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  #include "precomp.hpp"
  #include "gcgraph.hpp"
  #include <limits>
  
  using namespace cv;
  
  /*
  This is implementation of image segmentation algorithm GrabCut described in
  "GrabCut — Interactive Foreground Extraction using Iterated Graph Cuts".
  Carsten Rother, Vladimir Kolmogorov, Andrew Blake.
   */
  
  /*
   GMM - Gaussian Mixture Model
  */
  class GMM
  {
  public:
      static const int componentsCount = 5;
  
      GMM( Mat& _model );
      double operator()( const Vec3d color ) const;
      double operator()( int ci, const Vec3d color ) const;
      int whichComponent( const Vec3d color ) const;
  
      void initLearning();
      void addSample( int ci, const Vec3d color );
      void endLearning();
  
  private:
      void calcInverseCovAndDeterm( int ci );
      Mat model;
      double* coefs;
      double* mean;
      double* cov;
  
      double inverseCovs[componentsCount][3][3];
      double covDeterms[componentsCount];
  
      double sums[componentsCount][3];
      double prods[componentsCount][3][3];
      int sampleCounts[componentsCount];
      int totalSampleCount;
  };
  
  GMM::GMM( Mat& _model )
  {
      const int modelSize = 3/*mean*/ + 9/*covariance*/ + 1/*component weight*/;
      if( _model.empty() )
      {
          _model.create( 1, modelSize*componentsCount, CV_64FC1 );
          _model.setTo(Scalar(0));
      }
      else if( (_model.type() != CV_64FC1) || (_model.rows != 1) || (_model.cols != modelSize*componentsCount) )
          CV_Error( CV_StsBadArg, "_model must have CV_64FC1 type, rows == 1 and cols == 13*componentsCount" );
  
      model = _model;
  
      coefs = model.ptr<double>(0);
      mean = coefs + componentsCount;
      cov = mean + 3*componentsCount;
  
      for( int ci = 0; ci < componentsCount; ci++ )
          if( coefs[ci] > 0 )
               calcInverseCovAndDeterm( ci );
  }
  
  double GMM::operator()( const Vec3d color ) const
  {
      double res = 0;
      for( int ci = 0; ci < componentsCount; ci++ )
          res += coefs[ci] * (*this)(ci, color );
      return res;
  }
  
  double GMM::operator()( int ci, const Vec3d color ) const
  {
      double res = 0;
      if( coefs[ci] > 0 )
      {
  		CV_Assert( covDeterms[ci] > std::numeric_limits<double>::epsilon() );
          Vec3d diff = color;
          double* m = mean + 3*ci;
          diff[0] -= m[0]; diff[1] -= m[1]; diff[2] -= m[2];
          double mult = diff[0]*(diff[0]*inverseCovs[ci][0][0] + diff[1]*inverseCovs[ci][1][0] + diff[2]*inverseCovs[ci][2][0])
                     + diff[1]*(diff[0]*inverseCovs[ci][0][1] + diff[1]*inverseCovs[ci][1][1] + diff[2]*inverseCovs[ci][2][1])
                     + diff[2]*(diff[0]*inverseCovs[ci][0][2] + diff[1]*inverseCovs[ci][1][2] + diff[2]*inverseCovs[ci][2][2]);
          res = 1.0f/sqrt(covDeterms[ci]) * exp(-0.5f*mult);
      }
      return res;
  }
  
  int GMM::whichComponent( const Vec3d color ) const
  {
      int k = 0;
      double max = 0;
  
      for( int ci = 0; ci < componentsCount; ci++ )
      {
  		double p = (*this)( ci, color );
          if( p > max )
          {
              k = ci;
              max = p;
          }
      }
      return k;
  }
  
  void GMM::initLearning()
  {
      for( int ci = 0; ci < componentsCount; ci++)
      {
          sums[ci][0] = sums[ci][1] = sums[ci][2] = 0;
          prods[ci][0][0] = prods[ci][0][1] = prods[ci][0][2] = 0;
          prods[ci][1][0] = prods[ci][1][1] = prods[ci][1][2] = 0;
          prods[ci][2][0] = prods[ci][2][1] = prods[ci][2][2] = 0;
          sampleCounts[ci] = 0;
      }
      totalSampleCount = 0;
  }
  
