Mapping Images
        with the
Coherence Length Diagram



          Amelia Sparavigna - DIFIS
         Roberto Marazzato...
Introduction




Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
                          ...
Involved Sci-Tech Fields
                           Optical             Computer            Geometry,
     Robotics
      ...
Early works (1998-2000)
                                             Texture transitions in
                             ...
Early works (1998-2000)
                                             Smectic (layered) to
                               ...
Recent Works (2004-05)
                                             Skin ageing analysis
                                ...
Recent Works (2004-05)
                                             Normalisation of
                                    ...
Recent Works (2004-05)
                      Cell area analysis
                      Ageing enlarges cells
            ...
First outline of a CLD

                                             Alternate Skin Ageing
                              ...
First outline of a CLD
                                             Continuous
                                          ...
First outline of a CLD
                                             Saturation in Moment
                                ...
First outline of a CLD
                                             Stochastic Geometry
                                 ...
Formalisation of CLD and MAPs
             Discrete description
             Develepment of a software tool




Amelia S...
Results
                                                Given Image
                                                CLD ...
The Coherence
         Length Diagram (CLD)




Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Le...
Grayscale Bitmap
   Brightness as function of pixel coords




    Amelia Sparavigna, Roberto Marazzato, Mapping Images w...
Average Brightness




       h




                              w


Amelia Sparavigna, Roberto Marazzato, Mapping Images...
Discrete Directions




Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
                   ...
Local First Order Moment
                                             Start at (x,y)
                                    ...
Local CLD
                                                     Minimum length
                                           ...
Domain of the Local CLD
                  t                         The local CLD is not
           Di                  θ...
CLD
                                             Local CLDs are
                                              averaged ov...
The Support Map (SMAP)




Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
                ...
Directional support Set
                                             Each Domain can be
            t                    ...
Average Indicator Function

          t                                  Too many sets
       Dtit t
       D t
        D...
SMAP Visual Layout
                                             Blue = OK
                                             G...
The Defect Map (DMAP)




Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
                 ...
Existing Defect Detection Methods
“Too dark” areas                                Comparison of local
                   ...
What is compared
                                             Local CLD to CLD
                                          ...
Bounds
                                             For each direction the
                                              ...
Directional Success Function
             0
  1
                                             1 if the local CLD
         ...
Defect Map (DMAP)
                                             Consider all directions
                                  ...
How DMAP is rendered
                                             Positive values (more
                                 ...
The Directional
             Defect Map (DMAP)




Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence...
Comparing Shapes
                                             All defined directions
                                    ...
Square Difference Sum



                                                (red)


                            (blue)
      ...
Need for Scaling


                                             Similar shapes can
                                      ...
Rescaling Function
   Ratio of both average coherence lengths

                 Local CLD




            Image
         ...
Normalized Sum
                       Rescali
                       ng




                                              ...
Comparison to Average
             Average                     over all pixels




             Set a treshold t''
     ...
Directional Defect Map (DDMAP)

                                                                             0

          ...
How DDMAP is rendered
                                             Gray pixels → OK
                                     ...
Examples: Mineral Structures

             Watch CLD Generator running
             Read reports




Amelia Sparavigna, ...
Amelia Sparavigna
    Department of Physics - Politecnico di Torino
           amelia.sparavigna@polito.it

              ...
Upcoming SlideShare
Loading in …5
×

Mapping Images with the Coherence Length Diagram

782 views

Published on

The Coherence Length Diagram and its derived Maps. Presented in Bozen last year.

0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
782
On SlideShare
0
From Embeds
0
Number of Embeds
3
Actions
Shares
0
Downloads
11
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Mapping Images with the Coherence Length Diagram

