// returns pair of x and y
static Pair<Float, Float> bwCentroid(BWImage img, bool dark) {
  int w = img.getWidth(), h = img.getHeight();
  double sumX = 0, sumY = 0;
  double midX = (w-1)/2.0, midY = (h-1)/2.0; // optimized for odd image dimensions
  for y to h: for x to w: {
    float weight = img.getPixel(x, y);
    if (dark) weight = 1-weight;
    sumX += weight*(x-midX);
    sumY += weight*(y-midY);
  }
  double baseX = midX*h, baseY = midY*w;
  ret new Pair((float) (midX+sumX/baseX), (float) (midY+sumY/baseY));
}