thesis defence presentation 4_2

8/6/2019 Thesis Defence Presentation 4_2

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Study on A New Content-Based Image Retrieval Usingthe Multidimensional Generalization of Wald-Wolfowitz

Runs Test

Thurdsak LEAUHATONGProf. Shozo KONDO

Graduate School of Science and TechnologyTokai University

December 12, 2008
http://find/http://goback/


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1 Introduction

2 The Graph Theory, the Minimal Spanning Tree, and theMultidimensional Generalization of the Wald-Wolfowitz Runs Test

3 Two Similarity Measures Using the Multidimensional Generalization of

Wald-Wolfowitz Runs Test

4 Experimental Results and Evaluations of the Proposed System

5 Conclusions


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Introduction


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Image Retrieval System.

Image RetrievalSystem


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Text Annotation-Based Image Retrieval System

Image Database

Abstract Desert Water Fall Sheep Chicken Africa Church

Alaska Antelope Alps in Spring Zebra Africa People Africa

Architecture

ArchitectureHorses Antiques Car Racing Autumn Butterfly


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Text Annotation-Based Image Retrieval System

Text Key Word : Thailand

Retrieved Images


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The Problem of the Text Annotation-Based System

Manual : A cumbersome and expensive task

Abstract Antiques

Bali Java


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The Problem of the Text Annotation-Based System

Results : subjective, context-sensitive, and incomplete


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The Content-Based Image Retrieval System.

CBIR System


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The Visual Content of an Image


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ColorContent


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ColorContent

TextureContent


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ColorContent

TextureContent

ShapeContent


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ColorContent

TextureContent

ShapeContent

SpatialLayout

Content


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The Feature Vector of the Color Content

The most extensive-used color content : a color distribution


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Robustness to background complications and object distortion and

Th F V f h C l C


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Robustness to background complications and object distortion andInvariance to translation, scale, and rotation.

Th F V f h C l C


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Robustness to background complications and object distortion andInvariance to translation, scale, and rotation.

The most famous feature vector of the color distribution : color histogram

Th C l Hi


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The Color Histogram

R

G

B

Th C l Hi t


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The Color Histogram

R

G

B

Partition each color component into k levels with the same size

Th C l Hi t


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The Color Histogram

R

G

B

The color space is divided into k3

bins.

The Color Histogram


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The Color Histogram

R

G

B

The color histogram of ith bin of an image : the number of colors used inthe image which belong to the ith bin

The Similarity Measures between two Color Histograms


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The Similarity Measures between two Color Histograms.

Minkowsky Distance (MD)



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Histogram Intersection (HI)



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Kullback-Leibler Divergence (KL)



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Jeffrey Divergence (JD)



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Jeffrey Divergence (JD)

2 Statistics2

The Problem of the Color Histogram


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The Problem of the Color Histogram.

Partitioning the color space into equal-size bins is an inefficient method.

The originalimage.

The Problem of the Color Histogram


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The originalimage.

4 4 4color-bin image.

High SpeedLow Accuracy



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The originalimage.




Medium Speedand Accuracy



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The originalimage.




Medium Speedand Accuracy


Low SpeedHigh Accuracy

Theoharatoss Similarity Measure


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y

Based on the multidimensional generalization of Wald-Wolfowitz(MWW) runs test



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y


Based on the minimal spanning tree



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y



Outperform Histogram Intersection, Kullback-Leibler divergence, 2

Statistics, and the Earth Movers Distance.



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y





Require large computational time to provide the high accuracy.



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Require large computational time to provide the high accuracy.

My thesis proposed two similarity measures to overcome this problem.


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The Graph Theory, the Minimal

Spanning Tree, and theMultidimensional Generalization of

the Wald-Wolfowitz Runs Test

The Graph Theory


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The Graph Theory


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Vertexes

The Minimal Spanning Tree


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A spanning tree : a graph which has edges connecting all vertexes and hasnot cycle.



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The minimal spanning tree : a spanning tree which summation of all edgelengths is minimal.



