Anti-Aliased Euclidean Distance Transform on 3D Sampling Lattices

  • Elisabeth Linnér
  • Robin Strand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8668)


The Euclidean distance transform (EDT) is used in many essential operations in image processing, such as basic morphology, level sets, registration and path finding. The anti-aliased Euclidean distance transform (AAEDT), previously presented for two-dimensional images, uses the gray-level information in, for example, area sampled images to calculate distances with sub-pixel precision. Here, we extend the studies of AAEDT to three dimensions, and to the Body-Centered Cubic (BCC) and Face-Centered Cubic (FCC) lattices, which are, in many respects, considered the optimal three-dimensional sampling lattices. We compare different ways of converting gray-level information to distance values, and find that the lesser directional dependencies of optimal sampling lattices lead to better approximations of the true Euclidean distance.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Elisabeth Linnér
    • 1
  • Robin Strand
    • 1
  1. 1.Center for Image AnalysisUppsala UniversitySweden

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