Mapping Images with the Coherence Length Diagram

Mapping Imageswith the

Coherence Length Diagram

Amelia Sparavigna - DIFISRoberto Marazzato – DAUIN

Politecnico di Torino

Introduction

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

Involved Sci-Tech Fields


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

Early works (1998-2000)

Texture transitions in nematic liquid crystals

Montrucchio, Sparavigna, Mello, Strigazzi


Early works (1998-2000)

Smectic (layered) to nematic (unlayered) phases

Smooth changes Need for a sensitive

transition detecting tool


Recent Works (2004-05)

Skin ageing analysis Bevilacqua, Gherardi,

Guerrieri Capacitance sensors Fingerprint equipment

used on forearm skin



Normalisation of image data

Segmentation



Cell area analysis Ageing enlarges cells Treshold value


First outline of a CLD

Alternate Skin Ageing Analysis

Continuous description



Continuous description

Moments



Saturation in Moment calculation

Coherence Length


Average → Defect Detection


Stochastic Geometry Similarity to Rose of

Directions/ Rose of Intersections

No direct connection found up to now


Formalisation of CLD and MAPs

Discrete description Develepment of a software tool


Results

Given Image CLD (Coherence

Length Diagram) SMAP (Support

Map) DMAP (Defect Map) DDMAP (Directional

Defect Map)


The CoherenceLength Diagram (CLD)


Grayscale Bitmap

Brightness as function of pixel coords


Average Brightness


w

h

Discrete Directions


Local First Order Moment

Start at (x,y) Follow Sum brightness Average


Local CLD

Minimum length such that the 0th order momentum saturates

A treshold t is considered


l

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


Di

θit

Di'

θi't

CLD

Local CLDs are averaged over all pixels

For each direction, only pixels belonging to the corresponding domain are taken into account


The Support Map (SMAP)


Directional support Set

Each Domain can be described through an indicator function


Di'

t

Di'

tDi'

tDi'

tDi'

tDi'

tDi'

tDi'

tDi

t

=0 =1

Average Indicator Function

Too many sets Some shorter

description is needed


Di'

t

Di'

tDi'

tDi'

tDi'

tDi'

tDi'

tDi'

tDi

t

Di

t

SMAP Visual Layout

Blue = OK Gray = KO Intermediate values:

only some directions OK


The Defect Map (DMAP)


Existing Defect Detection Methods

Comparison of local to average brightness


“Too bright” areas

“Too dark” areas

What is compared

Local CLD to CLD “Successful” and

“failing” directions are counted


Bounds

For each direction the appropriate interval is considered

The reference value is

Another treshold value is used


θi

Directional Success Function

1 if the local CLD belongs to the previous bound

0 if it doesn't


θi

10

Defect Map (DMAP)

Consider all directions for each pixel

Normalized signed count


“Successful” directions

Compute only if the local CLD exists

Count involved contributionsNormalize to [-1,+1]

How DMAP is rendered

Positive values (more successful than failing directions) → Green

Negative values (more failing than successful directions) → Red


The Directional Defect Map (DMAP)


Comparing Shapes

All defined directions are compared

The overall effect is considered

Focus on shape difference


“Similar” shapes

“Quite different” shapes

Square Difference Sum


θi

(red)

(blue)

Need for Scaling

Similar shapes can differ in size

Rescaling one of them allows a shape focused comparison


Similar shape, different size

Rescaling Function

Ratio of both average coherence lengths


Local CLD

Image CLD

Normalized Sum


Rescaling

Comparing

Comparison to Average

Average over all pixels


Set a treshold t'' Obtain the admittance interval

Directional Defect Map (DDMAP)


(red)

0

1

How DDMAP is rendered

Gray pixels → OK Yellow pixels → KO Note boundaries


Examples: Mineral Structures

Watch CLD Generator running Read reports


Amelia SparavignaDepartment of Physics - Politecnico di Torino

[email protected]

Roberto MarazzatoDepartment of Automation and Computer Science

Politecnico di TorinoFaculty of Science and TechnologyFree University of Bozen / Bolzano

[email protected]

Members of the Academic Society for Mathematics and Physics

Bozen / Bolzano


mailto:[email protected]

mailto:[email protected]

Mapping Images with the Coherence Length Diagram

Documents

mapping images

strigazzi amelia sparavigna

introduction amelia

toolamelia sparavigna

forearm skin amelia

cld saturation

formalisation of cld

recent works