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42 
43 /*
44  * Implementation of the paper Shape Matching and Object Recognition Using Shape Contexts
45  * Belongie et al., 2002 by Juan Manuel Perez for GSoC 2013.
46  */
47 
48 #include "precomp.hpp"
49 #include "opencv2/core.hpp"
50 #include "scd_def.hpp"
51 #include <limits>
52 
53 namespace cv
54 {
55 class ShapeContextDistanceExtractorImpl : public ShapeContextDistanceExtractor
56 {
57 public:
58     /* Constructors */
ShapeContextDistanceExtractorImpl(int _nAngularBins,int _nRadialBins,float _innerRadius,float _outerRadius,int _iterations,const Ptr<HistogramCostExtractor> & _comparer,const Ptr<ShapeTransformer> & _transformer)59     ShapeContextDistanceExtractorImpl(int _nAngularBins, int _nRadialBins, float _innerRadius, float _outerRadius, int _iterations,
60                                       const Ptr<HistogramCostExtractor> &_comparer, const Ptr<ShapeTransformer> &_transformer)
61     {
62         nAngularBins=_nAngularBins;
63         nRadialBins=_nRadialBins;
64         innerRadius=_innerRadius;
65         outerRadius=_outerRadius;
66         rotationInvariant=false;
67         comparer=_comparer;
68         iterations=_iterations;
69         transformer=_transformer;
70         bendingEnergyWeight=0.3f;
71         imageAppearanceWeight=0.0f;
72         shapeContextWeight=1.0f;
73         sigma=10.0f;
74         name_ = "ShapeDistanceExtractor.SCD";
75     }
76 
77     /* Destructor */
~ShapeContextDistanceExtractorImpl()78     ~ShapeContextDistanceExtractorImpl()
79     {
80     }
81 
82     //! the main operator
83     virtual float computeDistance(InputArray contour1, InputArray contour2);
84 
85     //! Setters/Getters
setAngularBins(int _nAngularBins)86     virtual void setAngularBins(int _nAngularBins){CV_Assert(_nAngularBins>0); nAngularBins=_nAngularBins;}
getAngularBins() const87     virtual int getAngularBins() const {return nAngularBins;}
88 
setRadialBins(int _nRadialBins)89     virtual void setRadialBins(int _nRadialBins){CV_Assert(_nRadialBins>0); nRadialBins=_nRadialBins;}
getRadialBins() const90     virtual int getRadialBins() const {return nRadialBins;}
91 
setInnerRadius(float _innerRadius)92     virtual void setInnerRadius(float _innerRadius) {CV_Assert(_innerRadius>0); innerRadius=_innerRadius;}
getInnerRadius() const93     virtual float getInnerRadius() const {return innerRadius;}
94 
setOuterRadius(float _outerRadius)95     virtual void setOuterRadius(float _outerRadius) {CV_Assert(_outerRadius>0); outerRadius=_outerRadius;}
getOuterRadius() const96     virtual float getOuterRadius() const {return outerRadius;}
97 
setRotationInvariant(bool _rotationInvariant)98     virtual void setRotationInvariant(bool _rotationInvariant) {rotationInvariant=_rotationInvariant;}
getRotationInvariant() const99     virtual bool getRotationInvariant() const {return rotationInvariant;}
100 
setCostExtractor(Ptr<HistogramCostExtractor> _comparer)101     virtual void setCostExtractor(Ptr<HistogramCostExtractor> _comparer) { comparer = _comparer; }
getCostExtractor() const102     virtual Ptr<HistogramCostExtractor> getCostExtractor() const { return comparer; }
103 
setShapeContextWeight(float _shapeContextWeight)104     virtual void setShapeContextWeight(float _shapeContextWeight) {shapeContextWeight=_shapeContextWeight;}
getShapeContextWeight() const105     virtual float getShapeContextWeight() const {return shapeContextWeight;}
106 
setImageAppearanceWeight(float _imageAppearanceWeight)107     virtual void setImageAppearanceWeight(float _imageAppearanceWeight) {imageAppearanceWeight=_imageAppearanceWeight;}
getImageAppearanceWeight() const108     virtual float getImageAppearanceWeight() const {return imageAppearanceWeight;}
109 
setBendingEnergyWeight(float _bendingEnergyWeight)110     virtual void setBendingEnergyWeight(float _bendingEnergyWeight) {bendingEnergyWeight=_bendingEnergyWeight;}
getBendingEnergyWeight() const111     virtual float getBendingEnergyWeight() const {return bendingEnergyWeight;}
112 
setStdDev(float _sigma)113     virtual void setStdDev(float _sigma) {sigma=_sigma;}
