Lattice of octagonal distances in digital geometry

@article{Das1990LatticeOO,
  title={Lattice of octagonal distances in digital geometry},
  author={P. P. Das},
  journal={Pattern Recognition Letters},
  year={1990},
  volume={11},
  pages={663-667}
}
Abstract In this paper we identify a natural ordering relation R between octagonnal distances ( d ( B )), defined by neighbourhood sequences ( B ) in two-dimensional digital geometry. We prove that R induces a complete compact distributive lattice over the set of B 's (and hence the set of d ( B )'s) in 2-D. 

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