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 = integralImage_sumRect(img, x1, y1, x2, y2, 0)/area;
      out.setByte(x, y, (byte) pixel);
    }
  ret out;
}