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sinterface IBWIntegralImage extends MakesBufferedImage {
  public int getWidth();
  public int getHeight();
  public int getIIValue(int x, int y);
  
  // 0.0 to 255.0
  default public double getPixelAverage(int x1, int y1, int x2, int y2) {
    int area = (x2-x1)*(y2-y1);
    ret doubleRatio(getPixelSum(x1, y1, x2, y2), area);
  }
  
  default public double getPixelAverage(Rect r) {
    ret getPixelAverage(r.x, r.y, r.x2(), r.y2());
  }
  
  default public int getPixelSum(int x1, int y1, int x2, int y2) {
    ret bwIntegralImage_sumRect(this, x1, y1, x2, y2);
  }
  
  default public int getPixel(int x, int y) {
    ret getPixelSum(x, y, x+1, y+1);
  }
  
  default public int getPixel(Pt p) { ret getPixel(p.x, p.y); }
  
  // unoptimized
  default public BufferedImage getBufferedImage() {
    ret scaleDownUsingIntegralImageBW(this, getWidth(), getHeight()).getBufferedImage();
  }
}