// split image into 8-bit channels
  // N.B.: when casting the transformation result to unsigned shorts
  // (8-bit channel), major rounding errors will occur.
  // As a result, the merging operation might
  // produce negative values or values > 1,  which are truncated subsequently.
  // When accurate X, Y and Z channels are required, prefer float channels!
  bool splitImageToxyY::apply(const image& img,
                              channel8& c1,
                              channel8& c2,
                              channel8& c3) const {
    point p;       // coordinates
    rgbPixel pix;          // single Pixel Element in RGB-values...
    float Y;               // channels
    float X, XYZ;          // help variables

    // make the channels size of source image...
    c1.resize(img.rows(),img.columns(),0,false,false);
    c2.resize(img.rows(),img.columns(),0,false,false);
    c3.resize(img.rows(),img.columns(),0,false,false);

    for (p.y=0;p.y<img.rows();p.y++)
      for (p.x=0;p.x<img.columns();p.x++) {
        // take pixel at position p
        pix = img.at(p);

  // see Gonzales & Woods for explanation of magic numbers
        X   = (((float)(pix.getRed())) *0.412453f +
               ((float)(pix.getGreen())) *0.357580f +
               ((float)(pix.getBlue())) *0.180423f)/255.0f;   // x
        Y   = (((float)(pix.getRed())) *0.212671f +
               ((float)(pix.getGreen())) *0.715160f +
               ((float)(pix.getBlue())) *0.072169f)/255.0f;   // y
        XYZ = (((float)(pix.getRed())) *0.644458f +
               ((float)(pix.getGreen())) *1.191933f +
               ((float)(pix.getBlue())) *1.202819f)/255.0f;   // Y

        if (XYZ>0.0f) {
          c1.at(p) = (ubyte)(X/XYZ*255.0f);  // x
          c2.at(p) = (ubyte)(Y/XYZ*255.0f);  // y
        }
        else {
          c1.at(p) = 0;   // x
          c2.at(p) = 0;   // y
        }

        c3.at(p) = (ubyte)(Y*255.0f);     // Y
      } // loop
    return true;
  }
  // On copy apply for type channel8!
  bool harrisCorners::apply(const channel8& src,channel8& dest) const {
    pointList pts;
    if (apply(src,pts)) {
      const parameters& par = getParameters();
      pointList::iterator it;
      dest.resize(src.size(),par.noCornerValue,false,true);
      for (it=pts.begin();it!=pts.end();++it) {
        dest.at(*it)=par.cornerValue;
      }
      return true;
    }

    return false;
  };
  // Quantization takes place here!
  bool medianCut::performQuantization(const image& src,
                                      image& dest,
                                      channel8& mask,
                                      palette &thePalette) const {

    // parameters and const variables
    const parameters& param = getParameters();
    const int imageRows=src.rows();          // number of rows in src
    const int imageCols=src.columns();       // number of columns in src

    // resize destination containers
    dest.resize(imageRows,imageCols,rgbPixel(),false,false);
    mask.resize(imageRows,imageCols,ubyte(),false,false);

    // Variables
    int row,col;            // row, column counters
    int r,g,b;              // red,green,blue
    ivector iVec(3);        // int-vector

    std::list<boxInfo> theLeaves; // list of leaves (tree without root
                                  // and nodes)
    std::list<boxInfo>::iterator  splitPos;   // position to split
    std::list<boxInfo>::iterator  iter;       // iterator for theLeaves

    // create histogram with desired pre-quantization dimensions from src
    histogram theHist(3,param.preQuant);

    const float factor = param.preQuant/256.0f;

    for (row = 0 ; row < imageRows ; row++) {
      for (col = 0 ; col < imageCols ; col++) {

        r = static_cast<int>(src.at( row,col ).getRed()   * factor);
        g = static_cast<int>(src.at( row,col ).getGreen() * factor);
        b = static_cast<int>(src.at( row,col ).getBlue()  * factor);
        
        // insert point with quantized color
        dest.at(row,col).set((r*256+128)/param.preQuant,
                             (g*256+128)/param.preQuant,
                             (b*256+128)/param.preQuant,0); 

        iVec[0] = r;
        iVec[1] = g;
        iVec[2] = b;

        theHist.put(iVec);
      }
    }

    // initialization of first box of list (the whole histogram)
    boxInfo theBox(rgbPixel(0,0,0),
                   rgbPixel(param.preQuant-1,
                            param.preQuant-1,
                            param.preQuant-1));

    computeBoxInfo(theHist,theBox);

    // return, if desired number of colors smaller than colors in
    // pre-quantized image
    if (theBox.colors < param.numberOfColors) {

      thePalette.resize(theBox.colors,rgbPixel(),false,false);

      // prepare palette     
      int i = 0;
      for (r=0;r<param.preQuant;++r) {
        for (g=0;g<param.preQuant;++g) {
          for (b=0;b<param.preQuant;++b) {
            iVec[0] = r;
            iVec[1] = g;
            iVec[2] = b;
            if (theHist.at(iVec) > 0) {
              thePalette.at(i).set((r*256+128)/param.preQuant,
                                   (g*256+128)/param.preQuant,
                                   (b*256+128)/param.preQuant);
            }
          }
        }
      }

