Extended grassfire transform on medial axes of 2D shapes

Lu Liu, Erin W. Chambers, David Letscher, Tao Ju

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


The medial axis is an important shape descriptor first introduced by Blum (1967) [1] via a grassfire burning analogy. However, the medial axes are sensitive to boundary perturbations, which calls for global shape measures to identify meaningful parts of a medial axis. On the other hand, a more compact shape representation than the medial axis, such as a "center point", is needed in various applications ranging from shape alignment to geography. In this paper, we present a uniform approach to define a global shape measure (called extended distance function, or EDF) along the 2D medial axis as well as the center of a 2D shape (called extended medial axis, or EMA). We reveal a number of properties of the EDF and EMA that resemble those of the boundary distance function and the medial axis, and show that EDF and EMA can be generated using a fire propagation process similar to Blum's grassfire analogy, which we call the extended grassfire transform. The EDF and EMA are demonstrated on many 2D examples, and are related to and compared with existing formulations. Finally, we demonstrate the utility of EDF and EMA in pruning medial axes, aligning shapes, and shape description.

Original languageEnglish
Pages (from-to)1496-1505
Number of pages10
JournalCAD Computer Aided Design
Issue number11
StatePublished - Nov 2011


  • Medial axis
  • Shape center
  • Shape description
  • Significance measure


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