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Planting, Growing, and Pruning Trees: Connected Filters Applied to Document Image Analysis Guillaume Lazzara, Thierry G eraud, Roland Levillain EPITA Research and Development Laboratory (LRDE) April 8, 2014 G. Lazzara, T. G eraud, R.

  1. Planting, Growing, and Pruning Trees: Connected Filters Applied to Document Image Analysis Guillaume Lazzara, Thierry G´ eraud, Roland Levillain EPITA Research and Development Laboratory (LRDE) April 8, 2014 G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 1

  2. Quotation Reviewer 1: I wasn’t overly impressed with this paper until I saw Figure 9. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 2

  3. Quotation Reviewer 1: I wasn’t overly impressed with this paper until I saw Figure 9. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 2

  4. Quotation Reviewer 1: I wasn’t overly impressed with this paper until I saw Figure 9. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 2

  5. Hum. . . We know that mathematical morphology can often look impressive. . . . . . yet, today you just need to understand ≤ and ⊂ . . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 3

  6. Hum. . . We know that mathematical morphology can often look impressive. . . . . . yet, today you just need to understand ≤ and ⊂ . . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 3

  7. Hum. . . We know that mathematical morphology can often look impressive. . . . . . yet, today you just need to understand ≤ and ⊂ . . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 3

  8. Fig. 9 Sample uses of connected operators. Top: input images; Bottom: filtered images (results). G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 4

  9. The Meta Outline Why this talk? MM filters are good for DIA people! Why is that interesting? Connected filters are little known. How does this work? By planting, growing and pruning trees. What can it be used for? Denoising, image simplification, object identification, etc. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 5

  10. The Meta Outline Why this talk? MM filters are good for DIA people! Why is that interesting? Connected filters are little known. How does this work? By planting, growing and pruning trees. What can it be used for? Denoising, image simplification, object identification, etc. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 5

  11. The Meta Outline Why this talk? MM filters are good for DIA people! Why is that interesting? Connected filters are little known. How does this work? By planting, growing and pruning trees. What can it be used for? Denoising, image simplification, object identification, etc. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 5

  12. The Meta Outline Why this talk? MM filters are good for DIA people! Why is that interesting? Connected filters are little known. How does this work? By planting, growing and pruning trees. What can it be used for? Denoising, image simplification, object identification, etc. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 5

  13. The Meta Outline Why this talk? MM filters are good for DIA people! Why is that interesting? Connected filters are little known. How does this work? By planting, growing and pruning trees. What can it be used for? Denoising, image simplification, object identification, etc. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 5

  14. The Meta Outline Why this talk? MM filters are good for DIA people! Why is that interesting? Connected filters are little known. How does this work? By planting, growing and pruning trees. What can it be used for? Denoising, image simplification, object identification, etc. Evangelization from the Church of Mathematical Morphology :-) G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 5

  15. Three Messages from the Church Regarding. . . . . . Mathematical Morphology (MM) Refresh your vision of MM → forget ε and δ ! . . . Connected Filters Powerful, simple, and well-suited to DIA. . . . Methodology Advocate gray-level morphological strategies (vs approaches based on binarization). G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 6

  16. Three Messages from the Church Regarding. . . . . . Mathematical Morphology (MM) Refresh your vision of MM → forget ε and δ ! . . . Connected Filters Powerful, simple, and well-suited to DIA. . . . Methodology Advocate gray-level morphological strategies (vs approaches based on binarization). G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 6

  17. Three Messages from the Church Regarding. . . . . . Mathematical Morphology (MM) Refresh your vision of MM → forget ε and δ ! . . . Connected Filters Powerful, simple, and well-suited to DIA. . . . Methodology Advocate gray-level morphological strategies (vs approaches based on binarization). G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 6

  18. Three Messages from the Church Regarding. . . . . . Mathematical Morphology (MM) Refresh your vision of MM → forget ε and δ ! . . . Connected Filters Powerful, simple, and well-suited to DIA. . . . Methodology Advocate gray-level morphological strategies (vs approaches based on binarization). G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 6

  19. Departing From this Typical DIA Workflow connected binarization component labeling document binary label image image image low-level analysis of components high-level analysis page component segmen- "classifi- tation cation" G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 7

  20. Departing From this Typical DIA Workflow connected binarization component labeling document binary label image image image low-level analysis of components high-level analysis page component segmen- "classifi- tation cation" Starting with binarization is hell! G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 7

  21. Components and Decomposition Principle O C D A F u = B E A connected component of the set [ u ≤ 1 ] = { p ∈ D , u ( p ) ≤ 1 } is included (so ⊂ ) into a component of the set [ u ≤ 2 ] ⇒ Connected components can be arranged into trees. . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 8

  22. Components and Decomposition Principle O C D A F u = B E A connected component of the set [ u ≤ 1 ] = { p ∈ D , u ( p ) ≤ 1 } is included (so ⊂ ) into a component of the set [ u ≤ 2 ] ⇒ Connected components can be arranged into trees. . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 8

  23. Components and Decomposition Principle O C D A F u = B E A connected component of the set [ u ≤ 1 ] = { p ∈ D , u ( p ) ≤ 1 } is included (so ⊂ ) into a component of the set [ u ≤ 2 ] ⇒ Connected components can be arranged into trees. . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 8

  24. Components and Decomposition Principle O C D A F u = B E A connected component of the set [ u ≤ 1 ] = { p ∈ D , u ( p ) ≤ 1 } is included (so ⊂ ) into a component of the set [ u ≤ 2 ] ⇒ Connected components can be arranged into trees. . . G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 8

  25. Components and Trees O C A D F B E (a) image > 0 B O 0 O 3 > 4 A, F 2 A 1 > C, D, E 2 > 2 C D E 1 B C 2 > A F 1 O E F 3 D B 0 > 2 > 2 2 > (b) max-tree (c) tree of shapes (d) min-tree G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 9

  26. Mathematical Morphology: Connected Operators An interesting class of filters: Not based on structuring elements (so not like ε or δ ) Considering all the connected components obtained by thresholding the image. Don’t shift contours; don’t create new ones. Intuitive, powerful, and efficient. Can be implemented as tree filtering. G. Lazzara, T. G´ eraud, R. Levillain (EPITA) Connected Filters Applied to Document Image Analysis 2014-04-08 10

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