      // use the palette to generate the corresponding channel
      usePalette colorizer;
      colorizer.apply(dest,thePalette,mask);
      
      return true;
    }

    // Push first box into List
    theLeaves.push_back(theBox);

    // MAIN LOOP (do this until you have enough leaves (count), or no
    // splittable boxes (entries))
    int count, entries=1;  // auxiliary variables for the main loop
    for (count=1; (count<param.numberOfColors) && (entries!=0); count++) {

      // find box with largest number of entries from list
      entries = 0;
      for (iter = theLeaves.begin() ; iter != theLeaves.end() ; iter++) {
        if ( (*iter).colorFrequency > entries ) {
          // Avoid choosing single colors, i.e. unsplittable boxes
          if (  ((*iter).max.getRed()   > (*iter).min.getRed())   ||
                ((*iter).max.getGreen() > (*iter).min.getGreen()) ||
                ((*iter).max.getBlue()  > (*iter).min.getBlue()) ) {
            entries   = (*iter).colorFrequency;
            splitPos  = iter;
          }
        }
      }

      // A splittable box was found.
      // The iterator "splitPos" indicates its position in the List
      if (entries >0) {
        // Determine next axis to split (largest variance) and box dimensions
        int splitAxis;  // split axis indicator
        if ( ((*splitPos).var[0] >= (*splitPos).var[1]) &&
             ((*splitPos).var[0] >= (*splitPos).var[2]) ) {
          splitAxis = 0;  // red axis
        }
        else if ( (*splitPos).var[1] >= (*splitPos).var[2] ) {
          splitAxis = 1;  // green axis
        }
        else {
          splitAxis = 2;  // blue axis
        }

        int rMax  = ((*splitPos).max.getRed());
        int rMin  = ((*splitPos).min.getRed());
        int gMax  = ((*splitPos).max.getGreen());
        int gMin  = ((*splitPos).min.getGreen());
        int bMax  = ((*splitPos).max.getBlue());
        int bMin  = ((*splitPos).min.getBlue());

        // pass through box along the axis to split
        bool found;             // becomes true when split plane is found
        int nrOfCols=0;         // counter: number of colors of box
        int prevNrOfCols=0;     // forerunner of nrOfCols
        rgbPixel lower1;   // lower pixel from box 1
        rgbPixel upper1;   // upper pixel from box 1
        rgbPixel lower2;   // lower pixel from box 2
        rgbPixel upper2;   // upper pixel from box 2

        switch (splitAxis) {
          case 0: // red axis
            nrOfCols = 0;
            for (r = rMin , found = false ; (!found) && (r<=rMax) ; r++) {
              prevNrOfCols = nrOfCols;
              for (g = gMin ; g <= gMax ; g++) {
                for (b=bMin;b<=bMax;b++) {
                  iVec[0] = r;
                  iVec[1] = g;
                  iVec[2] = b;
                  if (theHist.at(iVec) > 0.0) {
                    nrOfCols += static_cast<long int>(theHist.at(iVec));
                  }
                }
              }
              if ( nrOfCols >= (*splitPos).colorFrequency/2 ) {
                found=true;
              }
            }
            if (fabs(prevNrOfCols -
                     static_cast<float>((*splitPos).colorFrequency)/2) <
                fabs(nrOfCols     -
                     static_cast<float>((*splitPos).colorFrequency)/2)) {
                r--;
                nrOfCols = prevNrOfCols;
            }
            // first box
            lower1.setRed(rMin);  lower1.setGreen(gMin);  lower1.setBlue(bMin);
            upper1.setRed(r-1);   upper1.setGreen(gMax);  upper1.setBlue(bMax);
            // second box
            lower2.setRed(r);     lower2.setGreen(gMin);  lower2.setBlue(bMin);
            upper2.setRed(rMax);  upper2.setGreen(gMax);  upper2.setBlue(bMax);
            break;

          case 1: // g axis
            nrOfCols = 0;
            for (g = gMin , found = false ; (!found) && (g<=gMax) ; g++) {
              prevNrOfCols = nrOfCols;
              for (r = rMin ; r <= rMax ; r++) {
                for (b = bMin ; b <= bMax ; b++) {
                  iVec[0] = r;
                  iVec[1] = g;
                  iVec[2] = b;
                  if (theHist.at(iVec) > 0.0) {
                    nrOfCols += static_cast<long int>(theHist.at(iVec));
                  }
                }
              }
              if ( nrOfCols >= (*splitPos).colorFrequency/2 ) {
                found=true;
              }
            }
            if (fabs(prevNrOfCols -
                     static_cast<float>((*splitPos).colorFrequency)/2) <
                fabs(nrOfCols     -
                     static_cast<float>((*splitPos).colorFrequency)/2)) {
                g--;
                nrOfCols = prevNrOfCols;
            }
            // first box
            lower1.setRed(rMin);  lower1.setGreen(gMin);  lower1.setBlue(bMin);
            upper1.setRed(rMax);  upper1.setGreen(g-1);   upper1.setBlue(bMax);
            // second box
            lower2.setRed(rMin);  lower2.setGreen(g);     lower2.setBlue(bMin);
            upper2.setRed(rMax);  upper2.setGreen(gMax);  upper2.setBlue(bMax);
            break;

