-
Notifications
You must be signed in to change notification settings - Fork 0
/
Metric.cpp
458 lines (382 loc) · 14.4 KB
/
Metric.cpp
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
/*
* Metric.cpp
*
* Created on: Nov, 2014
* Author: dailos
*/
#include "Metric.h"
#include "ToolBox.h"
#include "OpticalSetup.h"
#include "CustomException.h"
#include "Zernike.h"
#include "FITS.h"
//nomenclature:
//Sj -> Optical Tranfer Function (OTF) for each independent optical path "j"
//D -> vector containing all data images for each optical path
//F -> Object estimate = P/Q
//Isolate meanPowerNoise into an independent noise filter class together with cutoff pixel information
//and cutoff_mask to apply to the data spectrums
//To bind the arguments of the member function "hello", within "object"
//Metric m;
//auto f = std::bind(&Metric::metric_from_coefs, &m, std::placeholders::_1);
Metric::Metric(const std::vector<cv::Mat>& D, const std::shared_ptr<Zernike>& zrnk, const double& meanPowerNoise)
: zrnk_(zrnk), meanPowerNoise_(meanPowerNoise)
{
for(auto Dk : D) D_.push_back(Dk.clone());
}
Metric::~Metric()
{
// TODO Auto-generated destructor stub
}
void Metric::characterizeOpticalSystem(const cv::Mat& coeffs, std::vector<Optics>& OS)
{
//check input dimensions
if(coeffs.cols != 1) throw CustomException("Wrong input dimensions");
//Start populating vector from scratch
OS.clear();
OpticalSetup tsettings(D_.front().size().width);
unsigned int pupilSideLength = D_.front().size().width;
unsigned int K = D_.size(); //number of images to use in the algorithm
unsigned int M = zrnk_->base().size(); //number of zernike coefficients to use in the representation of each image phase
if(K * M != coeffs.total()) throw CustomException("Coeffcient vector should contain K*M elements.");
cv::Mat phase_div = cv::Mat::zeros(coeffs.size(), coeffs.type());
phase_div.at<double>(M + 3, 0) = tsettings.k() * 3.141592/(2.0*std::sqrt(3.0));
cv::Mat coeffs_new = coeffs + phase_div;
for(unsigned int k=0; k<K; ++k)
{ //every image coeffcients are within the vector coeefs in the range (a,b), "a" inclusive, "b" exclusive
cv::Mat pupilPhase_i;
zrnk_->synthesize(coeffs_new(cv::Range(k*M, k*M + M), cv::Range::all()), pupilPhase_i);
OS.push_back(Optics(pupilPhase_i, zrnk_->base().at(0))); //Characterized optical system
}
}
void Metric::computeQ(const cv::Mat& coeffs, const std::vector<Optics>& OS, cv::Mat& Q)
{
//We use 'depth' here instead of 'type' because we want 1-channel image
Q = cv::Mat::zeros(D_.front().size(), D_.front().type());
for(size_t j = 0; j < D_.size(); ++j)
{
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj);
cv::Mat absSj2;
bool conjB(true);
cv::mulSpectrums(Sj, Sj, absSj2, cv::DFT_COMPLEX_OUTPUT, conjB); //Sj x Sj* == |Sj|^2
