Cit112010

Introduction The system Conclusions

Membrane Detector by Texture AnalisysAn Analysis of Edge Detection by Using the Jensen-Shannon Divergence,

Gomez-Lopera, Juan Francisco and Martınez-Aroza, Jose andRobles-Perez, Aureliano M. and Roman-Roldan, Ramon

Rodrigo Rojas Moraleda

July 4, 2012

Rodrigo Rojas Moraleda — Membrane Detector by Texture Analisys 1/24


Outline

1 Introduction

2 The system

3 Conclusions



Outline

1 Introduction

2 The system

3 Conclusions



IntroductionTexture analisys

Definition

Texture and texture analisys is the most important visual clue in identifying types ofhomogeneous regions. This is called texture classification. The goal of textureclassification then is to produce a classification map of the input image where eachuniform textured region is identified with the texture class it belongs to.

Problem features

In many machine vision and image processing algorithms, simplifying assumptionsare made about the uniformity of intensities in local image regions. However,images of real objects often do not exhibit regions of uniform intensities.

The patterns in a image can be the result of physical surface properties such asroughness or oriented strands which often have a tactile quality, or they could bethe result of reflectance differences such as the color on a surface.

One immediate application of image texture is the recognition of image regionsusing texture properties.



IntroductionJensen–Shannon divergence

Jensen–Shannon divergence

Jensen–Shannon divergence is a popular method of measuring the similaritybetween two probability distributions. It is also known as information radius(IRad) or total divergence to the average.

JSD(P ‖ Q) =1

2D(P ‖ M) +

1

2D(Q ‖ M)

M = 1/2(P + Q)

D(P ‖ Q) = DKL(P ‖ Q) =∑i

P(i)logP(i)

Q(i)

The average of the logarithmic difference between the probabilities P and Q,where the average is taken using the probabilities P.

Divergence grows as the differences between its arguments (the probabilitydistributions involved) increase, and vanishes when all the probabilitydistributions are identical.




Texture and texture analisys is the most important visual clue in identifyingtypes of homogeneous regions. Texture analisys aim to produce a classificationmap of the input image where each uniform textured region is identified.

Considerations about texture analisys and the real world

In image processing is possible made assumptions about the uniformity ofintensities in local regions. Despite of in real objects often do not exhibitregions of uniform intensities.

The patterns in a image can be the result of physical surface propertiessuch as roughness, oriented strands or reflectance differences such as thecolor on a surface.

Image Intensities and probabilities

Image histograms represents how frequent brightness levels from 0 to 255appear in the image, showing a visual impression of the distribution of data. Itis an estimate of the probability distribution of a continuous variable. The totalarea of a histogram used for probability density is always normalized to 1.




Jensen–Shannon divergence is a popular method of measuring the cohesion ofa finite set of probability distributions having the same number of possibleevents.Its value grows as the differences between its arguments (the probabilitydistributions involved) increase, and vanishes when all the probabilitydistributions are identical.

If we consider a window W made up of two identical subwindows W1 and W2,sliding over a straight horizontal edge between two different homogeneousregions a and b, Jensen-Shannon divergence between the normalisedhistograms of the subwindows reaches maximum value just when eachsubwindow lies completely within one region.

W1

W2

W1

W2W1

W2

W1

W2

W1

W2W1

W2




Trying several window orientations for each pixel is possible to obtain anestimate for the edge orientation which maximize the divergence value.

W1

W2

W1

W2

W1

W2

W1

W2

JS1 JS2 JS3 JS4

Figure: The values JS1,JS2,JS3 and JS4 are calculated for the fixed windoworientations 0, π/4, π/2and3π/4



Outline

1 Introduction

2 The system

3 Conclusions



The systemTexture analisys

Steps

Step 1. Calculation of divergence and direction matrices.

Step 2. Edge-pixel selection.

Step 3. Edge linking.



Step 1Calculation of divergence and direction matrices

Window sliding

W1

W2

W1

W2W1

W2

W1

W2

W1

W2W1

W2

Figure: Behavior of Jensen Shanon divergence versus sliding window over an perfectedge




Window sliding

W1

W2

W1

W2

W1

W2

W1

W2

JS1 JS2 JS3 JS4

Figure: The values JS1,JS2,JS3 and JS4 are calculated for the fixed windoworientations 0, π/4, π/2and3π/4

Problem

How to obtain an estimate of the direction fromthese four values that maximizes theJS and then the value of this maximum, JSmax . For a given pixel, the JS value is aπ − periodic function of window orientation over the image. It reaches its maximumvalue for a given orientation, β, and a minimum in β + π. A periodic function can beexpressed as:

JS(x) = a + bcos(β + 2πx), x ∈ [0, 1]

Here β ∈ [0, π) is the edge direction in the pixel, a,b are constants used to specify theamplitude.

