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Hierarchical Graph-based Representations

Basic research on graph based representations has focused on combinatorial maps. In [BK06] we have treated the problem of identifying the inside and the outside of self loops in 2D combinatorial maps, using only local calculations. Self loops are important because they encode containment (surrounding) relations in 2D. Using 3D combinatorial pyramids, in [IIHK06a] we have concentrated on obtaining minimal configurations which correctly encode the topology of the initial data. We have defined a set of rules to preserve the essential properties of the representation during the incremental contraction process. We pointed out some of their future applications i.e. dynamic scene description, matching, etc.

Reduction of a 3D Combinatorial Map - original Map

Reduction of a 3D Combinatorial Map - reduced Map

Reduction of a 3D Combinatorial Map - volume visualisation of reduced Map
(image produced by Ray Booster)

External Collaborations

  1. Prof. Luc Brun, LERI, Université de Reims, France
  2. Prof. Pascal Lienhardt, SIC, Université de Poitiers, France

Related Bibliography

  1. See Topological Representations.
  2. See Pyramidal Representations.
  3. See the List of PRIP publications created during this project.