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

1. Mapping Images
with the
Coherence Length Diagram
Amelia Sparavigna - DIFIS
Roberto Marazzato – DAUIN
Politecnico di Torino

2. Introduction
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. 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. 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. 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. Recent Works (2004-05)
 Normalisation of
image data
 Segmentation
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. First outline of a CLD
 Alternate Skin Ageing
Analysis
 Continuous
description
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

10. First outline of a CLD
 Continuous
description
 Moments
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. 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. Formalisation of CLD and MAPs
 Discrete description
 Develepment of a software tool
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. The Coherence
Length Diagram (CLD)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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

17. Average Brightness
h
w
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

18. Discrete Directions
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. 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. 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. 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. The Support Map (SMAP)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. 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. 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. The Defect Map (DMAP)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. 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. 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. 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. 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. 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. The Directional
Defect Map (DMAP)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. Square Difference Sum
(red)
(blue)
θi
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. Rescaling Function
 Ratio of both average coherence lengths
Local CLD
Image
CLD
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

39. Normalized Sum
Rescali
ng
Compari
ng
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. Directional Defect Map (DDMAP)
0
(red)
1
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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. Examples: Mineral Structures
 Watch CLD Generator running
 Read reports
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length
Diagram

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