Optimal Differential Filter on Hexagonal Lattice

  • Suguru Saito
  • Masayuki Nakajiama
  • Tetsuo Shima
Part of the Studies in Computational Intelligence book series (SCI, volume 386)


Digital two-dimensional images are usually sampled on square lattices, whose adjacent pixel distances in the horizontal-perpendicular and diagonal directions are not equal. On the other hand, a hexagonal lattice, however, covers an area with sampling points whose adjacent pixel distances are the same; therefore, it has te potential advantage that it can be used to calculate accurate two-dimensional gradient.

The fundamental image filter in many image processing algorithms is used to extract the gradient information. For the extraction, various gradient filters have been proposed on square lattices, and some of them have been thoroughly optimized but not on a hexagonal lattice.

In this chapter, consistent gradient filters on hexagonal lattices are derived, the derived filters are compared with existing optimized filters on square lattices, and the relationship between the derived filters and existing filters on a hexagonal lattice is investigated. The results of the comparison show that the derived filters on a hexagonal lattice achieve better signal-to-noise ratio and localization than filters on a square lattice.


IEEE Transaction Input Image Point Spread Function Hexagonal Lattice Gradient Intensity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Berlin Heidelberg 2012

Authors and Affiliations

  • Suguru Saito
    • 1
  • Masayuki Nakajiama
    • 1
  • Tetsuo Shima
    • 1
  1. 1.Department of Computer ScienceTokyo Institute of TechnologyTokyoJapan

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