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Prims algorithm :connect the ith fragment subgraph to its nearest neighbour vertex

The Definition of the Multidimensional Generalization ofW ld W lf i R T


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X1

X2 X3

X4X5 X6

X7

X8

f(z)

X = {X1, ,XN} with common distribution f(z)

The Definition of the Multidimensional Generalization ofW ld W lf it R T t


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Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8

g(z)

Y = {Y1, ,YN} with common distribution g(z)

The Definition of the Multidimensional Generalization ofW ld W lf it R T t


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X1

X2 X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8

Create the minimal spanning tree of X Y

The Definition of the Multidimensional Generalization ofWald Wolfowitz Runs Test


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X1

X2 X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8

Create the minimal spanning tree of X Y



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An inter-set (IS) edge : an edge joining a vertex of X to a vertex of Y

X1

X2 X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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The MWW runs test, R, is the number of disjoint trees which result fromremoving all IS edges.

X1

X2 X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8

How the MWW Runs Test Works


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Removing an edge will split the acyclic graph into two disjoint tree.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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The number of disjointed trees is the number of IS edges plus 1.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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According to Prims algorithm, an IS edge joins a pair of vertexes whichare close to each other.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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R is the number of pairs of vertexes which are close to each other plus 1.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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If X is a set of colors of pixels in image I1;

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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and Y is a set of colors of pixels in image I2;

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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R is the number of colors of pixels in I1 which are similar to colors ofpixels in I2 plus 1.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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If R is big, it can be assumed that the color content of I1 is similar to thecolor content of I2.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5 Y6

Y7

Y8



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If R is small, it can be assumed that the color content of I1 is dissimilar tothe color content of I2.

R = 0

X1

X2X3

X4X5 X6

X7

X8

Y1Y2

Y3

Y4

Y5

Y6

Y7

Y8

Examples of the MWW Runs Test


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R = 24

The Advantage of the MWW Runs Test


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Since the MWW runs test compares two distribution

functions f and g by using the minimal spanning tree,there is no problem about partitioning the color space.

The Permutation Distribution


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known information unknown informationm, n X, Y



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known information unknown informationm, n X, Y

The permutation distribution : Pr [R = k] .



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1) Randomly initialize the positions of m + n points



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2) Permute symbols of X and Y into the initialized positions



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There are (m+n)!m!n! =

10!5!5! = 252 permutations.



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R = 7 R = 6 R = 6 R = 5

2) Permute symbols of X and Y into the initialized positions3) Calculate R of each permutation



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4) Evaluate Pr [R = k] of all permutations

R

Pr [R = k]

2 4 6 8 10



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Four experiments of the permutation distributions

R

Pr [R = k]

2 4 6 8 1 0R

Pr [R = k]

2 4 6 8 1 0

R

Pr [R = k]

2 4 6 8 1 0 R

Pr [R = k]

2 4 6 8 10


[ ]


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Four experiments of the permutation distributions

All experiments have E [R] = 6.

R

Pr [R = k]

2 4 6 8 1 0R

Pr [R = k]

2 4 6 8 1 0

R

Pr [R = k]

2 4 6 8 1 0 R

Pr [R = k]

2 4 6 8 10



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R

Pr [R = k]

2 4 6 8 10



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R

Pr [R = k]

2 4 6 8 10

Pr [R = k] = Normal Distribution



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R

Pr [R = k]

2 4 6 8 10


E [R] = 2mnm+n + 1



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R

Pr [R = k]

2 4 6 8 10


E [R] = 2mnm+n + 1

= 2555+5 + 1 = 6



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W = RE[R]Var[R|C]

is used as the similarity measure in the CBIR in a way that



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W = RE[R]Var[R|C]


the bigger W is,



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W = RE[R]Var[R|C]


the bigger W is,

the more similar the distribution are.


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The Problem of the MWW Runs Test.

In order to apply the MWW runs test to the CBIR system, three problems


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must be addressed:


In order to apply the MWW runs test to the CBIR system, three problemsb dd d


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must be addressed:

1 perceptually uniform color space,


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In order to apply the MWW runs test to the CBIR system, three problemst b dd d


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must be addressed:

1 perceptually uniform color space,2 data reduction, and

3 the balance between the computational time and the accuracy of theCBIR systems.

The Perceptually Uniform Color Space.


