A self-referred approach to lacunarity
  This letter describes an approach to lacunarity which adopts the pattern under analysis as the reference for the sliding window procedure. The superiority of such a scheme with respect to more traditional methodologies, especially when dealing with finite-size objects, is established and illustrated through applications to DLA pattern characterization. It is also shown that, given the enhanced accuracy and sensitivity of this scheme, the shape of the window becomes an important parameter, with advantage for circular windows. 
Erbe P. Rodrigues, Marconi S. Barbosa and Luciano da F. Costa