A Discrete Scale Space Neighborhood for Robust Deep Structure Extraction

  • Martin Tschirsich
  • Arjan Kuijper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7626)


Linear or Gaussian scale space is a well known multi-scale representation for continuous signals. The exploration of its so-called deep structure by tracing critical points over scale has various theoretical applications and allows for the construction of a scale space hierarchy tree. However, implementational issues arise, caused by discretization and quantization errors. In order to develop more robust scale space based algorithms, the discrete nature of computer processed signals has to be taken into account. Aiming at a computationally practicable implementation of the discrete scale space framework, we investigated suitable neighborhoods, boundary conditions and sampling methods. We show that the resulting discrete scale space respects important topological invariants such as the Euler number, a key criterion for the successful implementation of algorithms operating on its deep structure. We discuss promising properties of topological graphs under the influence of smoothing, setting the stage for more robust deep structure extraction algorithms.


Deep Structure Scale Space Euler Number Topological Graph Discrete Signal 
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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Martin Tschirsich
    • 1
  • Arjan Kuijper
    • 1
    • 2
  1. 1.Technische Universität DarmstadtGermany
  2. 2.Fraunhofer IGDDarmstadtGermany

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