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Digital Lines

Digital Lines. Today’s items. Rosenfeld How to digitize How to recognize a digitized line How to do parallel translation Khalimsky Some guidelines and ideas. Rosenfeld Digitization. Modified Rosenfeld cross. Original vs. modified cross in action. Basics. y = ax + b 0 < a < 1 Note:

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Digital Lines

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  1. Digital Lines

  2. Today’s items • Rosenfeld • How to digitize • How to recognize a digitized line • How to do parallel translation • Khalimsky • Some guidelines and ideas

  3. Rosenfeld Digitization

  4. Modified Rosenfeld cross

  5. Original vs. modified cross in action

  6. Basics • y = ax + b • 0 < a < 1 • Note: • a = 0 : trivial • a = 1 : may cause “fat” lines • I begin digitization in (1, ½)

  7. Terms • Digitization level • Block • Sequence • Object • Element • Main • Single • Object length

  8. Digitization level 1

  9. Digitization level 2

  10. Digitization level 3

  11. Special case: y = ax + 0 • No block is shorter than block 1 • No block is longer than block 0

  12. The Digitization parameters: sigma and k

  13. Two object lengths

  14. Main object in level

  15. Only two possible blocklengths: Geometrical interpretation of sigma0 = a

  16. Geometrical interpretation of sigma1

  17. More on sigma1

  18. Rational coefficient

  19. Euclidic algorithm

  20. Today’s items • Rosenfeld • How to digitize • How to recognize a digitized line • How to do parallel translation • Khalimsky • Some guidelines and ideas

  21. Proposition for recognition

  22. Proposition for recognition, arithmetical example

  23. Proposition for recognition, geometrical example

  24. Five level example

  25. Today’s items • Rosenfeld • How to digitize • How to recognize a digitized line • How to do parallel translation • Khalimsky • Some guidelines and ideas

  26. Digitization of translated lines

  27. Translations

  28. Today’s items • Rosenfeld • How to digitize • How to recognize a digitized line • How to do parallel translation • Khalimsky • Some guidelines and ideas

  29. Khalimsky

  30. Khalimsky and modified Khalimsky

  31. Khalimsky translations part 1

  32. Khalimsky translations part 2

  33. Khalimsky translations, different parities

  34. Thank you for your attention!

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