final sclass BWIntegralImage implements MakesBufferedImage, IBWIntegralImage {
  int w, h;
  int[] data; // 1 entry per pixel
  ifdef BWIntegralImage_CountAccesses
    long accesses;
  endifdef
  
  *() {}
  *(File f) { this(loadImage2(f)); }
  *(BufferedImage img) { this(BWImage(img)); }
  *(MakesBufferedImage img) { this(toBufferedImage(img)); }
  
  *(BWImage img) {
    w = img.w();
    h = img.h();
    data = new int[w*h];
    int i = 0;
    for y to h: {
      int sum = 0;
      for x to w: {
        sum += img.getByte(x, y) & 0xFF;
        data[i] = y > 0 ? sum + data[i-w] : sum;
        i++;
      }
    }
  }
  
  // pixels outside of image are considered black
  int get(int x, int y) {
    ifdef BWIntegralImage_CountAccesses
      ++accesses;
    endifdef
    ret x < 0 || y < 0 || x >= w || y >= h ? 0
      : data[min(y, h-1)*w+min(x, w-1)];
  }
  
  int get(Pt p) { ret get(p.x, p.y); }
  
  public double getPixelAverage(int x1, int y1, int x2, int y2) {
    int area = (x2-x1)*(y2-y1);
    ret doubleRatio(bwIntegralImage_sumRect(this, x1, y1, x2, y2), area);
  }
  
  public int getWidth() { ret w; }
  public int getHeight() { ret h; }
  
  // unoptimized
  public BufferedImage getBufferedImage() {
    ret scaleDownUsingIntegralImageBW(this, w).getBufferedImage();
  }
}