October 14 – 19 , 2018, Dagstuhl Seminar 18422

Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods


Michael Breuß (BTU Cottbus, DE)
Alfred M. Bruckstein (Technion – Haifa, IL)
Christer Oscar Kiselman (Uppsala University, SE)
Petros Maragos (National Technical University of Athens, GR)

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Dagstuhl Report, Volume 8, Issue 10 Dagstuhl Report
Aims & Scope
List of Participants


Dagstuhl Seminar 18422 Shape Analysis: Euclidean, Discrete and Algebraic Geometric Methods took place October 14–19, 2018. 26 researchers from North America and Europe discussed state-of-the-art, current challenges, and promising future research directions in the areas of 2-D and 3-D shape analysis from a cross-disciplinary point of view. Participants included international experts from the fields of continuous-scale shape analysis, discrete shape analysis, tropical geometry and numerical computing. The seminar consisted of an opening and getting to know session and 26 scientific presentation sessions. Furthermore, there was time for extensive discussions both between the talks and in the evenings.

The topics in our seminar addressed the sketched challenges and developments that will be useful for shape analysis. Especially we aimed to discuss the possibilities of combining fields like tropical geometry with more classical techniques as for instance from mathematical morphology. We discussed possibilities of applying machine learning methods in this context and considered recent advances from more classical fields like differential geometry and partial differential equations that can be useful for setting up and understanding shape analysis methods in all of these approaches.

The purpose of this seminar was to address these challenges with the latest tools related to geometric, algorithmic and numerical concepts. To do so, we brought together researchers working on shape analysis topics from different perspectives. The purpose in bringing together researchers from those different communities sharing substantial interest in shape analysis was to explore the benefits of a cross-disciplinary point of view.

Promising new ways to combine the latest techniques from these different fields were identified during in-depth discussions in small groups. Some especially promising research directions in the areas of deep learning, mathematical morphology, shape from shading, modelling deformable shapes, and tropical geometry were discussed in small groups between the talks and in the evenings.

Summary text license
  Creative Commons BY 3.0 Unported license
  Michael Breuß, Alfred M. Bruckstein, Christer Oscar Kiselman, and Petros Maragos

Dagstuhl Seminar Series


  • Computer Graphics / Computer Vision
  • Modelling / Simulation
  • Optimization / Scheduling


  • Shape analysis
  • Shape reconstruction
  • Mathematical morphology
  • Algebraic geometry
  • Optimization


In the series Dagstuhl Reports each Dagstuhl Seminar and Dagstuhl Perspectives Workshop is documented. The seminar organizers, in cooperation with the collector, prepare a report that includes contributions from the participants' talks together with a summary of the seminar.


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