Graph Based Representations in different application Domains


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Graph Based Representations in different application Domains

  • Luc Brun and Myriam Mokhtari
  • L.E.R.I.
  • Reims University (France)

Content of the talk

2D Segmentation

2D Segmentation

  • Encoding the 2D partition
  • Simple graph
  • [Piroddi 01]

2D Segmentation

  • Encoding the 2D partition
  • Simple graph

2D Segmentation

  • Encoding the 2D partition
  • Simple graph

2D Segmentation

  • Encoding the 2D partition
  • Simple graph

2D Segmentation

  • Encoding the 2D partition
  • Simple graph
  • Dual graph

2D Segmentation

  • Encoding the 2D partition
  • Simple graph
  • Dual graph
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2D Segmentation

  • Simple Graph
  • Dual Graph
      • Encodes topological features: multiple boundaries, surrounding relationships. May be encoded by usual graph libraries.
  • 2D Combinatorial maps
      • Encodes topological features. Allows an implicit encoding of the dual graph. May be extended to higher dimensions

Shape Representation

  • Encoding the shape of an object: Pattern Recognition, Matching
    • Skeleton
    • Medial Axis

Shape Representation

  • Medial graph
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  • Illustration from [Salotti 01]

Shape Representation

  • Crest graph/River Graph
    • Crest Graph
      • Vertex: Hill altitude
      • edge: lowest altitude of the paths between two hills
    • River Graph
      • Dual vertex: Basin altitude
      • dual edge: higher altitude of the paths between two basins.

Shape Representation

  • Crest Graph
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Shape Representation

  • Crest Graph
  • Original Image
  • Sobel operator
  • Crest Graph
  • Illustration from [Glantz 01]

Shape Representation

  • Shock Graph
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  • Illustration from [Siddiqi98]

Shape Representation

  • Medial graph
      • Exact reconstruction
  • Crest graph
  • Shock Graph
      • Exact reconstruction, Highly structurated graph.

3D Segmentation

  • Encoding a 3D scene
  • CUBE
  • CUBE,
  • HOLE
  • 3HBAR,
  • HOLE
  • BOLT
  • HEAD
  • [Bauckhage 01]

3D Segmentation

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  • Encoding 3D partition : 3D combi. maps
      • G=(D,,)G=(D, ,,)
  • Example from [Braquelaire98]

3D Segmentation

  • Two approaches:
    • Splitting scheme: Braquelaire, Desbarats, Domenger, Wüthrich
    • Bottom-up scheme: Bertrand, Damiand, Fiorio
      • Successive simplifications of the 3D map encoding the partition

Links

  • 3D dual graph - 3D combinatorial maps
  • Medial graph, Crest Graph, Shock Graph: which choice for which application ?
  • 3D Irregular Pyramids based on 3D combinatorial maps
  • 3D Split & Merge algorithms based on a combination of [Braquelaire] and [Bertrand]


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