// background must be white
static Pair<Pt> bwii_detectSingleLine(BWIntegralImage ii) {
  int whiteValue = 255;
  int imgW = ii.getWidth(), imgH = ii.getHeight();
  IPred<Int, Int> predX = (x1, x2) -> ii.getPixelAverage(x1, 0, x2, imgH) != whiteValue;
  IPred<Int, Int> predY = (y1, y2) -> ii.getPixelAverage(0, y1, imgW, y2) != whiteValue;
  Pair<Pt> endpoints = pair(
    pt(indexOfRangePredicate    (imgW, predX),
       indexOfRangePredicate    (imgH, predY)),
    pt(lastIndexOfRangePredicate(imgW, predX),
       lastIndexOfRangePredicate(imgH, predY)));
  ret ii.get(endpoints.a) == whiteValue
    ? pair(pt(endpoints.b.x, endpoints.a.y),
           pt(endpoints.a.x, endpoints.b.y) : endpoints;
}