meta-for IIntegralImage in IIntegralImage, IntegralImage {
  // one channel
  static int integralImage_sumRect(IntegralImage img, int x1, int y1, int x2, int y2, int channel) {
    int bottomLeft  = img.get(x1-1, y2-1, channel);
    int bottomRight = img.get(x2-1, y2-1, channel);
    int topLeft     = img.get(x1-1, y1-1, channel);
    int topRight    = img.get(x2-1, y1-1, channel);
    ret bottomRight+topLeft-topRight-bottomLeft;
  }
  
  // sum all channels. TODO: might exceed int range on huge images
  static int integralImage_sumRect(IntegralImage img, int x1, int y1, int x2, int y2) {
    int bottomLeft  = img.get(x1-1, y2-1);
    int bottomRight = img.get(x2-1, y2-1);
    int topLeft     = img.get(x1-1, y1-1);
    int topRight    = img.get(x2-1, y1-1);
    ret bottomRight+topLeft-topRight-bottomLeft;
  }
}