// x1/y1/x2/y2 are dimensions of the inner (empty) part of the rectangle
// w/h = line width/height
static int bwIntegralImage_whiteRectWithBlackBorder(BWIntegralImage img, int x1, int y1, int x2, int y2, int w, int h) {
  ret
    bwIntegralImage_sumRect(img, x1, y1, x2, y2)*2
    -bwIntegralImage_sumRect(img, x1-w, y1-h, x2+w, y2+h);
}