static double[][] integralImage_45deg(BufferedImage img) {
  ret integralImage(new BWImage(img));
}

static double[][] integralImage_45deg(BWImage bw) {
  int w = bw.getWidth(), h = bw.getHeight();
  double[][] ii = new double[h][w];
  
  // instead of looking above, we look above to the left
  // instead of looking left, we look left and down
  for (int y1 = 0; y1 < h; y++) {
    double rowSum = 0;
    for (int x = 0; x <= y1; x++) {
      int y = y1-x;
      rowSum += bw.getPixel(x, y);
      ii[y][x] = y > 0 && x > 0 ? rowSum + ii[y-1][x-1] : rowSum;
    }
  }
    
  for (int x1 = 1; x1 < w; x1++) {
    double rowSum = 0;
    for (int yup = 0; yup < ?; yup++) {
      int x = x1+yup, y = h-1-yup;
      rowSum += bw.getPixel(x, y);
      ii[y][x] = y > 0 && x > 0 ? rowSum + ii[y-1][x-1] : rowSum;
    }
  }

  ret ii;
}

Began life as a copy of #1009125