(Point2D(desiredEdgeWidth, 0), Size2D(w, h))),
433 destImage(otf));
434
435 // create an image where the edge is skipped - presumably it only contains the
436 // noise which can then be subtracted
437 Image noise(w,h);
438 copyImage(srcImageRange(i, Rect2D(Point2D(0,0), Size2D(w/2, h))),
439 destImage(noise));
440 copyImage(srcImageRange(i, Rect2D(Point2D(i.width()-w/2, 0), Size2D(w/2, h))),
441 destImage(noise, Point2D(w/2, 0)));
442 FFTWComplexImage fnoise(w, h);
443 fourierTransform(srcImageRange(noise), destImage(fnoise));
444
445 // subtract the noise power spectrum from the total power spectrum
446 magnitude.resize(w, h);
447 for(unsigned int y = 0; y < h; ++y)
448 {
449 for(unsigned int x = 0; x < w; ++x)
450 {
451 magnitude(x, y) = VIGRA_CSTD::sqrt(std::max(0.0, squaredNorm(otf(x, y))-squaredNorm(fnoise(x, y))));
452 }
453 }
454 }
455
456 Kernel1D<double> gauss;
457 gauss.initGaussian(options.mtf_smoothing_scale);
458 Image smooth(w,h);
459 separableConvolveX(srcImageRange(magnitude), destImage(smooth), kernel1d(gauss));
460
461 unsigned int ww = w/4;
462 double maxVal = smooth(0,0),
463 minVal = maxVal;
464 for(unsigned int k = 1; k < ww; ++k)
465 {
466 if(smooth(k,0) >= 0.0 && smooth(k,0) < minVal)
467 minVal = smooth(k,0);
468 }
469 double norm = maxVal-minVal;
470
471 typedef typename BackInsertable::value_type Result;
472 mtf.push_back(Result(0.0, 1.0));
473 for(unsigned int k = 1; k < ww; ++k)
474 {
475 double n = (smooth(k,0) - minVal)/norm*sq(M_PI*k/w/VIGRA_CSTD::sin(M_PI*k/w));
476 double xx = 4.0*k/w/slantCorrection;
477 if(n < 0.0 || xx > 1.0)
478 break;
479 mtf.push_back(Result(xx, n));
480 }
481 }
482
483 } // namespace detail
484
485 /** \addtogroup SlantedEdgeMTF Camera MTF Estimation
486 Determine the magnitude transfer function (MTF) of a camera using the slanted edge method.
487 */
488 //@{
489
490 /********************************************************/
491 /* */
492 /* slantedEdgeMTF */
493 /* */
494 /********************************************************/
495
496 /** \brief Determine the magnitude transfer function of the camera.
497
498 This operator estimates the magnitude transfer function (MTF) of a camera by means of the
499 slanted edge method described in:
500
501 ISO Standard No. 12233: <i>"Photography - Electronic still picture cameras - Resolution measurements"</i>, 2000
502
503 The input must be an image that contains a single step edge with bright pixels on one side and dark pixels on
504 the other. However, the intensity values must be neither saturated nor zero. The algorithms computes the MTF
505 from the Fourier transform of the edge's derivative. Thus, if the actual MTF is anisotropic, the estimated
506 MTF does actually only apply in the direction perpendicular to the edge - several edges at different
507 orientations are required to estimate an anisotropic MTF.
508
509 The algorithm returns a sequence of frequency / attenuation pairs. The frequency axis is normalized so that the
510 Nyquist frequency of the original image is 0.5. Since the edge's derivative is computed with subpixel accuracy,
511 the attenuation can usually be computed for frequencies significantly above the Nyquist frequency as well. The
512 MTF estimate ends at either the first zero crossing of the MTF or at frequency 1, whichever comes earlier.
513
514 The present implementation improves the original slanted edge algorithm according to ISO 12233 in a number of
515 ways:
516
517 <ul>
518 <li> The edge is not required to run nearly vertically or horizontally (i.e. with a slant of approximately 5 degrees).
519 The algorithm will automatically compute the edge's actual angle and adjust estimates accordingly.
520 However, it is still necessary for the edge to be somewhat slanted, because subpixel-accurate estimation
521 of the derivative is impossible otherwise (i.e. the edge position perpendicular to the edge direction must
522 differ by at least 1 pixel between the two ends of the edge).