getStdDev() const114     virtual float getStdDev() const {return sigma;}
115 
setImages(InputArray _image1,InputArray _image2)116     virtual void setImages(InputArray _image1, InputArray _image2)
117     {
118         Mat image1_=_image1.getMat(), image2_=_image2.getMat();
119         CV_Assert((image1_.depth()==0) && (image2_.depth()==0));
120         image1=image1_;
121         image2=image2_;
122     }
123 
getImages(OutputArray _image1,OutputArray _image2) const124     virtual void getImages(OutputArray _image1, OutputArray _image2) const
125     {
126         CV_Assert((!image1.empty()) && (!image2.empty()));
127         _image1.create(image1.size(), image1.type());
128         _image2.create(image2.size(), image2.type());
129         _image1.getMat()=image1;
130         _image2.getMat()=image2;
131     }
132 
setIterations(int _iterations)133     virtual void setIterations(int _iterations) {CV_Assert(_iterations>0); iterations=_iterations;}
getIterations() const134     virtual int getIterations() const {return iterations;}
135 
setTransformAlgorithm(Ptr<ShapeTransformer> _transformer)136     virtual void setTransformAlgorithm(Ptr<ShapeTransformer> _transformer) {transformer=_transformer;}
getTransformAlgorithm() const137     virtual Ptr<ShapeTransformer> getTransformAlgorithm() const {return transformer;}
138 
139     //! write/read
write(FileStorage & fs) const140     virtual void write(FileStorage& fs) const
141     {
142         fs << "name" << name_
143            << "nRads" << nRadialBins
144            << "nAngs" << nAngularBins
145            << "iters" << iterations
146            << "img_1" << image1
147            << "img_2" << image2
148            << "beWei" << bendingEnergyWeight
149            << "scWei" << shapeContextWeight
150            << "iaWei" << imageAppearanceWeight
151            << "costF" << costFlag
152            << "rotIn" << rotationInvariant
153            << "sigma" << sigma;
154     }
155 
read(const FileNode & fn)156     virtual void read(const FileNode& fn)
157     {
158         CV_Assert( (String)fn["name"] == name_ );
159         nRadialBins = (int)fn["nRads"];
160         nAngularBins = (int)fn["nAngs"];
161         iterations = (int)fn["iters"];
162         bendingEnergyWeight = (float)fn["beWei"];
163         shapeContextWeight = (float)fn["scWei"];
164         imageAppearanceWeight = (float)fn["iaWei"];
165         costFlag = (int)fn["costF"];
166         sigma = (float)fn["sigma"];
167     }
168 
169 protected:
170     int nAngularBins;
171     int nRadialBins;
172     float innerRadius;
173     float outerRadius;
174     bool rotationInvariant;
175     int costFlag;
176     int iterations;
177     Ptr<ShapeTransformer> transformer;
178     Ptr<HistogramCostExtractor> comparer;
179     Mat image1;
180     Mat image2;
181     float bendingEnergyWeight;
182     float imageAppearanceWeight;
183     float shapeContextWeight;
184     float sigma;
185     String name_;
186 };
187 
computeDistance(InputArray contour1,InputArray contour2)188 float ShapeContextDistanceExtractorImpl::computeDistance(InputArray contour1, InputArray contour2)
189 {
190     // Checking //
191     Mat sset1=contour1.getMat(), sset2=contour2.getMat(), set1, set2;
192     if (set1.type() != CV_32F)
193         sset1.convertTo(set1, CV_32F);
194     else
195         sset1.copyTo(set1);
196 
197     if (set2.type() != CV_32F)
198         sset2.convertTo(set2, CV_32F);
199     else
200         sset2.copyTo(set2);
201 
202     CV_Assert((set1.channels()==2) && (set1.cols>0));
203     CV_Assert((set2.channels()==2) && (set2.cols>0));
204     if (imageAppearanceWeight!=0)
205     {
206         CV_Assert((!image1.empty()) && (!image2.empty()));
207     }
208 
209     // Initializing Extractor, Descriptor structures and Matcher //
210     SCD set1SCE(nAngularBins, nRadialBins, innerRadius, outerRadius, rotationInvariant);
211     Mat set1SCD;
212     SCD set2SCE(nAngularBins, nRadialBins, innerRadius, outerRadius, rotationInvariant);
213     Mat set2SCD;
214     SCDMatcher matcher;
215     std::vector<DMatch> matches;
216 
217     // Distance components (The output is a linear combination of these 3) //
