static RGBImage scaleDownUsingIntegralImage(IntegralImage img, int w) {
  ret scaleDownUsingIntegralImage(img, w, iround(w*img.h/(double) img.w));
}

static RGBImage scaleDownUsingIntegralImage(IntegralImage img, int w, int h) {
  int w1 = img.w, h1 = img.h;
  RGBImage 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 r = roundedRatio(img.rectSum(x1, y1, x2, y2, 0), area);
      int g = roundedRatio(img.rectSum(x1, y1, x2, y2, 1), area);
      int b = roundedRatio(img.rectSum(x1, y1, x2, y2, 2), area);
      out.setPixel(x, y, r, g, b);
    }
  ret out;
}