          case 2: // b axis
            nrOfCols = 0;
            for (b = bMin , found = false ; (!found) && (b<=bMax) ; b++) {
              prevNrOfCols = nrOfCols;
              for (r = rMin ; r <= rMax ; r++) {
                for (g = gMin ; g <= gMax ; g++) {
                  iVec[0] = r;
                  iVec[1] = g;
                  iVec[2] = b;
                  if (theHist.at(iVec) > 0.0) {
                    nrOfCols += static_cast<long int>(theHist.at(iVec));
                  }
                }
              }
              if ( nrOfCols >= (*splitPos).colorFrequency/2 ) {
                found=true;
              }
            }
            if (fabs(prevNrOfCols -
                     static_cast<float>((*splitPos).colorFrequency)/2) <
                fabs(nrOfCols     -
                     static_cast<float>((*splitPos).colorFrequency)/2)) {
                b--;
                nrOfCols = prevNrOfCols;
            }
            // first box
            lower1.setRed(rMin); lower1.setGreen(gMin); lower1.setBlue(bMin);
            upper1.setRed(rMax); upper1.setGreen(gMax); upper1.setBlue(b-1);
            // second box
            lower2.setRed(rMin); lower2.setGreen(gMin); lower2.setBlue(b);
            upper2.setRed(rMax); upper2.setGreen(gMax); upper2.setBlue(bMax);
            break;
          default:
            break;
        } // end of switch

        // compute box info of new boxes and
        // append both at the end of list
        theBox.min = lower1;
        theBox.max = upper1;
        computeBoxInfo(theHist,theBox);
        theLeaves.push_back(theBox);

        theBox.min = lower2;
        theBox.max = upper2;
        computeBoxInfo(theHist,theBox);
        theLeaves.push_back(theBox);

        // delete splited box from list
        theLeaves.erase(splitPos);
      }

    } // end of for (MAIN LOOP)

    // compute block histogram and respective color palette
    thePalette.resize(theLeaves.size());
    int i;
    for (iter = theLeaves.begin() , i=0 ;
         iter != theLeaves.end() ;
         iter++ , i++) {
      // misuse histogram as a look-up-table
      for (r = (*iter).min.getRed(); r <= (*iter).max.getRed(); r++) {
        for (g = (*iter).min.getGreen(); g <= (*iter).max.getGreen(); g++) {
          for (b = (*iter).min.getBlue(); b <= (*iter).max.getBlue(); b++) {
            iVec[0] = r;
            iVec[1] = g;
            iVec[2] = b;
            theHist.at(iVec) = i; // insert palette-index (refers to
                                  // color in palette)
          }
        }
      }

      // create palette
      r = (static_cast<int>((*iter).mean[0]*factor)*256+128)/param.preQuant;
      g = (static_cast<int>((*iter).mean[1]*factor)*256+128)/param.preQuant;
      b = (static_cast<int>((*iter).mean[2]*factor)*256+128)/param.preQuant;
      thePalette[i].set(r,g,b,0);  // insert color
    }

    // create new image with palette and theHist
    dest.resize(imageRows,imageCols);
    mask.resize(imageRows,imageCols,0,false,true);

    // <= 256 colors? then also fill the mask
    if (thePalette.size() <= 256) {
      for (row = 0 ; row < imageRows ; row++) {
        for (col = 0 ; col < imageCols ; col++) {
          iVec[0] = static_cast<int>(src.at( row,col ).getRed()   * factor);
          iVec[1] = static_cast<int>(src.at( row,col ).getGreen() * factor);
          iVec[2] = static_cast<int>(src.at( row,col ).getBlue()  * factor);

          i = static_cast<int>(theHist.at( iVec ));

          dest.at(row,col) = thePalette[i];// insert point with quantized color
          mask.at(row,col) = i;     // insert palette index of quantized color
        }
      }
    }
    else {
      for (row = 0 ; row < imageRows ; row++) {
        for (col = 0 ; col < imageCols ; col++) {
          iVec[0] = static_cast<int>(src.at( row,col ).getRed()   * factor);
          iVec[1] = static_cast<int>(src.at( row,col ).getGreen() * factor);
          iVec[2] = static_cast<int>(src.at( row,col ).getBlue()  * factor);

          i = static_cast<int>(theHist.at( iVec ));

          r = thePalette[i].getRed();
          g = thePalette[i].getGreen();
          b = thePalette[i].getBlue();

          dest.at(row,col).set(r,g,b,0); // insert point with quantized color
        }
      }
    }

    return true;
  }