A Note on Computable Proximity of $\mathcal{L}_1$-Discs on the Digital   Plane
  This paper investigates problems in the characterization of the proximity of digital discs. Based on the $\mathcal{L}_1$-metric structure for the 2D digital plane and using a Jaccard-like metric, we determine numerical characters for intersecting digital discs. 
J.F. Peters, K. Kordzaya, I. Dochviri
math.MG