// returns [<cell, average color>]
static LPair<DoubleRect, RGB> ii_scanGrid(IntegralImage ii, int cols, int rows) {
  ret map(
    concat(gridOfDoubleRects3(ii.getWidth(), ii.getHeight(), cols, rows)),
      r -> pair(r, ii_averageColorOfArea(ii, toRect(r))));
}

static LPair<DoubleRect, RGB> ii_scanGrid(IntegralImage ii, int cols) {
  ret ii_scanGrid(ii, cols, rowsForColsWithAspectRatio(cols, ii.getWidth(), ii.getHeight()));
}

static LPair<DoubleRect, RGB> ii_scanGrid(IntegralImage ii, DoubleRect outer, int cols, int rows) {
  ret map(
    concat(gridOfDoubleRects3(outer, cols, rows)),
      r -> pair(r, ii_averageColorOfArea(ii, toRect(r))));
}