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The most important task of constructing the MST :

Measuring a distance between two vertexes



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The distance must correspond to color difference perceived by human



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The distance must correspond to color difference perceived by human

The perceptually uniform color space

Data Reduction


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The number of colors of pixels in I1 and I2 are very large.

Data Reduction


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Data Reduction


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Data Reduction


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Require a data reduction technique.

Data Reduction


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The data reduction technique must preserve the original color distribution

as much as possible.

Data Reduction


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The data reduction technique must preserve the original color distribution

as much as possible.


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The Balance between the Computational Time and theAccuracy


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High Speed : Low Accuracy

CBIR System


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Balance between Speed and Accuracy

CBIR System



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Accuracy

Computational Time


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Accuracy

Computational Time

Bad CBIR System

ImpracticalCBIR

System


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Reducing the number of colors of pixels Reduce the accuracy of the


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g p y

CBIR system.


Reducing the number of colors of pixels Reduce the accuracy of the


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CBIR system.

Then an effective technique to increase the accuracy must be developed.

The Proposed Similarity Measure.

This thesis proposed two similarity measures using the k-means clusteringalgorithm and the MWW runs test.


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1

centroid-based MWW runs test.The centroid-based MWW runs test is proposed to solve:




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1


the perceptually uniform color space and




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1


the perceptually uniform color space andthe data reduction.




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1


the perceptually uniform color space andthe data reduction.

2 weighted MWW runs test.

The weighted MWW runs test is an extension of the centroid-basedMWW runs test to solve the problem of the balance between thecomputational time and the accuracy of the CBIR systems.


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The CIE La

b

Color Space and

Its Color Differences

The RGB Color Space and the Euclidean Distance

G


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R

B


G


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R

B(R1, b1,B1)

(R2, b2,B2)

ERGB =

(R1 R2)2 + (b1 b2)2 + (B1 B2)2


G


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R

B(R1

,b1,

B1)

(R2, b2,B2)

ERGB =

(R1 R2)2 + (b1 b2)2 + (B1 B2)2

Non-Perceptually Uniform Color Space.


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The CIE Lab Color Space

+L

+b


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Lb

+

a +a

X

Y

Z =

100

255

0.412453 0.357580 0.1804230.212671 0.715160 0.072169

0.019334 0.119193 0.950227

R

G

B


+L

+b


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Lb

a +a

L = 116fYY0

16,

a = 500

f XX0 f YY0 ,

b = 200

fYY0

f

ZZ0

,


+L

+b


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Lb

a +a

f(q) =

3

q, (q> 0.008856)7.787q, (q

0.008856)

The CIE Lab Color Differences

+L

+b(L, a, b)


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Lb

a +a

(L1, a1, b

1)

(2 2 2

)


+L

+b(L2, a2, b

2)


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Lb

a +a

(L1, a1, b

1)

ECIELab =

(L1 L2)2 + (a1 a2)2 + (b1 b2)2


+L

+b(L2, a2, b

2)


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Lb

a +a

(L1, a1, b

1)

ECIELab =

(L1 L2)2 + (a1 a2)2 + (b1 b2)2

ECIE94 =L

kLSL2

+C

abkCSC2

+H

abkHSH2


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The Vector Quantization and thek-Means Clustering Algorithm

The Vector Quantization


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C = {ci |ci }Ni=1



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Si = {z |z ci z cj} ,

where j [1, , N] and denotes a given distance.


The number of data belonging to the

i h id i ll d i i h


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ith centroid is called its weight.



i h id i ll d i i h


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ith t id i ll d it i ht


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ith t id i ll d it i ht


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ith centroid is called its eight


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ith centroid is called its weight


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ith centroid is called its weight


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D (Q p) 1

N z c r


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D(QN,C, p) = 1d

Ni=1

Si

z cirp(z) dz.

The k-Means Clustering Algorithm with the BinarySplitting


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The Centroid-Based MWW RunsTest.

The Centroid-Based MWW Runs Test.