218     float sDistance=0, bEnergy=0, iAppearance=0;
219     float beta;
220 
221     // Initializing some variables //
222     std::vector<int> inliers1, inliers2;
223 
224     Ptr<ThinPlateSplineShapeTransformer> transDown = transformer.dynamicCast<ThinPlateSplineShapeTransformer>();
225 
226     Mat warpedImage;
227     int ii, jj, pt;
228 
229     for (ii=0; ii<iterations; ii++)
230     {
231         // Extract SCD descriptor in the set1 //
232         set1SCE.extractSCD(set1, set1SCD, inliers1);
233 
234         // Extract SCD descriptor of the set2 (TARGET) //
235         set2SCE.extractSCD(set2, set2SCD, inliers2, set1SCE.getMeanDistance());
236 
237         // regularization parameter with annealing rate annRate //
238         beta=set1SCE.getMeanDistance();
239         beta *= beta;
240 
241         // match //
242         matcher.matchDescriptors(set1SCD, set2SCD, matches, comparer, inliers1, inliers2);
243 
244         // apply TPS transform //
245         if ( !transDown.empty() )
246             transDown->setRegularizationParameter(beta);
247         transformer->estimateTransformation(set1, set2, matches);
248         bEnergy += transformer->applyTransformation(set1, set1);
249 
250         // Image appearance //
251         if (imageAppearanceWeight!=0)
252         {
253             // Have to accumulate the transformation along all the iterations
254             if (ii==0)
255             {
256                 if ( !transDown.empty() )
257                 {
258                     image2.copyTo(warpedImage);
259                 }
260                 else
261                 {
262                     image1.copyTo(warpedImage);
263                 }
264             }
265             transformer->warpImage(warpedImage, warpedImage);
266         }
267     }
268 
269     Mat gaussWindow, diffIm;
270     if (imageAppearanceWeight!=0)
271     {
272         // compute appearance cost
273         if ( !transDown.empty() )
274         {
275             resize(warpedImage, warpedImage, image1.size());
276             Mat temp=(warpedImage-image1);
277             multiply(temp, temp, diffIm);
278         }
279         else
280         {
281             resize(warpedImage, warpedImage, image2.size());
282             Mat temp=(warpedImage-image2);
283             multiply(temp, temp, diffIm);
284         }
285         gaussWindow = Mat::zeros(warpedImage.rows, warpedImage.cols, CV_32F);
286         for (pt=0; pt<sset1.cols; pt++)
287         {
288             Point2f p = sset1.at<Point2f>(0,pt);
289             for (ii=0; ii<diffIm.rows; ii++)
290             {
291                 for (jj=0; jj<diffIm.cols; jj++)
292                 {
293                     float val = float(std::exp( -float( (p.x-jj)*(p.x-jj) + (p.y-ii)*(p.y-ii) )/(2*sigma*sigma) ) / (sigma*sigma*2*CV_PI));
294                     gaussWindow.at<float>(ii,jj) += val;
295                 }
296             }
297         }
298 
299         Mat appIm(diffIm.rows, diffIm.cols, CV_32F);
300         for (ii=0; ii<diffIm.rows; ii++)
301         {
302             for (jj=0; jj<diffIm.cols; jj++)
303             {
304                 float elema=float( diffIm.at<uchar>(ii,jj) )/255;
305                 float elemb=gaussWindow.at<float>(ii,jj);
306                 appIm.at<float>(ii,jj) = elema*elemb;
307             }
308         }
309         iAppearance = float(cv::sum(appIm)[0]/sset1.cols);
310     }
311     sDistance = matcher.getMatchingCost();
312 
313     return (sDistance*shapeContextWeight+bEnergy*bendingEnergyWeight+iAppearance*imageAppearanceWeight);
314 }
315 
createShapeContextDistanceExtractor(int nAngularBins,int nRadialBins,float innerRadius,float outerRadius,int iterations,const Ptr<HistogramCostExtractor> & comparer,const Ptr<ShapeTransformer> & transformer)316 Ptr <ShapeContextDistanceExtractor> createShapeContextDistanceExtractor(int nAngularBins, int nRadialBins, float innerRadius, float outerRadius, int iterations,
317                                                                         const Ptr<HistogramCostExtractor> &comparer, const Ptr<ShapeTransformer> &transformer)
318 {