  void GMM::addSample( int ci, const Vec3d color )
  {
      sums[ci][0] += color[0]; sums[ci][1] += color[1]; sums[ci][2] += color[2];
      prods[ci][0][0] += color[0]*color[0]; prods[ci][0][1] += color[0]*color[1]; prods[ci][0][2] += color[0]*color[2];
      prods[ci][1][0] += color[1]*color[0]; prods[ci][1][1] += color[1]*color[1]; prods[ci][1][2] += color[1]*color[2];
      prods[ci][2][0] += color[2]*color[0]; prods[ci][2][1] += color[2]*color[1]; prods[ci][2][2] += color[2]*color[2];
      sampleCounts[ci]++;
      totalSampleCount++;
  }
  
  void GMM::endLearning()
  {
      const double variance = 0.01;
      for( int ci = 0; ci < componentsCount; ci++ )
      {
          int n = sampleCounts[ci];
          if( n == 0 )
              coefs[ci] = 0;
          else
          {
              coefs[ci] = (double)n/totalSampleCount;
  
              double* m = mean + 3*ci;
              m[0] = sums[ci][0]/n; m[1] = sums[ci][1]/n; m[2] = sums[ci][2]/n;
  
              double* c = cov + 9*ci;
              c[0] = prods[ci][0][0]/n - m[0]*m[0]; c[1] = prods[ci][0][1]/n - m[0]*m[1]; c[2] = prods[ci][0][2]/n - m[0]*m[2];
              c[3] = prods[ci][1][0]/n - m[1]*m[0]; c[4] = prods[ci][1][1]/n - m[1]*m[1]; c[5] = prods[ci][1][2]/n - m[1]*m[2];
              c[6] = prods[ci][2][0]/n - m[2]*m[0]; c[7] = prods[ci][2][1]/n - m[2]*m[1]; c[8] = prods[ci][2][2]/n - m[2]*m[2];
  
              double dtrm = c[0]*(c[4]*c[8]-c[5]*c[7]) - c[1]*(c[3]*c[8]-c[5]*c[6]) + c[2]*(c[3]*c[7]-c[4]*c[6]);
              if( dtrm < std::numeric_limits<double>::epsilon() )
              {
                  // Adds the white noise to avoid singular covariance matrix.
                  c[0] += variance;
                  c[4] += variance;
                  c[8] += variance;
              }
  
              calcInverseCovAndDeterm(ci);
          }
      }
  }
  
  void GMM::calcInverseCovAndDeterm( int ci )
  {
      if( coefs[ci] > 0 )
      {
          double *c = cov + 9*ci;
          double dtrm =
                covDeterms[ci] = c[0]*(c[4]*c[8]-c[5]*c[7]) - c[1]*(c[3]*c[8]-c[5]*c[6]) + c[2]*(c[3]*c[7]-c[4]*c[6]);
  
  		CV_Assert( dtrm > std::numeric_limits<double>::epsilon() );
          inverseCovs[ci][0][0] =  (c[4]*c[8] - c[5]*c[7]) / dtrm;
          inverseCovs[ci][1][0] = -(c[3]*c[8] - c[5]*c[6]) / dtrm;
          inverseCovs[ci][2][0] =  (c[3]*c[7] - c[4]*c[6]) / dtrm;
          inverseCovs[ci][0][1] = -(c[1]*c[8] - c[2]*c[7]) / dtrm;
          inverseCovs[ci][1][1] =  (c[0]*c[8] - c[2]*c[6]) / dtrm;
          inverseCovs[ci][2][1] = -(c[0]*c[7] - c[1]*c[6]) / dtrm;
          inverseCovs[ci][0][2] =  (c[1]*c[5] - c[2]*c[4]) / dtrm;
          inverseCovs[ci][1][2] = -(c[0]*c[5] - c[2]*c[3]) / dtrm;
          inverseCovs[ci][2][2] =  (c[0]*c[4] - c[1]*c[3]) / dtrm;
      }
  }
  