R

G

Color

+L

+b

a +a


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R

B

ColorTransformation

Lb

a +a



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Data Reduction


a1


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a2

a3

a4

a5

a6

a7

a8

Data Reduction



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Data Reduction


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a1

b1b2

b3b5b


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a2

a3

a4

a5

a6

a7

a8

b4

b5b6

b7

b8

Computing the MWW Runs Test


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a1

b1b2

b3b5b


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a2

a3

a4

a5

a6

a7

a8

b4

b5b6

b7

b8

Computing the MWW Runs Test

R = 9, E [R] = 9, Var [R|C] = 3.48718,W = 993.48718 = 0.

The Block Diagram of the Centroid-Based MWW RunsTest

C l k Means


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ColorTransform

ColorTransform

k-MeansClustering

k-MeansClustering

MST

MWWW

(I1, I

2) =RE[R]Var[R|C]

The Advantage and Disadvantage of the Centroid-BasedMWW Runs Test.

The advantage:


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The advantage:Can solve the problems of the perceptually uniform color space


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The advantage:Can solve the problems of the perceptually uniform color space and the

data reduction.


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The disadvantage:


The advantage:Can solve the problems of the perceptually uniform color space and the

data reduction.


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The disadvantage:The accuracy of the CBIR system is not high.


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The Weighted MWW Runs Test


a1

b1b2

b3b5

b6b7


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a2

a3

a4

a5

a6

a7

a8

b4

b6

b8


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a1

b1b2

b3b5

b6b7

b5


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a2

a3

a4

a5

a6

a7

a8

b4

b6

b8

a7a2

b8


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R = 9



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E [R] = 2mnm+n + 1



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E [R] = 2mnm+n + 1

R = The number of IS edges plus 1.



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E [R] = 2mnm+n + 1

R = The number of IS edges plus 1.

The approximated number of IS edges =2mnm+n



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m = Wa2 + Wa7, n = Wb5 + Wb8



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m = Wa2 + Wa7, n = Wb5 + Wb8The approximated number of IS edges around a7

R(a7) = 2(W

a2 +W

a7 )(W

b5 +W

b8 )(Wa2 +Wa7 )+(Wb5 +Wb8 )


a1

a2a

b1b2

b3b5b6

b7


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a3

a4

a5

a6

a7

a8

b4

b8


a1

a2a7

b1b2

b3b5b6

b7

a1b7


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a3

a4

a5

a6

a7

a8

b4

b8

R(a1) =2(Wa1 )(Wb7 )(Wa1 )+(Wb

7

)


a1

a2a7

b1b2

b3b5b6

b7

a2a7

b7


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a3

a4

a5

a6

a7

a8

b4

b8

a7

R(a2) =2(Wa2 +Wa7 )(Wb7 )(Wa2 +Wa7 )+(Wb7 )


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a1

a2a7

b1b2

b3

b4

b5b6

b7

b1b2

b3


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a3

a4

a5

a6

a8

b4

b8

R(b1) =2(0)(Wb1 +Wb2 +Wb3 )(0)+(Wb1 +Wb2 +Wb3 )


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a1

a2a7

b1b2

b3

b4

b5b6

b7

b1

b3

b6


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a3

a4

a5

a6

a8

b4

b8

R(b3) =2(0)(Wb1 +Wb3 +Wb6 )(0)+(Wb1 +Wb3 +Wb6 )


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a1

a2a7

b1b2

b3

b4

b5b6

b7

a1

a2

b7


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a3

a4

a5

a6

a8 b8a3

R(b7) =2(Wa1 +Wa2 +Wa3 )(Wb7 )(Wa1 +Wa2 +Wa3 )+(Wb7 )


a1

a2a7

b1b2

b3

b4

b5b6

b7

a7


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a3

a4

a5

a6

a8 b8

a6

a8 b8

R(b8) =2(Wa6 +Wa7 +Wa8 )(Wb8 )(Wa6 +Wa7 +Wa8 )+(Wb8 )



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The weighted MWW runs test between I1 and I2

R(I1, I2) =M

i=1 R(ai) +M

i=1 R(bi)


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The Block Diagram of the Weighted MWW Runs Test

ColorTransform

k-MeansClustering

MST


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Color

Transform

k-Means

Clustering

IS edgesApproxima-

tion

R(I1, I2) =

Mi=1

R(ai) + Mi=1

R(bi)