319     return Ptr <ShapeContextDistanceExtractor> ( new ShapeContextDistanceExtractorImpl(nAngularBins, nRadialBins, innerRadius,
320                                                                                        outerRadius, iterations, comparer, transformer) );
321 }
322 
323 //! SCD
extractSCD(cv::Mat & contour,cv::Mat & descriptors,const std::vector<int> & queryInliers,const float _meanDistance)324 void SCD::extractSCD(cv::Mat &contour, cv::Mat &descriptors, const std::vector<int> &queryInliers, const float _meanDistance)
325 {
326     cv::Mat contourMat = contour;
327     cv::Mat disMatrix = cv::Mat::zeros(contourMat.cols, contourMat.cols, CV_32F);
328     cv::Mat angleMatrix = cv::Mat::zeros(contourMat.cols, contourMat.cols, CV_32F);
329 
330     std::vector<double> logspaces, angspaces;
331     logarithmicSpaces(logspaces);
332     angularSpaces(angspaces);
333     buildNormalizedDistanceMatrix(contourMat, disMatrix, queryInliers, _meanDistance);
334     buildAngleMatrix(contourMat, angleMatrix);
335 
336     // Now, build the descriptor matrix (each row is a point) //
337     descriptors = cv::Mat::zeros(contourMat.cols, descriptorSize(), CV_32F);
338 
339     for (int ptidx=0; ptidx<contourMat.cols; ptidx++)
340     {
341         for (int cmp=0; cmp<contourMat.cols; cmp++)
342         {
343             if (ptidx==cmp) continue;
344             if ((int)queryInliers.size()>0)
345             {
346                 if (queryInliers[ptidx]==0 || queryInliers[cmp]==0) continue; //avoid outliers
347             }
348 
349             int angidx=-1, radidx=-1;
350             for (int i=0; i<nRadialBins; i++)
351             {
352                 if (disMatrix.at<float>(ptidx, cmp)<logspaces[i])
353                 {
354                     radidx=i;
355                     break;
356                 }
357             }
358             for (int i=0; i<nAngularBins; i++)
359             {
360                 if (angleMatrix.at<float>(ptidx, cmp)<angspaces[i])
361                 {
362                     angidx=i;
363                     break;
364                 }
365             }
366             if (angidx!=-1 && radidx!=-1)
367             {
368                 int idx = angidx+radidx*nAngularBins;
369                 descriptors.at<float>(ptidx, idx)++;
370             }
371         }
372     }
373 }
374 
logarithmicSpaces(std::vector<double> & vecSpaces) const375 void SCD::logarithmicSpaces(std::vector<double> &vecSpaces) const
376 {
377     double logmin=log10(innerRadius);
378     double logmax=log10(outerRadius);
379     double delta=(logmax-logmin)/(nRadialBins-1);
380     double accdelta=0;
381 
382     for (int i=0; i<nRadialBins; i++)
383     {
384         double val = std::pow(10,logmin+accdelta);
385         vecSpaces.push_back(val);
386         accdelta += delta;
387     }
388 }
389 
angularSpaces(std::vector<double> & vecSpaces) const390 void SCD::angularSpaces(std::vector<double> &vecSpaces) const
391 {
392     double delta=2*CV_PI/nAngularBins;
393     double val=0;
394 
395     for (int i=0; i<nAngularBins; i++)
396     {
397         val += delta;
398         vecSpaces.push_back(val);
399     }
400 }
401 
buildNormalizedDistanceMatrix(cv::Mat & contour,cv::Mat & disMatrix,const std::vector<int> & queryInliers,const float _meanDistance)402 void SCD::buildNormalizedDistanceMatrix(cv::Mat &contour, cv::Mat &disMatrix, const std::vector<int> &queryInliers, const float _meanDistance)
403 {
404     cv::Mat contourMat = contour;
405     cv::Mat mask(disMatrix.rows, disMatrix.cols, CV_8U);
406 
407     for (int i=0; i<contourMat.cols; i++)
408     {
409       for (int j=0; j<contourMat.cols; j++)
410       {
411           disMatrix.at<float>(i,j) = (float)norm( cv::Mat(contourMat.at<cv::Point2f>(0,i)-contourMat.at<cv::Point2f>(0,j)), cv::NORM_L2 );
412           if (_meanDistance<0)
413           {
414               if (queryInliers.size()>0)
415               {
416                   mask.at<char>(i,j)=char(queryInliers[j] && queryInliers[i]);
417               }
418               else
419               {
420                   mask.at<char>(i,j)=1;
421               }
422           }