  /*
    Calculate beta - parameter of GrabCut algorithm.
    beta = 1/(2*avg(sqr(||color[i] - color[j]||)))
  */
  double calcBeta( const Mat& img )
  {
      double beta = 0;
      for( int y = 0; y < img.rows; y++ )
      {
          for( int x = 0; x < img.cols; x++ )
          {
              Vec3d color = img.at<Vec3b>(y,x);
              if( x>0 ) // left
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y,x-1);
                  beta += diff.dot(diff);
              }
              if( y>0 && x>0 ) // upleft
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x-1);
                  beta += diff.dot(diff);
              }
              if( y>0 ) // up
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x);
                  beta += diff.dot(diff);
              }
              if( y>0 && x<img.cols-1) // upright
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x+1);
                  beta += diff.dot(diff);
              }
          }
      }
      beta = 1.f / (2 * beta/(4*img.cols*img.rows - 3*img.cols - 3*img.rows + 2) );
      return beta;
  }
  
  /*
    Calculate weights of noterminal vertices of graph.
    beta and gamma - parameters of GrabCut algorithm.
   */
  void calcNWeights( const Mat& img, Mat& leftW, Mat& upleftW, Mat& upW, Mat& uprightW, double beta, double gamma )
  {
      const double gammaDivSqrt2 = gamma / std::sqrt(2.0f);
      leftW.create( img.rows, img.cols, CV_64FC1 );
      upleftW.create( img.rows, img.cols, CV_64FC1 );
      upW.create( img.rows, img.cols, CV_64FC1 );
      uprightW.create( img.rows, img.cols, CV_64FC1 );
      for( int y = 0; y < img.rows; y++ )
      {
          for( int x = 0; x < img.cols; x++ )
          {
              Vec3d color = img.at<Vec3b>(y,x);
              if( x-1>=0 ) // left
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y,x-1);
                  leftW.at<double>(y,x) = gamma * exp(-beta*diff.dot(diff));
              }
              else
                  leftW.at<double>(y,x) = 0;
              if( x-1>=0 && y-1>=0 ) // upleft
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x-1);
                  upleftW.at<double>(y,x) = gammaDivSqrt2 * exp(-beta*diff.dot(diff));
              }
              else
                  upleftW.at<double>(y,x) = 0;
              if( y-1>=0 ) // up
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x);
                  upW.at<double>(y,x) = gamma * exp(-beta*diff.dot(diff));
              }
              else
                  upW.at<double>(y,x) = 0;
              if( x+1<img.cols-1 && y-1>=0 ) // upright
              {
                  Vec3d diff = color - (Vec3d)img.at<Vec3b>(y-1,x+1);
                  uprightW.at<double>(y,x) = gammaDivSqrt2 * exp(-beta*diff.dot(diff));
              }
              else
                  uprightW.at<double>(y,x) = 0;
          }
      }
  }
  
  /*
    Check size, type and element values of mask matrix.
   */
  void checkMask( const Mat& img, const Mat& mask )
  {
      if( mask.empty() )
          CV_Error( CV_StsBadArg, "mask is empty" );
      if( mask.type() != CV_8UC1 )
          CV_Error( CV_StsBadArg, "mask must have CV_8UC1 type" );
      if( mask.cols != img.cols || mask.rows != img.rows )
          CV_Error( CV_StsBadArg, "mask must have as many rows and cols as img" );
      for( int y = 0; y < mask.rows; y++ )
      {
          for( int x = 0; x < mask.cols; x++ )
          {
              uchar val = mask.at<uchar>(y,x);
              if( val!=GC_BGD && val!=GC_FGD && val!=GC_PR_BGD && val!=GC_PR_FGD )
                  CV_Error( CV_StsBadArg, "mask element value must be equel"
                      "GC_BGD or GC_FGD or GC_PR_BGD or GC_PR_FGD" );
          }
      }
  }
  
  /*
    Initialize mask using rectangular.
  */
  void initMaskWithRect( Mat& mask, Size imgSize, Rect rect )
  {
      mask.create( imgSize, CV_8UC1 );
      mask.setTo( GC_BGD );
  
      rect.x = max(0, rect.x);
      rect.y = max(0, rect.y);
      rect.width = min(rect.width, imgSize.width-rect.x);
      rect.height = min(rect.height, imgSize.height-rect.y);
  