cv::accumulate(absSj2, Q); //equivalent to Q += (absSj)^2 === absSj.mul(absSj);
}
OpticalSetup tsettings(D_.front().cols);
//Q.setTo(0, cutoff_mask_ == 0);
}
void Metric::compute_dQ(const cv::Mat& zernikeElement, const std::vector<Optics>& OS, const unsigned int& j, cv::Mat& dQ)
{
//We use 'depth' here instead of 'type' because we want 1-channel image
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj);
cv::Mat dSj, SjdSj, dSjSj;
compute_dSj(OS.at(j), zernikeElement, dSj);
bool conjB(true);
cv::mulSpectrums(Sj, dSj, SjdSj, cv::DFT_COMPLEX_OUTPUT, conjB); //Sj x dSj*
cv::mulSpectrums(dSj, Sj, dSjSj, cv::DFT_COMPLEX_OUTPUT, conjB); //Sj* x dSj
dQ = SjdSj + dSjSj;
}
void Metric::computeP(const cv::Mat& coeffs, const std::vector<Optics>& OS, cv::Mat& P)
{
P = cv::Mat::zeros(D_.front().size(), D_.front().type());
//P = accumulate over J { Dj * conj(Sj) }
for(size_t j = 0; j < D_.size(); ++j)
{
cv::Mat SjDj;
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj);
bool conjB(true);
cv::mulSpectrums(D_.at(j), Sj, SjDj, cv::DFT_COMPLEX_OUTPUT, conjB);
cv::accumulate(SjDj, P); //equivalent to P += SjDj;
}
OpticalSetup tsettings(D_.front().cols);
//P.setTo(0, cutoff_mask_ == 0);
}
void Metric::compute_dP(const cv::Mat& zernikeElement, const std::vector<Optics>& OS, const unsigned int& j, cv::Mat& dP)
{
//Simply compute one element of the sum in dP
cv::Mat dSj;
compute_dSj(OS.at(j), zernikeElement, dSj);
bool conjB(true);
cv::mulSpectrums(D_.at(j), dSj, dP, cv::DFT_COMPLEX_OUTPUT, conjB);
}
void Metric::noiseFilter(const cv::Mat& coeffs, const double& meanPowerNoise, const cv::Mat& P, const cv::Mat& Q, cv::Mat& filter)
{
throw CustomException("Noise filter not implemented yet.");
/*
const double filter_upper_limit(1.0);
const double filter_lower_limit(0.1);
cv::Mat absP = absComplex(P);
cv::Mat frac;
cv::divide(splitComplex(Q).first, absP.mul(absP), frac); //Both Q and absP are single channel images, real matrices
//These two inversion are needed to have the exact filter as in the old code
cv::pow(frac, -1, frac);
cv::blur(frac, frac, cv::Size(3,3));
cv::pow(frac, -1, frac);
cv::Mat fracFlip;
cv::flip(frac, fracFlip, -1); //flipCode => -1 < 0 means two axes flip
shift(fracFlip, fracFlip, 1, 1); //shift matrix => 1 means one pixel to the right
filter = 1.0 - (meanPowerNoise * (frac + fracFlip)/2.0);
//remove peaks
filter.setTo(0, filter < filter_lower_limit);
filter.setTo(filter_upper_limit, filter > filter_upper_limit);
//To zero-out frequencies beyond cutoff
OpticalSetup tsettings(D_.front().cols);
filter.setTo(0, cutoff_mask_ == 0);
//select only the central lobe of the filter when represented in the frequency domain
// Find total markers
std::vector<std::vector<cv::Point> > contours;
//cv::Mat binary = H_ > 0;
cv::Mat markers = cv::Mat::zeros(filter.size(), CV_8U);