423       }
424     }
425 
426     if (_meanDistance<0)
427     {
428       meanDistance=(float)mean(disMatrix, mask)[0];
429     }
430     else
431     {
432       meanDistance=_meanDistance;
433     }
434     disMatrix/=meanDistance+FLT_EPSILON;
435 }
436 
buildAngleMatrix(cv::Mat & contour,cv::Mat & angleMatrix) const437 void SCD::buildAngleMatrix(cv::Mat &contour, cv::Mat &angleMatrix) const
438 {
439     cv::Mat contourMat = contour;
440 
441     // if descriptor is rotationInvariant compute massCenter //
442     cv::Point2f massCenter(0,0);
443     if (rotationInvariant)
444     {
445         for (int i=0; i<contourMat.cols; i++)
446         {
447             massCenter+=contourMat.at<cv::Point2f>(0,i);
448         }
449         massCenter.x=massCenter.x/(float)contourMat.cols;
450         massCenter.y=massCenter.y/(float)contourMat.cols;
451     }
452 
453 
454     for (int i=0; i<contourMat.cols; i++)
455     {
456         for (int j=0; j<contourMat.cols; j++)
457         {
458             if (i==j)
459             {
460                 angleMatrix.at<float>(i,j)=0.0;
461             }
462             else
463             {
464                 cv::Point2f dif = contourMat.at<cv::Point2f>(0,i) - contourMat.at<cv::Point2f>(0,j);
465                 angleMatrix.at<float>(i,j) = std::atan2(dif.y, dif.x);
466 
467                 if (rotationInvariant)
468                 {
469                     cv::Point2f refPt = contourMat.at<cv::Point2f>(0,i) - massCenter;
470                     float refAngle = atan2(refPt.y, refPt.x);
471                     angleMatrix.at<float>(i,j) -= refAngle;
472                 }
473                 angleMatrix.at<float>(i,j) = float(fmod(double(angleMatrix.at<float>(i,j)+(double)FLT_EPSILON),2*CV_PI)+CV_PI);
474             }
475         }
476     }
477 }
478 
479 //! SCDMatcher
matchDescriptors(cv::Mat & descriptors1,cv::Mat & descriptors2,std::vector<cv::DMatch> & matches,cv::Ptr<cv::HistogramCostExtractor> & comparer,std::vector<int> & inliers1,std::vector<int> & inliers2)480 void SCDMatcher::matchDescriptors(cv::Mat &descriptors1, cv::Mat &descriptors2, std::vector<cv::DMatch> &matches,
481                                   cv::Ptr<cv::HistogramCostExtractor> &comparer, std::vector<int> &inliers1, std::vector<int> &inliers2)
482 {
483     matches.clear();
484 
485     // Build the cost Matrix between descriptors //
486     cv::Mat costMat;
487     buildCostMatrix(descriptors1, descriptors2, costMat, comparer);
488 
489     // Solve the matching problem using the hungarian method //
490     hungarian(costMat, matches, inliers1, inliers2, descriptors1.rows, descriptors2.rows);
491 }
492 
buildCostMatrix(const cv::Mat & descriptors1,const cv::Mat & descriptors2,cv::Mat & costMatrix,cv::Ptr<cv::HistogramCostExtractor> & comparer) const493 void SCDMatcher::buildCostMatrix(const cv::Mat &descriptors1, const cv::Mat &descriptors2,
494                                  cv::Mat &costMatrix, cv::Ptr<cv::HistogramCostExtractor> &comparer) const
495 {
496     comparer->buildCostMatrix(descriptors1, descriptors2, costMatrix);
497 }
498 
hungarian(cv::Mat & costMatrix,std::vector<cv::DMatch> & outMatches,std::vector<int> & inliers1,std::vector<int> & inliers2,int sizeScd1,int sizeScd2)499 void SCDMatcher::hungarian(cv::Mat &costMatrix, std::vector<cv::DMatch> &outMatches, std::vector<int> &inliers1,
500                            std::vector<int> &inliers2, int sizeScd1, int sizeScd2)
501 {
502     std::vector<int> free(costMatrix.rows, 0), collist(costMatrix.rows, 0);
503     std::vector<int> matches(costMatrix.rows, 0), colsol(costMatrix.rows), rowsol(costMatrix.rows);
504     std::vector<float> d(costMatrix.rows), pred(costMatrix.rows), v(costMatrix.rows);
505 
506     const float LOWV = 1e-10f;
507     bool unassignedfound;
508     int  i=0, imin=0, numfree=0, prvnumfree=0, f=0, i0=0, k=0, freerow=0;
509     int  j=0, j1=0, j2=0, endofpath=0, last=0, low=0, up=0;
510     float min=0, h=0, umin=0, usubmin=0, v2=0;
511 
512     // COLUMN REDUCTION //
513     for (j = costMatrix.rows-1; j >= 0; j--)
514     {
515         // find minimum cost over rows.