JS(x) = c + msen(2πx) + ncos(2πx), x ∈ [0, 1]




Maximum JS

f (x) ≈ sen(2πx), g(x) ≈ cos(2πx)

With a least-squares fir over the points JS1 + JS2 + JS3 + JS4

JS(x) =JS1 + JS2 + JS3 + JS4

4+

JS2 + JS4

2f (x) +

JS1 + JS3

2g(x)

Maximum JS

The direction, x , having the maximun JS can be obtained by:

if JS1 − JS3 ≥ 0, JS2 − JS4 ≥ 0⇒

x =JS2 − JS4

4[(JS1 − JS3)− (JS2 − JS4)]∈ [0, 1/4]

if JS1 − JS3 ≥ 0, JS2 − JS4 ≤ 0⇒

x =4(JS1 − JS3)− 3(JS2 − JS4)

4[(JS1 − JS3)− (JS2 − JS4)]∈ [3/4, 1]




Maximum JS

if JS1 − JS3 ≤ 0, JS2 − JS4 ≥ 0⇒

x =2(JS1 − JS3)− (JS2 − JS4)

4[(JS1 − JS3)− (JS2 − JS4)]∈ [1/4, 1/2]

if JS1 − JS3 ≤ 0, JS2 − JS4 ≤ 0⇒

x =2(JS1 − JS3) + 3(JS2 − JS4)

4[(JS1 − JS3)− (JS2 − JS4)]∈ [1/2, 3/4]

Finally δ = πx ∈ [0, π) as the estimated edge direction. The x directionmaximizes the JS.Now each pixel is labelled with a pair of values, (estimated edge direction, andthe estimated JSmax)




Attenuation Factor

Due the JS is too sensitive to any change in grey levels between regions is necesaryinclude extra information, as an attenuation factor.

JS∗i,j = JSi,j (1− α+ αWi,j )

Where

Wi,j =|Nw1 − Nw2|/Nw

Nw1,Nw2 are the average grey level of subwindows W1 and W2



Step 2Edge-pixel selection

Edge-pixel selection

In this step the procedure selects which pixels from the divergence matrix are edgepixels.Thresholding the divergence matrix is not always useful, since maximum JS valuesdepend on the composition of adjacent textures, and will thus vary according totexture. Consequently, it would seem more appropriate to use a local criterion.Accordingly, each edge-pixel candidate is the centre of an odd-length monodimensionalwindow, placed perpendicular to the estimated edge direction in that pixel

Estimated edgedirection

Pixel understudy

Figure: Monidimensional Window



Step 2Edge-pixel selection

Edge-pixel selection

JScentre − JSj = Td

Any other pixel j in that particular monodimensional window, where Td is a threshold.Pixels marked as edge pixels are then outstanding local maxima of the divergencematrix. Obviously, detection results depend directly on the parameter Td, which canbe modified by the user if necessary.This local edge-pixel detection method requires simple divergence matrixpre-processing. The divergence matrix is therefore smoothed out by repeatedlyapplying a 3 × 3 mean filter.



Step 3Edge-linking

Edge-linking

This step attempts to join the various sets of edge pixels using information from thedivergence matrix associated with the image, together with knowledge of the directionin which maximum JS is produced. In broad terms, the linking procedure consists inextracting edge pixels unmarked since they did not satisfy the condition, but nearlydid. Not all the pixels in the image are candidates for filling the gaps, only thoseclassified as neighbour candidates of end pixels.

Figure: End points and neighbour candidates for edge prolongation. E, end point; C,neighbour candidates. The remaining grey pixels are edge pixels.



Step 3Edge-linking

Join End-points

End pixel criteria, is a pixel having one or two marked pixels joined together.

Neighbour candidate must have a JS reasonably high.

The estimated edge direction of the end pixel Dirend , the edge-directionneighbour candidate and the edge-direction of the physical line joining themmust not differ more than a specified amount.

Join End-points

JSend − JSneighbourcandidate 5 τd

(Dir(end , neighbourcandidate))− Dirend )2

+(Dir(end , neighbourcandidate)

−Dirneighbourcandidate)2 5 τθ



Results Theoretical

Figure:Rodrigo Rojas Moraleda — Membrane Detector by Texture Analisys 20/24


Results Theoretical

Figure:



Outline

1 Introduction

2 The system

3 Conclusions



Discussion

Discussion

Although this work is still in preliminary stages, we have seen the Monfroy frameworkis suitable for use in the modeling and prototype a dynamic composition of WebServices in the import of goods constrained problem.

Solve the backtracking problem in an totally distributed environment is still a problem,and must be resolved for use in a real environment



Questions ?

Rodrigo Rojas [email protected]


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