static BWImage scaleDownUsingIntegralImageBW(int w, BWIntegralImage img) {
  ret scaleDownUsingIntegralImageBW(img, w);
}

static BWImage scaleDownUsingIntegralImageBW(BWIntegralImage img, int w) {
  ret scaleDownUsingIntegralImageBW(img, w, iround(w*img.h/(double) img.w));
}

static BWImage scaleDownUsingIntegralImageBW(BWIntegralImage img, int w, int h) {
  int w1 = img.w, h1 = img.h;
  BWImage out = new(w, h);
  for y to h:
    for x to w: {
      int x1 = x*w1/w, x2 = max(x1+1, (x+1)*w1/w);
      int y1 = y*h1/h, y2 = max(y1+1, (y+1)*h1/h);
      int area = (x2-x1)*(y2-y1);
      int pixel = bwIntegralImage_sumRect(img, x1, y1, x2, y2)/area;
      out.setByte(x, y, (byte) pixel);
    }
  ret out;
}

static BWImage scaleDownUsingIntegralImageBW(IBWIntegralImage img, int w, int h default iround(w*img.getHeight()/(double) img.getWidth())) {
  int w1 = img.getWidth(), h1 = img.getHeight();
  BWImage out = new(w, h);
  for y to h:
    for x to w: {
      int x1 = x*w1/w, x2 = max(x1+1, (x+1)*w1/w);
      int y1 = y*h1/h, y2 = max(y1+1, (y+1)*h1/h);
      int area = (x2-x1)*(y2-y1);
      int pixel = bwIntegralImage_sumRect(img, x1, y1, x2, y2)/area;
      out.setByte(x, y, (byte) pixel);
    }
  ret out;
}