// img must be square with width/height being a power of 2
static BWContrastQuadTree bwImageContrastQuadtree(BWImage img) {
  int w = img.getWidth(), h = img.getHeight();
  assertEquals("width/height", w, h);
  if (!isPowerOf2(w)) fail("image size not a power of 2: " + w);
  ret bwImageContrastQuadtree_make(img, 0, 0, w);
}

static BWContrastQuadTree bwImageContrastQuadtree_make(BWImage img, int x, int y, int w) {
  if (w == 1) ret BWContrastQuadTree(img.getInt(x, y));
  
  int r = w/2;
  BWContrastQuadTree
    a = bwImageContrastQuadtree_make(img, x, y, r),
    b = bwImageContrastQuadtree_make(img, x+r, y, r),
    c = bwImageContrastQuadtree_make(img, x, y+r, r),
    d = bwImageContrastQuadtree_make(img, x+r, y+r, r);
    
  int min = intMin(a.min(), b.min(), c.min(), d.min());
  int max = intMax(a.max(), b.max(), c.max(), d.max());
  if (min == max)
    ret BWContrastQuadTree(min, max);
    
  ret new BWContrastQuadTree.Composite(min, max, a, b, c, d);
}