static void darkenBWImagePart(BWImage img, Rect r) {
  darkenBWImagePart(img, r, 0.8f);
}

static void darkenBWImagePart(BWImage img, Rect r, float factor) {
  int x2 = r.x2(), y2 = r.y2();
  for (int y = r.y; y < y2; y++)
    for (int x = r.x; x < x2; x++)
      img.setPixel(x, y, img.getPixel(x, y)*factor);
}