523
524 <li> Our implementation uses a more accurate subpixel derivative algorithm. In addition, we first perform a shading
525 correction in order to reduce possible derivative bias due to nonuniform illumination.
526
527 <li> If the input image is large enough (i.e. there are at least 20 pixels on either side of the edge over
528 the edge's entire length), our algorithm attempts to subtract the estimated noise power spectrum
529 from the estimated MTF.
530 </ul>
531
532 The source value type <TT>T1</TT> must be a scalar type which is convertible to <tt>double</tt>.
533 The result is written into the \a result sequence, which must be back-insertable (supports <tt>push_back()</tt>)
534 and whose <tt>value_type</tt> must be constructible
535 from two <tt>double</tt> values. Algorithm options can be set via the \a options object
536 (see \ref vigra::NoiseNormalizationOptions for details).
537
538 <b> Declarations:</b>
539
540 pass 2D array views:
541 \code
542 namespace vigra {
543 template <class T1, class S1, class BackInsertable>
544 void
545 slantedEdgeMTF(MultiArrayView<2, T1, S1> const & src, BackInsertable & mtf,
546 SlantedEdgeMTFOptions const & options = SlantedEdgeMTFOptions());
547 }
548 \endcode
549
550 \deprecatedAPI{slantedEdgeMTF}
551 pass \ref ImageIterators and \ref DataAccessors :
552 \code
553 namespace vigra {
554 template <class SrcIterator, class SrcAccessor, class BackInsertable>
555 void
556 slantedEdgeMTF(SrcIterator sul, SrcIterator slr, SrcAccessor src, BackInsertable & mtf,
557 SlantedEdgeMTFOptions const & options = SlantedEdgeMTFOptions());
558 }
559 \endcode
560 use argument objects in conjunction with \ref ArgumentObjectFactories :
561 \code
562 namespace vigra {
563 template <class SrcIterator, class SrcAccessor, class BackInsertable>
564 void
565 slantedEdgeMTF(triple<SrcIterator, SrcIterator, SrcAccessor> src, BackInsertable & mtf,
566 SlantedEdgeMTFOptions const & options = SlantedEdgeMTFOptions())
567 }
568 \endcode
569 \deprecatedEnd
570
571 <b> Usage:</b>
572
573 <b>\#include</b> <vigra/slanted_edge_mtf.hxx><br>
574 Namespace: vigra
575
576 \code
577 MultiArray<2, float> src(w,h);
578 std::vector<vigra::TinyVector<double, 2> > mtf;
579
580 ...
581 // keep all options at their default values
582 slantedEdgeMTF(src, mtf);
583
584 // print the frequency / attenuation pairs found
585 for(int k=0; k<result.size(); ++k)
586 std::cout << "frequency: " << mtf[k][0] << ", estimated attenuation: " << mtf[k][1] << std::endl;
587 \endcode
588
589 \deprecatedUsage{slantedEdgeMTF}
590 \code
591 vigra::BImage src(w,h);
592 std::vector<vigra::TinyVector<double, 2> > mtf;
593
594 ...
