stats::stats(PNG& im) {
  sumRed.resize(im.width(), vector<long>(im.height()));
  sumGreen.resize(im.width(), vector<long>(im.height()));
  sumBlue.resize(im.width(), vector<long>(im.height()));

  sumsqRed.resize(im.width(), vector<long>(im.height()));
  sumsqGreen.resize(im.width(), vector<long>(im.height()));
  sumsqBlue.resize(im.width(), vector<long>(im.height()));

  RGBAPixel* pixel = im.getPixel(0,0);
  sumRed[0][0]   = pixel->r;
  sumGreen[0][0] = pixel->g;
  sumBlue[0][0]  = pixel->b;

  sumsqRed[0][0]   = pixel->r * pixel->r;
  sumsqGreen[0][0] = pixel->g * pixel->g;
  sumsqBlue[0][0]  = pixel->b * pixel->b;

  for (unsigned int w = 1; w < im.width(); w++) {
    RGBAPixel* p = im.getPixel(w,0);
    sumRed[w][0]     = p->r        + sumRed[w-1][0];
    sumGreen[w][0]   = p->g        + sumGreen[w-1][0];
    sumBlue[w][0]    = p->b        + sumBlue[w-1][0];
    sumsqRed[w][0]   = p->r * p->r + sumsqRed[w-1][0];
    sumsqGreen[w][0] = p->g * p->g + sumsqGreen[w-1][0];
    sumsqBlue[w][0]  = p->b * p->b + sumsqBlue[w-1][0];
  }

  for (unsigned int h = 1; h < im.height(); h++) {
    RGBAPixel* p = im.getPixel(0,h);
    sumRed[0][h]     = p->r        + sumRed[0][h-1];
    sumGreen[0][h]   = p->g        + sumGreen[0][h-1];
    sumBlue[0][h]    = p->b        + sumBlue[0][h-1];
    sumsqRed[0][h]   = p->r * p->r + sumsqRed[0][h-1];
    sumsqGreen[0][h] = p->g * p->g + sumsqGreen[0][h-1];
    sumsqBlue[0][h]  = p->b * p->b + sumsqBlue[0][h-1];
  }

  for (unsigned int w = 1; w < im.width(); w++) {
    for (unsigned int h = 1; h < im.height(); h++) {
      RGBAPixel* p = im.getPixel(w, h);
      sumRed[w][h]   = p->r + sumRed[w-1][h]   + sumRed[w][h-1]   - sumRed[w-1][h-1];
      sumGreen[w][h] = p->g + sumGreen[w-1][h] + sumGreen[w][h-1] - sumGreen[w-1][h-1];
      sumBlue[w][h]  = p->b + sumBlue[w-1][h]  + sumBlue[w][h-1]  - sumBlue[w-1][h-1];

      sumsqRed[w][h]   = p->r * p->r + sumsqRed[w-1][h]   + sumsqRed[w][h-1]   - sumsqRed[w-1][h-1];
      sumsqGreen[w][h] = p->g * p->g + sumsqGreen[w-1][h] + sumsqGreen[w][h-1] - sumsqGreen[w-1][h-1];
      sumsqBlue[w][h]  = p->b * p->b + sumsqBlue[w-1][h]  + sumsqBlue[w][h-1]  - sumsqBlue[w-1][h-1];
    }
  }
}