mapping images with the coherence length diagram
DESCRIPTION
The Coherence Length Diagram and its derived Maps. Presented in Bozen last year.TRANSCRIPT
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Mapping Imageswith the
Coherence Length Diagram
Amelia Sparavigna - DIFISRoberto Marazzato – DAUIN
Politecnico di Torino
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Introduction
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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Involved Sci-Tech Fields
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Computer vision
Image Analysis Multimedia Computer
Graphics
Machine Vision
Robotics Optical processing
Neuro-Physiology
Perception Psychology
Computer Science
Geometry, Algebra
Image Processing DSP
Pattern Recognitio
n
Machine Learning
Artificial Intelligence
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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
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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
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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
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Recent Works (2004-05)
Normalisation of image data
Segmentation
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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Recent Works (2004-05)
Cell area analysis Ageing enlarges cells Treshold value
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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First outline of a CLD
Alternate Skin Ageing Analysis
Continuous description
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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First outline of a CLD
Continuous description
Moments
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First outline of a CLD
Saturation in Moment calculation
Coherence Length
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Average → Defect Detection
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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
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Formalisation of CLD and MAPs
Discrete description Develepment of a software tool
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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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
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The CoherenceLength Diagram (CLD)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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Grayscale Bitmap
Brightness as function of pixel coords
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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Average Brightness
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w
h
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Discrete Directions
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Local First Order Moment
Start at (x,y) Follow Sum brightness Average
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Local CLD
Minimum length such that the 0th order momentum saturates
A treshold t is considered
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l
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Domain of the Local CLD
The local CLD is not defined for all pixels of the image
The set of points for which it exists depends on the direction
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Di
θit
Di'
θi't
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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
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The Support Map (SMAP)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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Directional support Set
Each Domain can be described through an indicator function
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Di'
t
Di'
tDi'
tDi'
tDi'
tDi'
tDi'
tDi'
tDi
t
=0 =1
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Average Indicator Function
Too many sets Some shorter
description is needed
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Di'
t
Di'
tDi'
tDi'
tDi'
tDi'
tDi'
tDi'
tDi
t
Di
t
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SMAP Visual Layout
Blue = OK Gray = KO Intermediate values:
only some directions OK
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The Defect Map (DMAP)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
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Existing Defect Detection Methods
Comparison of local to average brightness
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
“Too bright” areas
“Too dark” areas
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What is compared
Local CLD to CLD “Successful” and
“failing” directions are counted
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Bounds
For each direction the appropriate interval is considered
The reference value is
Another treshold value is used
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
θi
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Directional Success Function
1 if the local CLD belongs to the previous bound
0 if it doesn't
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
θi
10
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Defect Map (DMAP)
Consider all directions for each pixel
Normalized signed count
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
“Successful” directions
Compute only if the local CLD exists
Count involved contributionsNormalize to [-1,+1]
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How DMAP is rendered
Positive values (more successful than failing directions) → Green
Negative values (more failing than successful directions) → Red
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The Directional Defect Map (DMAP)
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Comparing Shapes
All defined directions are compared
The overall effect is considered
Focus on shape difference
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
“Similar” shapes
“Quite different” shapes
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Square Difference Sum
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
θi
(red)
(blue)
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Need for Scaling
Similar shapes can differ in size
Rescaling one of them allows a shape focused comparison
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Similar shape, different size
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Rescaling Function
Ratio of both average coherence lengths
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Local CLD
Image CLD
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Normalized Sum
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Rescaling
Comparing
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Comparison to Average
Average over all pixels
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
Set a treshold t'' Obtain the admittance interval
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Directional Defect Map (DDMAP)
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram
(red)
0
1
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How DDMAP is rendered
Gray pixels → OK Yellow pixels → KO Note boundaries
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Examples: Mineral Structures
Watch CLD Generator running Read reports
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Amelia SparavignaDepartment of Physics - Politecnico di Torino
Roberto MarazzatoDepartment of Automation and Computer Science
Politecnico di TorinoFaculty of Science and TechnologyFree University of Bozen / Bolzano
Members of the Academic Society for Mathematics and Physics
Bozen / Bolzano
Amelia Sparavigna, Roberto Marazzato, Mapping Images with the Coherence Length Diagram