595 vigra::slantedEdgeMTF(srcImageRange(src), mtf);
596
597 // print the frequency / attenuation pairs found
598 for(int k=0; k<result.size(); ++k)
599 std::cout << "frequency: " << mtf[k][0] << ", estimated attenuation: " << mtf[k][1] << std::endl;
600 \endcode
601 <b> Required Interface:</b>
602 \code
603 SrcIterator upperleft, lowerright;
604 SrcAccessor src;
605
606 typedef SrcAccessor::value_type SrcType;
607 typedef NumericTraits<SrcType>::isScalar isScalar;
608 assert(isScalar::asBool == true);
609
610 double value = src(uperleft);
611
612 BackInsertable result;
613 typedef BackInsertable::value_type ResultType;
614 double intensity, variance;
615 result.push_back(ResultType(intensity, variance));
616 \endcode
617 \deprecatedEnd
618 */
619 doxygen_overloaded_function(template <...> void slantedEdgeMTF)
620
621 template <class SrcIterator, class SrcAccessor, class BackInsertable>
622 void
623 slantedEdgeMTF(SrcIterator sul, SrcIterator slr, SrcAccessor src, BackInsertable & mtf,
624 SlantedEdgeMTFOptions const & options = SlantedEdgeMTFOptions())
625 {
626 DImage preparedInput;
627 unsigned int edgeWidth = detail::prepareSlantedEdgeInput(sul, slr, src, preparedInput, options);
628 detail::slantedEdgeShadingCorrection(preparedInput, edgeWidth);
629
630 ArrayVector<double> centers;
631 double angle = 0.0;
632 detail::slantedEdgeSubpixelShift(preparedInput, centers, angle, options);
633
634 DImage oversampledLine;
635 detail::slantedEdgeCreateOversampledLine(preparedInput, centers, oversampledLine);
636
637 detail::slantedEdgeMTFImpl(oversampledLine, mtf, angle, options);
638 }
639
640 template <class SrcIterator, class SrcAccessor, class BackInsertable>
641 inline void
642 slantedEdgeMTF(triple<SrcIterator, SrcIterator, SrcAccessor> src, BackInsertable & mtf,
643 SlantedEdgeMTFOptions const & options = SlantedEdgeMTFOptions())
644 {
645 slantedEdgeMTF(src.first, src.second, src.third, mtf, options);
646 }
647
648 template <class T1, class S1, class BackInsertable>
649 inline void
650 slantedEdgeMTF(MultiArrayView<2, T1, S1> const & src, BackInsertable & mtf,
651 SlantedEdgeMTFOptions const & options = SlantedEdgeMTFOptions())
652 {
653 slantedEdgeMTF(srcImageRange(src), mtf, options);
654 }
655
656 /********************************************************/
657 /* */
658 /* mtfFitGaussian */
659 /* */
660 /********************************************************/
661
662 /** \brief Fit a Gaussian function to a given MTF.
663
664 This function expects a sequence of frequency / attenuation pairs as produced by \ref slantedEdgeMTF()
665 and finds the best fitting Gaussian point spread function (Gaussian functions are good approximations
666 of the PSF of many real cameras). It returns the standard deviation (scale) of this function. The algorithm
667 computes the standard deviation by means of a linear least square on the logarithm of the MTF, i.e.
668 an algebraic fit rather than a Euclidean fit - thus, the resulting Gaussian may not be the one that
669 intuitively fits the data optimally.
670
671 <b> Declaration:</b>
672
673 \code
674 namespace vigra {
675 template <class Vector>
676 double mtfFitGaussian(Vector const & mtf);
677 }
678 \endcode
679
680 <b> Usage:</b>
681
682 <b>\#include</b> <vigra/slanted_edge_mtf.hxx><br>
683 Namespace: vigra
684
685 \code
686 MultiArray<2, float> src(w,h);
687 std::vector<vigra::TinyVector<double, 2> > mtf;
688
689 ...
690 slantedEdgeMTF(src, mtf);
691 double scale = vigra::mtfFitGaussian(mtf)
692
693 std::cout << "The camera PSF is approximately a Gaussian at scale " << scale << std::endl;
694 \endcode
695
696 <b> Required Interface:</b>
697
698 \code
699 Vector mtf;
700 int numberOfMeasurements = mtf.size()
701
702 double frequency = mtf[0][0];
703 double attenuation = mtf[0][1];
704 \endcode
705 */
706 template <class Vector>
707 double mtfFitGaussian(Vector const & mtf)
708 {
709 double minVal = mtf[0][1];
710 for(unsigned int k = 1; k < mtf.size(); ++k)
711 {
712 if(mtf[k][1] < minVal)
713 minVal = mtf[k][1];
714 }
715 double x2 = 0.0,
716 xy = 0.0;
717 for(unsigned int k = 1; k < mtf.size(); ++k)
718 {
719 if(mtf[k][1] <= 0.0)
720 break;
721 double x = mtf[k][0],
722 y = VIGRA_CSTD::sqrt(-VIGRA_CSTD::log(mtf[k][1])/2.0)/M_PI;
723 x2 += vigra::sq(x);
724 xy += x*y;
725 if(mtf[k][1] == minVal)
726 break;
727 }
728 return xy / x2;
729 }
730
731 //@}
732
733 } // namespace vigra
734
735 #endif // VIGRA_SLANTED_EDGE_MTF_HXX

© 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 (Mon Nov 18 2013)