Path-Based Mathematical Morphology on Tensor Fields

  • Jasper J. van de Gronde
  • Mikola Lysenko
  • Jos B. T. M. RoerdinkEmail author
Part of the Mathematics and Visualization book series (MATHVISUAL)


Traditional path-based morphology allows finding long, approximately straight, paths in images. Although originally applied only to scalar images, we show how this can be a very good fit for tensor fields. We do this by constructing directed graphs representing such data, and then modifying the traditional path opening algorithm to work on these graphs. Cycles are dealt with by finding strongly connected components in the graph. Some examples of potential applications are given, including path openings that are not limited to a specific set of orientations.


Tangent Vector Directed Acyclic Graph Tensor Field Orientation Score Mathematical Morphology 
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.



The first and third author were funded by the Netherlands Organisation for Scientific Research (NWO), project no. 612.001.001. Also, we thank Remco Renken and Jelmer Kok from the NeuroImaging Center Groningen for supplying us with the diffusion MRI data (including regions of interest and tractography results), as well as for some inspiring discussions.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Jasper J. van de Gronde
    • 1
  • Mikola Lysenko
    • 2
  • Jos B. T. M. Roerdink
    • 1
    Email author
  1. 1.Johann Bernoulli Institute for Mathematics and Computer ScienceUniversity of GroningenGroningenThe Netherlands
  2. 2.Department of Computer SciencesUniversity of Wisconsin - MadisonMadisonUSA

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