// not scaled
static IBWImage virtualScaledIntegralImageBW(BWIntegralImage img) {
  ret virtualScaledIntegralImageBW(img, img.getWidth(), img.getHeight());
}

static IBWImage virtualScaledIntegralImageBW(BWIntegralImage img, int w) {
  ret virtualScaledIntegralImageBW(img, w, iround(w*img.h/(double) img.w));
}

static IBWImage virtualScaledIntegralImageBW(BWIntegralImage img, int w, int h) {
  ret new IBWImage {
    int w1 = img.w, h1 = img.h;
    public int getWidth() { ret w; }
    public int getHeight() { ret h; }
    
    public float getFloatPixel(int x, int y) {
      int x1 = x*w1/w, x2 = max(x1+1, (x+1)*w1/w);
      int y1 = y*h1/h, y2 = max(y1+1, (y+1)*h1/h);
      int area = (x2-x1)*(y2-y1);
      int pixel = bwIntegralImage_sumRect(img, x1, y1, x2, y2)/area;
      ret pixel/255f;
    }
  };
}