cv::findContours(cv::Mat(filter > 0), contours, CV_RETR_EXTERNAL, CV_CHAIN_APPROX_NONE);
auto contsBegin = contours.cbegin();
for (auto conts = contsBegin, contsEnd = contours.cend(); conts != contsEnd; ++conts)
{
bool calcDistance(false);
if(cv::pointPolygonTest(*conts, cv::Point(filter.cols/2, filter.rows/2), calcDistance) > 0)
{
cv::drawContours(markers, contours, std::distance(contsBegin, conts), cv::Scalar::all(255), -1);
break;
}
}
filter.setTo(0, markers == 0);
cv::blur(filter, filter, cv::Size(9,9));
*/
}
//objective function: L = sum_i{ |D_i - F * S_i|^2 }
//Objective function : L = sum_i{ |y - Φ(x)|^2 }
double Metric::objective( const cv::Mat& coeffs )
{
double L(0.0);
//Intermal metrics
cv::Mat P, Q, H;
std::vector<Optics> OS;
characterizeOpticalSystem(coeffs, OS);
computeQ(coeffs, OS, Q);
computeP(coeffs, OS, P);
//noiseFilter(coeffs, meanPowerNoise_, P, Q, H);
//Object estimate: F = (P/Q) x filter
divSpectrums(P, Q, F_, cv::DFT_COMPLEX_OUTPUT);
//cv::mulSpectrums(F_, makeComplex(H), F_, cv::DFT_COMPLEX_OUTPUT);
size_t J = OS.size();
/////Create L = sum{ abs(D0H - FHT0)^2 + abs(DkH - FHTk)^2
cv::Mat accDiff = cv::Mat::zeros(F_.size(), F_.depth());
for(unsigned int j = 0; j < J; ++j)
{
cv::Mat DjH;
//cv::mulSpectrums(D_.at(j), makeComplex(H), DjH, cv::DFT_COMPLEX_OUTPUT);
DjH = D_.at(j).clone();
cv::Mat FHSj;
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj); //shifts fft spectrums and brings energy to the center of the image
cv::mulSpectrums(F_, Sj, FHSj, cv::DFT_COMPLEX_OUTPUT);
cv::accumulateSquare(absComplex(DjH - FHSj), accDiff);
}
L = cv::sum(accDiff).val[0];
/*
//Alternative way
cv::Mat absP2, absP2_Q;
bool conjB(true);
cv::mulSpectrums(P, P, absP2, cv::DFT_COMPLEX_OUTPUT, conjB);
divSpectrums(absP2, Q, absP2_Q, cv::DFT_COMPLEX_OUTPUT);
cv::Mat accD = cv::Mat::zeros(Q.size(), Q.type());
for(auto Di : D_)
{
cv::Mat absDi2;
cv::mulSpectrums(Di, Di, absDi2, cv::DFT_COMPLEX_OUTPUT, conjB);
accD += absDi2;
}
std::cout << "Values for objective function: " << cv::sum(accD-absP2_Q).val[0] << " " << L << std::endl;
*/
return L;
}
void Metric::phi( const cv::Mat& coeffs, cv::Mat& De )
{
std::vector<cv::Mat> De_v;
phi(coeffs, De_v);
std::vector<cv::Mat> de_v;
for(auto Dei : De_v )
{
cv::Mat Dei_t( Dei.t() );
de_v.push_back(Dei_t.reshape(0, Dei_t.total() ));
}
cv::vconcat(de_v, De);
}
//Object estimate convoluted with OTFi for a given phase coefficient vector
void Metric::phi( const cv::Mat& coeffs, std::vector<cv::Mat>& De )
{
cv::Mat P, Q, H, F;
std::vector<Optics> OS;
characterizeOpticalSystem(coeffs, OS);
computeQ(coeffs, OS, Q);
computeP(coeffs, OS, P);
//noiseFilter(coeffs, meanPowerNoise_, P, Q, H);
//Object estimate: F = (P/Q) x filter
divSpectrums(P, Q, F, cv::DFT_COMPLEX_OUTPUT);