      (mask(rect)).setTo( Scalar(GC_PR_FGD) );
  }
  
  /*
    Initialize GMM background and foreground models using kmeans algorithm.
  */
  void initGMMs( const Mat& img, const Mat& mask, GMM& bgdGMM, GMM& fgdGMM )
  {
      const int kMeansItCount = 10;
      const int kMeansType = KMEANS_PP_CENTERS;
  
      Mat bgdLabels, fgdLabels;
      vector<Vec3f> bgdSamples, fgdSamples;
      Point p;
      for( p.y = 0; p.y < img.rows; p.y++ )
      {
          for( p.x = 0; p.x < img.cols; p.x++ )
          {
              if( mask.at<uchar>(p) == GC_BGD || mask.at<uchar>(p) == GC_PR_BGD )
                  bgdSamples.push_back( (Vec3f)img.at<Vec3b>(p) );
              else // GC_FGD | GC_PR_FGD
                  fgdSamples.push_back( (Vec3f)img.at<Vec3b>(p) );
          }
      }
      CV_Assert( !bgdSamples.empty() && !fgdSamples.empty() );
      Mat _bgdSamples( (int)bgdSamples.size(), 3, CV_32FC1, &bgdSamples[0][0] );
      kmeans( _bgdSamples, GMM::componentsCount, bgdLabels,
              TermCriteria( CV_TERMCRIT_ITER, kMeansItCount, 0.0), 0, kMeansType, 0 );
      Mat _fgdSamples( (int)fgdSamples.size(), 3, CV_32FC1, &fgdSamples[0][0] );
      kmeans( _fgdSamples, GMM::componentsCount, fgdLabels,
              TermCriteria( CV_TERMCRIT_ITER, kMeansItCount, 0.0), 0, kMeansType, 0 );
  
      bgdGMM.initLearning();
      for( int i = 0; i < (int)bgdSamples.size(); i++ )
          bgdGMM.addSample( bgdLabels.at<int>(i,0), bgdSamples[i] );
      bgdGMM.endLearning();
  
      fgdGMM.initLearning();
      for( int i = 0; i < (int)fgdSamples.size(); i++ )
          fgdGMM.addSample( fgdLabels.at<int>(i,0), fgdSamples[i] );
      fgdGMM.endLearning();
  }
  
  /*
    Assign GMMs components for each pixel.
  */
  void assignGMMsComponents( const Mat& img, const Mat& mask, const GMM& bgdGMM, const GMM& fgdGMM, Mat& compIdxs )
  {
      Point p;
      for( p.y = 0; p.y < img.rows; p.y++ )
      {
          for( p.x = 0; p.x < img.cols; p.x++ )
          {
              Vec3d color = img.at<Vec3b>(p);
  			compIdxs.at<int>(p) = mask.at<uchar>(p) == GC_BGD || mask.at<uchar>(p) == GC_PR_BGD ?
                  bgdGMM.whichComponent(color) : fgdGMM.whichComponent(color);
          }
      }
  }
  
  /*
    Learn GMMs parameters.
  */
  void learnGMMs( const Mat& img, const Mat& mask, const Mat& compIdxs, GMM& bgdGMM, GMM& fgdGMM )
  {
      bgdGMM.initLearning();
      fgdGMM.initLearning();
      Point p;
      for( int ci = 0; ci < GMM::componentsCount; ci++ )
      {
          for( p.y = 0; p.y < img.rows; p.y++ )
          {
              for( p.x = 0; p.x < img.cols; p.x++ )
              {
                  if( compIdxs.at<int>(p) == ci )
                  {
                      if( mask.at<uchar>(p) == GC_BGD || mask.at<uchar>(p) == GC_PR_BGD )
                          bgdGMM.addSample( ci, img.at<Vec3b>(p) );
                      else
                          fgdGMM.addSample( ci, img.at<Vec3b>(p) );
                  }
              }
          }
      }
      bgdGMM.endLearning();
      fgdGMM.endLearning();
  }
  
  /*
    Construct GCGraph
  */
  void constructGCGraph( const Mat& img, const Mat& mask, const GMM& bgdGMM, const GMM& fgdGMM, double lambda,
                         const Mat& leftW, const Mat& upleftW, const Mat& upW, const Mat& uprightW,
                         GCGraph<double>& graph )
  {
      int vtxCount = img.cols*img.rows,
          edgeCount = 2*(4*img.cols*img.rows - 3*(img.cols + img.rows) + 2);
      graph.create(vtxCount, edgeCount);
      Point p;
      for( p.y = 0; p.y < img.rows; p.y++ )
      {
          for( p.x = 0; p.x < img.cols; p.x++)
          {
              // add node
              int vtxIdx = graph.addVtx();
              Vec3b color = img.at<Vec3b>(p);
  
