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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Susanne Bach-Bernhard for administrative matters

Andreas Dolzmann for scientific matters


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In computer vision and image analysis, 3-D shapes have traditionally been studied by analyzing a sparse set of marker positions on 3-D shapes. Within the last years, there have been many technological developments that expand the potential of methods dealing with 3-D digital shape representations. As examples let us mention the use of laser-range scanners, or depth cameras like the Kinect sensor. However, not only the acquisition of digitized 3-D shapes has become much easier, there are also interesting trends to make broader use of 3-D information. Developments in 3-D printing enable novel emerging technologies, whereas holographic displays are predicted to enter the mass market in a few years. The key to all the mentioned technologies is the proper use and manipulation of 3-D shapes.

The purpose of this seminar is to address upcoming challenges in the scientific and industrial use of shape analysis methods by combining recent developments in that field with the latest tools from different areas of geometry as well as modern algorithmic and numerical concepts.

Classic shape analysis tools from differential geometry have a fresh influence in the field, often powered by modern methods from optimization and numerical computing. At the same time, discrete geometric methods and related techniques such as from mathematical morphology have evolved significantly. Moreover, techniques like deep learning may also have a significant influence in the development of corresponding methods and tools. New developments from tropical geometry have a high potential for use in shape analysis. With the advent of novel potential applications and new possibilities to describe geometric shape properties, we conjecture that the proposed seminar may inspire important lines of shape analysis research.

The topics we will address in our seminar are in accordance with the sketched challenges and developments that can be useful for shape analysis. Especially we aim to discuss the possibilities of combining emerging fields like tropical geometry with more classical techniques as for instance from mathematical morphology. We also plan to investigate possibilities of applying machine learning methods in this context and discuss 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.

  Creative Commons BY 3.0 DE
  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

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