//cv::mulSpectrums(F, makeComplex(H), F, cv::DFT_COMPLEX_OUTPUT);
De.clear();
size_t J = OS.size();
for(unsigned int j = 0; j < J; ++j)
{
cv::Mat FSj;
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj); //shifts fft spectrums and takes energy to the center of the image
cv::mulSpectrums(F, Sj, FSj, cv::DFT_COMPLEX_OUTPUT);
De.push_back(FSj);
}
}
void Metric::jacobian( const cv::Mat& coeffs, cv::Mat& jacob )
{
std::vector<std::vector<cv::Mat> > jacob_v;
jacobian( coeffs, jacob_v );
std::vector<cv::Mat> blockMatrix;
std::vector<cv::Mat> res;
for(size_t j = 0; j < jacob_v.size(); ++j)
{
std::vector<cv::Mat> blockMatrixRow;
for(size_t m = 0; m < jacob_v.at(j).size(); ++m)
{
cv::Mat coo_t( jacob_v.at(j).at(m).t() );
blockMatrixRow.push_back(coo_t.reshape(0, coo_t.total() ));
}
cv::Mat blockMatrixRow_M;
cv::hconcat(blockMatrixRow, blockMatrixRow_M);
blockMatrix.push_back(blockMatrixRow_M);
}
cv::Mat blockMatrix_M;
cv::vconcat(blockMatrix, jacob);
}
//Compute the jacobian of Φ in the equation: y = Φ(x) + e
void Metric::jacobian( const cv::Mat& coeffs, std::vector<std::vector<cv::Mat> >& jacob )
{
cv::Mat P, Q, H, F;
std::vector<Optics> OS;
characterizeOpticalSystem(coeffs, OS);
computeQ(coeffs, OS, Q);
computeP(coeffs, OS, P);
//noiseFilter(coeffs, meanPowerNoise_, P, Q, H);
//Object estimate: F = (P/Q) x filter
divSpectrums(P, Q, F, cv::DFT_COMPLEX_OUTPUT);
//cv::mulSpectrums(F, makeComplex(H), F, cv::DFT_COMPLEX_OUTPUT);
cv::Mat Q2;
cv::mulSpectrums(Q, Q, Q2, cv::DFT_COMPLEX_OUTPUT);
size_t J = OS.size();
size_t M = zrnk_->base().size();
jacob.clear();
for(unsigned int j = 0; j < J; ++j)
{
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj);
cv::Mat PSj;
cv::mulSpectrums(P, Sj, PSj, cv::DFT_COMPLEX_OUTPUT);
std::vector<cv::Mat> vecM;
for(unsigned int k = 0; k < J; ++k)
{
for(size_t m = 0; m < M; ++m)
{
cv::Mat PdSj = cv::Mat::zeros(Sj.size(), Sj.type());
cv::Mat dPSj, dSj, dP, dQ, lterm, rterm, tt;
if(j == k)
{
compute_dSj(OS.at(j), zrnk_->base().at(m), dSj);
cv::mulSpectrums(P, dSj, PdSj, cv::DFT_COMPLEX_OUTPUT);
}
compute_dP(zrnk_->base().at(m), OS, k, dP);
cv::mulSpectrums(dP, Sj, dPSj, cv::DFT_COMPLEX_OUTPUT);
cv::mulSpectrums(Q, dPSj+PdSj, lterm, cv::DFT_COMPLEX_OUTPUT);
compute_dQ(zrnk_->base().at(m), OS, k, dQ);
cv::mulSpectrums(dQ, PSj, rterm, cv::DFT_COMPLEX_OUTPUT);
divSpectrums(lterm-rterm, Q2, tt, cv::DFT_COMPLEX_OUTPUT);
vecM.push_back(tt);
}
}
jacob.push_back(vecM);
}
}
//Computes derivative of OTF with respect to an element of the zernike base
void Metric::compute_dSj(const Optics& osj, const cv::Mat& zernikeElement, cv::Mat& dSj)
{
cv::Mat Pj = osj.generalizedPupilFunction();
cv::Mat ZH;
cv::mulSpectrums(makeComplex(zernikeElement), Pj, ZH, cv::DFT_COMPLEX_OUTPUT);
cv::Mat cross;
bool full(false), corr(true);
