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Valence-based Connectivity Coding

Valence-based Connectivity Coding. Hu Jianwei 2007-11-07. Why Mesh Compression. Slow networks require data compression to reduce the latency Small storage devices need data compression to save space. Surface Based Meshes. Connectivity How the vertices connect with each other Geometry

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Valence-based Connectivity Coding

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  1. Valence-based Connectivity Coding Hu Jianwei 2007-11-07

  2. Why Mesh Compression • Slow networks require data compression to reduce the latency • Small storage devices need data compression to save space

  3. Surface Based Meshes • Connectivity • How the vertices connect with each other • Geometry • Coordinates of the vertices vertex1 ( x, y, z ) vertex2 ( x, y, z ) vertex3 ( x, y, z ) vertexv face1 1 2 3 4 face2 3 4 3 face3 5 2 1 3 facef

  4. Classification • Connectivity encoding • Geometry encoding • Single-rate compression • Progressive compression

  5. Valence-based Compression • Triangle Mesh Compression [98 Touma & Gotsman] • Valence-Driven Connectivity Encoding for 3D Meshes [01 Alliez & Desbrun] • Near-Optimal Connectivity Encoding of 2-Manifold Polygon Meshes [02 Khodakovsky et al.] • Compressing Polygon Mesh Connectivity with Degree Duality Prediction [02 Isenburg]

  6. Key Observation 98 Touma & Gotsman • A genus-0 manifold mesh is topologically equivalent to a planar graph • The vertices incident on any mesh vertex may be ordered

  7. Code Words 98 Touma & Gotsman • The topology may be encoded with: • add<degree> • split<offset> • merge<index><offset> • Then entropy encoded • Huffman • arithmetic • run-length

  8. Example Traversal 98 Touma & Gotsman

  9. Example Traversal 98 Touma & Gotsman

  10. Example Traversal 98 Touma & Gotsman

  11. Example Traversal 98 Touma & Gotsman

  12. Example Traversal 98 Touma & Gotsman

  13. Example Traversal 98 Touma & Gotsman

  14. Example Traversal 98 Touma & Gotsman

  15. Example Traversal 98 Touma & Gotsman

  16. Example Traversal 98 Touma & Gotsman

  17. Example Traversal 98 Touma & Gotsman

  18. Example Traversal 98 Touma & Gotsman

  19. Example Traversal 98 Touma & Gotsman

  20. Example Traversal 98 Touma & Gotsman

  21. Add dummy vertices 98 Touma & Gotsman

  22. Example Traversal 98 Touma & Gotsman

  23. Encoding 98 Touma & Gotsman

  24. Encoding 98 Touma & Gotsman

  25. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ;

  26. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ;

  27. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ;

  28. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ;

  29. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ;

  30. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ;

  31. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 (focus full) ;

  32. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ;

  33. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ;

  34. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ;

  35. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ;

  36. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ;

  37. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ;

  38. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ;

  39. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 (focus full) ;

  40. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ;

  41. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ;

  42. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ;

  43. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4 (focus full);

  44. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4 ; (focus full)

  45. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4;

  46. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4;

  47. Encoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4; Huffman coding run-length coding

  48. Decoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4;

  49. Decoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4;

  50. Decoding 98 Touma & Gotsman Add 6; Add 7 ; Add 4 ; Add 4 ; Add 8 ; Add 5 ; Add 5 ; Add 4 ; Add 5 ; Split 5 ; Add 4 ; Add 4 ; Add Dummy 6 ; Add 4;

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