516         min = costMatrix.at<float>(0,j);
517         imin = 0;
518         for (i = 1; i < costMatrix.rows; i++)
519         if (costMatrix.at<float>(i,j) < min)
520         {
521             min = costMatrix.at<float>(i,j);
522             imin = i;
523         }
524         v[j] = min;
525 
526         if (++matches[imin] == 1)
527         {
528             rowsol[imin] = j;
529             colsol[j] = imin;
530         }
531         else
532         {
533             colsol[j]=-1;
534         }
535     }
536 
537     // REDUCTION TRANSFER //
538     for (i=0; i<costMatrix.rows; i++)
539     {
540         if (matches[i] == 0)
541         {
542             free[numfree++] = i;
543         }
544         else
545         {
546             if (matches[i] == 1)
547             {
548                 j1=rowsol[i];
549                 min=std::numeric_limits<float>::max();
550                 for (j=0; j<costMatrix.rows; j++)
551                 {
552                     if (j!=j1)
553                     {
554                         if (costMatrix.at<float>(i,j)-v[j] < min)
555                         {
556                             min=costMatrix.at<float>(i,j)-v[j];
557                         }
558                     }
559                 }
560                 v[j1] = v[j1]-min;
561             }
562         }
563     }
564     // AUGMENTING ROW REDUCTION //
565     int loopcnt = 0;
566     do
567     {
568         loopcnt++;
569         k=0;
570         prvnumfree=numfree;
571         numfree=0;
572         while (k < prvnumfree)
573         {
574             i=free[k];
575             k++;
576             umin = costMatrix.at<float>(i,0)-v[0];
577             j1=0;
578             usubmin = std::numeric_limits<float>::max();
579             for (j=1; j<costMatrix.rows; j++)
580             {
581                 h = costMatrix.at<float>(i,j)-v[j];
582                 if (h < usubmin)
583                 {
584                     if (h >= umin)
585                     {
586                         usubmin = h;
587                         j2 = j;
588                     }
589                     else
590                     {
591                         usubmin = umin;
592                         umin = h;
593                         j2 = j1;
594                         j1 = j;
595                     }
596                 }
597             }
598             i0 = colsol[j1];
599 
600             if (fabs(umin-usubmin) > LOWV) //if( umin < usubmin )
601             {
602                 v[j1] = v[j1] - (usubmin - umin);
603             }
604             else // minimum and subminimum equal.
605             {
606                 if (i0 >= 0) // minimum column j1 is assigned.
607                 {
608                     j1 = j2;
609                     i0 = colsol[j2];
610                 }
611             }
612             // (re-)assign i to j1, possibly de-assigning an i0.
613             rowsol[i]=j1;
614             colsol[j1]=i;
615 
616             if (i0 >= 0)
617             {
618                 //if( umin < usubmin )
619                 if (fabs(umin-usubmin) > LOWV)
620                 {
621                     free[--k] = i0;
622                 }
623                 else
624                 {
625                     free[numfree++] = i0;
626                 }
627             }
628         }
629     }while (loopcnt<2); // repeat once.
630 
631     // AUGMENT SOLUTION for each free row //
632     for (f = 0; f<numfree; f++)
633     {
634         freerow = free[f];       // start row of augmenting path.
635         // Dijkstra shortest path algorithm.
636         // runs until unassigned column added to shortest path tree.
