IntegralImage with ~2 bytes per pixel
  (instead of 4)
  
  -- doesn't work... probably need column and row high bytes instead. complicated
  
It can almost be done (the actual feasible byte count is 3.03125)

Image itself: 2 bytes per pixel (just cut off and interpret as signed integer)

Helper structure: For every 8*8 block,
  store the missing highest byte
  of pixel in top-left corner
  
(Explanation: In an 8*8 block, the pixel sum
  is at most 8*8*255=16320 which is < the signed int range.)
  
So additional bytes needed per pixel:
  1/64 (for small images)
  1/32 (for big images)
  
=> Total bytes per pixel:
  between 2.01562 and 2.03125
  
Cost for a pixel lookup:
  three fixed shifts, an AND, an array lookup and an addition