  1. 1. Mapping Images with the Coherence Length Diagram Amelia Sparavigna - DIFIS Roberto Marazzato – DAUIN Politecnico di Torino
  2. 2. Introduction Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  3. 3. Involved Sci-Tech Fields Optical Computer Geometry, Robotics processing Science Algebra Machine Computer Image DSP Vision vision Processing Pattern Machine Recognitio Learning n Neuro- Artificial Physiology Intelligence Perception Image Computer Multimedia Psychology Analysis Graphics Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  4. 4. Early works (1998-2000)  Texture transitions in nematic liquid crystals  Montrucchio, Sparavigna, Mello, Strigazzi Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  5. 5. Early works (1998-2000)  Smectic (layered) to nematic (unlayered) phases  Smooth changes  Need for a sensitive transition detecting tool Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  6. 6. Recent Works (2004-05)  Skin ageing analysis  Bevilacqua, Gherardi, Guerrieri  Capacitance sensors  Fingerprint equipment used on forearm skin Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  7. 7. Recent Works (2004-05)  Normalisation of image data  Segmentation Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  8. 8. Recent Works (2004-05)  Cell area analysis  Ageing enlarges cells  Treshold value Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  9. 9. First outline of a CLD  Alternate Skin Ageing Analysis  Continuous description Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  10. 10. First outline of a CLD  Continuous description  Moments Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  11. 11. First outline of a CLD  Saturation in Moment calculation  Coherence Length  Average → Defect Detection Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  12. 12. First outline of a CLD  Stochastic Geometry  Similarity to Rose of Directions/ Rose of Intersections  No direct connection found up to now Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  13. 13. Formalisation of CLD and MAPs  Discrete description  Develepment of a software tool Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  14. 14. Results  Given Image  CLD (Coherence Length Diagram)  SMAP (Support Map)  DMAP (Defect Map)  DDMAP (Directional Defect Map) Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  15. 15. The Coherence Length Diagram (CLD) Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  16. 16. Grayscale Bitmap  Brightness as function of pixel coords Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  17. 17. Average Brightness h w Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  18. 18. Discrete Directions Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  19. 19. Local First Order Moment  Start at (x,y)  Follow  Sum brightness  Average Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  20. 20. Local CLD  Minimum length such that the 0th order momentum saturates  A treshold t is l considered Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  21. 21. Domain of the Local CLD t  The local CLD is not Di θi defined for all pixels of the image  The set of points for which it exists t Di' θi' depends on the direction Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  22. 22. CLD  Local CLDs are averaged over all pixels  For each direction, only pixels belonging to the corresponding domain are taken into account Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  23. 23. The Support Map (SMAP) Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  24. 24. Directional support Set  Each Domain can be t described through an Dtit t D t indicator function Di' t t Di' t Di' i' Di' Di' Di' =0 =1 Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  25. 25. Average Indicator Function t  Too many sets Dtit t D t Di' t t Di' t  Some shorter Di' i' Di' description is needed Di' Di' t Di Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  26. 26. SMAP Visual Layout  Blue = OK  Gray = KO  Intermediate values: only some directions OK Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  27. 27. The Defect Map (DMAP) Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  28. 28. Existing Defect Detection Methods “Too dark” areas  Comparison of local to average brightness “Too bright” areas Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  29. 29. What is compared  Local CLD to CLD  “Successful” and “failing” directions are counted Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  30. 30. Bounds  For each direction the appropriate interval is considered θi  The reference value is  Another treshold value is used Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  31. 31. Directional Success Function 0 1  1 if the local CLD belongs to the θi previous bound  0 if it doesn't Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  32. 32. Defect Map (DMAP)  Consider all directions for each pixel  Normalized signed count “Successful” directions Compute only if the local CLD exists Count involved Normalize to [-1,+1] contributions Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  33. 33. How DMAP is rendered  Positive values (more successful than failing directions) → Green  Negative values (more failing than successful directions) → Red Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  34. 34. The Directional Defect Map (DMAP) Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  35. 35. Comparing Shapes  All defined directions are compared  The overall effect is “Similar” considered shapes  Focus on shape difference “Quite different” shapes Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  36. 36. Square Difference Sum (red) (blue) θi Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  37. 37. Need for Scaling  Similar shapes can differ in size  Rescaling one of them allows a shape focused comparison Similar shape, different size Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  38. 38. Rescaling Function  Ratio of both average coherence lengths Local CLD Image CLD Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  39. 39. Normalized Sum Rescali ng Compari ng Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  40. 40. Comparison to Average  Average over all pixels  Set a treshold t''  Obtain the admittance interval Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  41. 41. Directional Defect Map (DDMAP) 0 (red) 1 Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  42. 42. How DDMAP is rendered  Gray pixels → OK  Yellow pixels → KO  Note boundaries Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  43. 43. Examples: Mineral Structures  Watch CLD Generator running  Read reports Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
  44. 44. Amelia Sparavigna Department of Physics - Politecnico di Torino amelia.sparavigna@polito.it Roberto Marazzato Department of Automation and Computer Science Politecnico di Torino Faculty of Science and Technology Free University of Bozen / Bolzano roberto.marazzato@polito.it Members of the Academic Society for Mathematics and Physics Bozen / Bolzano Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram

×