convolveDFT(Pj, ZH, cross, corr, full);
fftShift(cross);
cv::Mat H_ZH;
cross.copyTo(H_ZH);
cv::Mat H_ZHFlipped;
cv::flip(H_ZH, H_ZHFlipped, -1); //flipCode => -1 < 0 means two axes flip
shift(H_ZHFlipped, H_ZHFlipped, 1, 1); //shift matrix => 1,1 means one pixel to the right, one pixel down
cv::Mat diff = H_ZH - conjComplex(H_ZHFlipped);
std::pair<cv::Mat, cv::Mat> splitComplexMatrix = splitComplex(diff);
dSj = makeComplex((-1)*splitComplexMatrix.second, splitComplexMatrix.first).clone();//equivalent to multiply by imaginary unit i
fftShift(dSj);
}
//gradient of the whole objective function: L = sum_i{ |D_i - F * S_i|^2 } with respect to every parameter of the phase
cv::Mat Metric::gradient( const cv::Mat& coeffs )
{
//Intermal metrics
cv::Mat P, Q, H, F;
std::vector<Optics> OS;
characterizeOpticalSystem(coeffs, OS);
computeP(coeffs, OS, P);
computeQ(coeffs, OS, Q);
//Some useful calculations
bool conjB(true);
//noiseFilter(coeffs, meanPowerNoise_, P, Q, H);
//Object estimate: F = (P/Q) x filter
divSpectrums(P, Q, F, cv::DFT_COMPLEX_OUTPUT);
//cv::mulSpectrums(F, makeComplex(H), F, cv::DFT_COMPLEX_OUTPUT); //Filter the object estimate out
size_t J = OS.size();
size_t M = zrnk_->base().size();
cv::Mat g = cv::Mat::zeros(J*M, 1, cv::DataType<double>::type);
Zernike zrnk;
for(size_t j = 0; j < J; ++j)
{
cv::Mat FDj;
cv::mulSpectrums(F, D_.at(j), FDj, cv::DFT_COMPLEX_OUTPUT, conjB);
cv::Mat Sj = OS.at(j).otf().clone();
fftShift(Sj);
OpticalSetup tsettings(D_.front().cols);
// Sj.setTo(0, cutoff_mask_ == 0); //restore when filter noise implemented again
cv::Mat abs2F, abs2FSj;
cv::mulSpectrums(F, F, abs2F, cv::DFT_COMPLEX_OUTPUT, conjB);
cv::mulSpectrums(abs2F, Sj, abs2FSj, cv::DFT_COMPLEX_OUTPUT, conjB);
//Put V value aside
cv::Mat V = FDj - abs2FSj;
for(size_t m = 0; m < M; ++m)
{
cv::Mat dSj, dSjV;
compute_dSj(OS.at(j), zrnk_->base().at(m), dSj);
cv::mulSpectrums(dSj, V, dSjV, cv::DFT_COMPLEX_OUTPUT);
g.at<double>((j * M) + m, 0) = cv::sum(dSjV).val[0];
}
}
/*
//Alternate way of getting the gradient through dP and dQ
std::vector<cv::Mat> De;
std::vector<std::vector<cv::Mat> > jacob;
phi(coeffs, De);
jacobian(coeffs, jacob);
cv::Mat g_phi = cv::Mat::zeros(J*M, 1, cv::DataType<double>::type);
for(size_t j = 0; j < J; ++j)
{
cv::Mat diff = D_.at(j)-De.at(j);
for(size_t m = 0; m < J*M; ++m)
{
cv::Mat tt;
//cv::mulSpectrums(diff, jacob.at(k).at(m), tt, cv::DFT_COMPLEX_OUTPUT, conjB);
cv::mulSpectrums(diff, jacob.at(j).at(m), tt, cv::DFT_COMPLEX_OUTPUT, conjB);
g_phi.at<double>(m, 0) += cv::sum(tt).val[0];
}
}
std::cout << "g: " << g.t() << std::endl;
std::cout << "g_phi: " << g_phi.t() << std::endl;
std::cout << "g/g_phi: " << g.t()/g_phi.t() << std::endl;
//g_phi.copyTo(g);
*/
g = g / zrnk_->base().front().total();
return g;
}