              // set t-weights
              double fromSource, toSink;
              if( mask.at<uchar>(p) == GC_PR_BGD || mask.at<uchar>(p) == GC_PR_FGD )
              {
                  fromSource = -log( bgdGMM(color) );
                  toSink = -log( fgdGMM(color) );
              }
              else if( mask.at<uchar>(p) == GC_BGD )
              {
                  fromSource = 0;
                  toSink = lambda;
              }
              else // GC_FGD
              {
                  fromSource = lambda;
                  toSink = 0;
              }
              graph.addTermWeights( vtxIdx, fromSource, toSink );
  
              // set n-weights
              if( p.x>0 )
              {
                  double w = leftW.at<double>(p);
                  graph.addEdges( vtxIdx, vtxIdx-1, w, w );
              }
              if( p.x>0 && p.y>0 )
              {
                  double w = upleftW.at<double>(p);
                  graph.addEdges( vtxIdx, vtxIdx-img.cols-1, w, w );
              }
              if( p.y>0 )
              {
                  double w = upW.at<double>(p);
                  graph.addEdges( vtxIdx, vtxIdx-img.cols, w, w );
              }
              if( p.x<img.cols-1 && p.y>0 )
              {
                  double w = uprightW.at<double>(p);
                  graph.addEdges( vtxIdx, vtxIdx-img.cols+1, w, w );
              }
          }
      }
  }
  
  /*
    Estimate segmentation using MaxFlow algorithm
  */
  void estimateSegmentation( GCGraph<double>& graph, Mat& mask )
  {
      graph.maxFlow();
      Point p;
      for( p.y = 0; p.y < mask.rows; p.y++ )
      {
          for( p.x = 0; p.x < mask.cols; p.x++ )
          {
              if( mask.at<uchar>(p) == GC_PR_BGD || mask.at<uchar>(p) == GC_PR_FGD )
              {
                  if( graph.inSourceSegment( p.y*mask.cols+p.x /*vertex index*/ ) )
                      mask.at<uchar>(p) = GC_PR_FGD;
                  else
                      mask.at<uchar>(p) = GC_PR_BGD;
              }
          }
      }
  }
  
  void cv::grabCut( const Mat& img, Mat& mask, Rect rect,
               Mat& bgdModel, Mat& fgdModel,
               int iterCount, int mode )
  {
      if( img.empty() )
          CV_Error( CV_StsBadArg, "image is empty" );
      if( img.type() != CV_8UC3 )
          CV_Error( CV_StsBadArg, "image mush have CV_8UC3 type" );
  
      GMM bgdGMM( bgdModel ), fgdGMM( fgdModel );
      Mat compIdxs( img.size(), CV_32SC1 );
  
      if( mode == GC_INIT_WITH_RECT || mode == GC_INIT_WITH_MASK )
      {
          if( mode == GC_INIT_WITH_RECT )
              initMaskWithRect( mask, img.size(), rect );
          else // flag == GC_INIT_WITH_MASK
              checkMask( img, mask );
          initGMMs( img, mask, bgdGMM, fgdGMM );
      }
  
      if( iterCount <= 0)
          return;
  
      if( mode == GC_EVAL )
          checkMask( img, mask );
  
      const double gamma = 50;
      const double lambda = 9*gamma;
      const double beta = calcBeta( img );
  
      Mat leftW, upleftW, upW, uprightW;
      calcNWeights( img, leftW, upleftW, upW, uprightW, beta, gamma );
  
      for( int i = 0; i < iterCount; i++ )
      {
          GCGraph<double> graph;
          assignGMMsComponents( img, mask, bgdGMM, fgdGMM, compIdxs );
          learnGMMs( img, mask, compIdxs, bgdGMM, fgdGMM );
          constructGCGraph(img, mask, bgdGMM, fgdGMM, lambda, leftW, upleftW, upW, uprightW, graph );
          estimateSegmentation( graph, mask );
      }
  }
  