637         for (j = 0; j < costMatrix.rows; j++)
638         {
639             d[j] = costMatrix.at<float>(freerow,j) - v[j];
640             pred[j] = float(freerow);
641             collist[j] = j;        // init column list.
642         }
643 
644         low=0; // columns in 0..low-1 are ready, now none.
645         up=0;  // columns in low..up-1 are to be scanned for current minimum, now none.
646         unassignedfound = false;
647         do
648         {
649             if (up == low)
650             {
651                 last=low-1;
652                 min = d[collist[up++]];
653                 for (k = up; k < costMatrix.rows; k++)
654                 {
655                     j = collist[k];
656                     h = d[j];
657                     if (h <= min)
658                     {
659                         if (h < min) // new minimum.
660                         {
661                             up = low; // restart list at index low.
662                             min = h;
663                         }
664                         collist[k] = collist[up];
665                         collist[up++] = j;
666                     }
667                 }
668                 for (k=low; k<up; k++)
669                 {
670                     if (colsol[collist[k]] < 0)
671                     {
672                         endofpath = collist[k];
673                         unassignedfound = true;
674                         break;
675                     }
676                 }
677             }
678 
679             if (!unassignedfound)
680             {
681                 // update 'distances' between freerow and all unscanned columns, via next scanned column.
682                 j1 = collist[low];
683                 low++;
684                 i = colsol[j1];
685                 h = costMatrix.at<float>(i,j1)-v[j1]-min;
686 
687                 for (k = up; k < costMatrix.rows; k++)
688                 {
689                     j = collist[k];
690                     v2 = costMatrix.at<float>(i,j) - v[j] - h;
691                     if (v2 < d[j])
692                     {
693                         pred[j] = float(i);
694                         if (v2 == min)
695                         {
696                             if (colsol[j] < 0)
697                             {
698                                 // if unassigned, shortest augmenting path is complete.
699                                 endofpath = j;
700                                 unassignedfound = true;
701                                 break;
702                             }
703                             else
704                             {
705                                 collist[k] = collist[up];
706                                 collist[up++] = j;
707                             }
708                         }
709                         d[j] = v2;
710                     }
711                 }
712             }
713         }while (!unassignedfound);
714 
715         // update column prices.
716         for (k = 0; k <= last; k++)
717         {
718             j1 = collist[k];
719             v[j1] = v[j1] + d[j1] - min;
720         }
721 
722         // reset row and column assignments along the alternating path.
723         do
724         {
725             i = int(pred[endofpath]);
726             colsol[endofpath] = i;
727             j1 = endofpath;
728             endofpath = rowsol[i];
729             rowsol[i] = j1;
730         }while (i != freerow);
731     }
732 
733     // calculate symmetric shape context cost
734     cv::Mat trueCostMatrix(costMatrix, cv::Rect(0,0,sizeScd1, sizeScd2));
735     float leftcost = 0;
736     for (int nrow=0; nrow<trueCostMatrix.rows; nrow++)
737     {
738         double minval;
739         minMaxIdx(trueCostMatrix.row(nrow), &minval);
740         leftcost+=float(minval);
741     }
742     leftcost /= trueCostMatrix.rows;
743 
744     float rightcost = 0;
745     for (int ncol=0; ncol<trueCostMatrix.cols; ncol++)
746     {
747         double minval;
748         minMaxIdx(trueCostMatrix.col(ncol), &minval);
749         rightcost+=float(minval);
750     }
751     rightcost /= trueCostMatrix.cols;
752 
753     minMatchCost = std::max(leftcost,rightcost);
754 
755     // Save in a DMatch vector
756     for (i=0;i<costMatrix.cols;i++)
757     {
758         cv::DMatch singleMatch(colsol[i],i,costMatrix.at<float>(colsol[i],i));//queryIdx,trainIdx,distance
759         outMatches.push_back(singleMatch);
760     }
761 
762     // Update inliers
763     inliers1.reserve(sizeScd1);
764     for (size_t kc = 0; kc<inliers1.size(); kc++)
765     {
766         if (rowsol[kc]<sizeScd1) // if a real match
767             inliers1[kc]=1;
768         else
769             inliers1[kc]=0;
770     }
771     inliers2.reserve(sizeScd2);
772     for (size_t kc = 0; kc<inliers2.size(); kc++)
773     {
774         if (colsol[kc]<sizeScd2) // if a real match
775             inliers2[kc]=1;
776         else
777             inliers2[kc]=0;
778     }
779 }
780 
781 }
782