Assessing Hierarchies by Their Consistent Segmentations

Zeev Gutman, Ritvik Vij, Laurent Najman, Michael Lindenbaum

Research output: Contribution to journalArticlepeer-review


Current approaches to generic segmentation start by creating a hierarchy of nested image partitions and then specifying a segmentation from it. Our first contribution is to describe several ways, most of them new, for specifying segmentations using the hierarchy elements. Then, we consider the best hierarchy-induced segmentation specified by a limited number of hierarchy elements. We focus on a common quality measure for binary segmentations, the Jaccard index (also known as IoU). Optimizing the Jaccard index is highly nontrivial, and yet we propose an efficient approach for doing exactly that. This way we get algorithm-independent upper bounds on the quality of any segmentation created from the hierarchy. We found that the obtainable segmentation quality varies significantly depending on the way that the segments are specified by the hierarchy elements, and that representing a segmentation with only a few hierarchy elements is often possible.

Original languageEnglish
JournalJournal of Mathematical Imaging and Vision
StateAccepted/In press - 2024


  • Evaluation
  • Hierarchical segmentation
  • Image segmentation
  • Jaccard index

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Condensed Matter Physics
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Applied Mathematics


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