Experimental Results andevaluations of the Proposed


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evaluations of the ProposedSystem

The Current MWW Runs Test


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Dividing the image into M nonoverlapping rectangle blocks


AC4 AC5 AC6

AC7 AC8 AC9


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AC1 AC2 AC3

Computing the average RGB color ACi of each block


PC4 PC5 PC6

PC7 PC8 PC9


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PC1 PC2 PC3

Computing the first principal component PCi of each block



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AC11 , ,AC1M,

PC11 , ,PC1M

AC21 , ,AC2M,PC21 , ,PC2M


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AC11 , ,AC1M,

PC11 , ,PC1M


MST


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AC11 , ,AC1M,

PC11 , ,PC1M


MST


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MWW


AC11 , ,AC1M,

PC11 , ,PC1M


MST


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MWWW (I1, I2) =

RE[R]Var[R|C]

Setting Up the Experiments


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g p p

Image Database.

The database consists of 20 categories. Each category consists of 50images with the size of 192128 or 128192.

Autumn Food Interior Design


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The Accuracy Computation

ImageRetrievalSystem

Query

Rank 1 Rank 2 Rank 3



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The retrieved images are ranked based on the output of the similaritymeasures.



Query

W (Q, I1) W (Q, I2) W (Q, I3)

W (Q, I4) W (Q, I5) W (Q, I6)


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W (Q, I7) W (Q, I8) W (Q, I9)

The centroid-based MWW runs test and Theoharatoss similarity measure



Query

R(Q, I1) R(Q, I2) R(Q, I3)

R(Q, I4) R(Q, I5) R(Q, I6)


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R(Q, I7) R(Q, I8) R(Q, I9)

The weighted MWW runs test



InteriorDesign

InteriorDesign

InteriorDesign

InteriorDesign

InteriorDesign

InteriorDesign

InteriorDesign


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g g g g

Royal GuardsInteriorDesign Food

A retrieved image is called relevant if it belongs to the same category ofthe query image.


The precision, Pr, is defined as:


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For the retrieved image which Rank(Q, Ii) 10Pr = the number of relevant images

the number of retrieved images.


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Randomly select three images from each category as query images.


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Randomly select three images from each category as query images.Compute average precision, AP, for all selected query images.


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Randomly select three images from each category as query images.Compute average precision, AP, for all selected query images.

AP = the probability that a relevant image would be found in the first 10


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p y g

retrieved images.

The Computational Complexity

The centroid-based MWW runs test

Query

Color

Transform

ColorTransform

k-Means

Clustering

k-MeansClustering

MST


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An image in thedatabase

Transform C g

MWWW (I1, I2) =RE[R]Var[R|C]



Query

Color

Transform

ColorTransform

k-Means

Clustering

k-MeansClustering

MST

Process 1


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Transform g


On-line process : Operation (1)



Query

Color

Transform

ColorTransform

k-MeansClustering

k-MeansClustering

MST

Process 1

Process 2


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g


On-line process : Operation (1)Off-line process : Operation (size of image database)



Query

Color

Transform

ColorTransform

k-MeansClustering

k-MeansClustering

MST

Process 1

Process 2

Process 3


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g



On-line process : Operation (size of image database the number ofsearchin



Query

Color

Transform

ColorTransform

k-MeansClustering

k-MeansClustering

MST

Process 1

Process 2

Process 3


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On-line process : Operation (size of image database the number ofsearchin



Color

Transform

ColorTransform

k-Means

Clustering

k-MeansClustering

MSTQuery

Process 1

Process 2

Part 3


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g

IS edgesApproxima-

tion

R(I1, I2) =

Mi=1 R(ai) +

Mi=1 R(bi)



On-line rocess : O eration size of ima e database the number of


Theoharatoss similarity measure

AC11 , , AC1M,

PC

1

1 , ,PC1

M

AC21 , , AC2M,PC21 , ,PC

2M

MSTQuery

Process 1

Process 2

Part 3


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1 M




On-line process : Operation (size of image database the number of


The most time consuming process is Process 3.


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The most time consuming part of Process 3 is constructing theminimal spanning tree.


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The computational complexity of constructing the MST is


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The computational complexity of constructing the MST isO

N2

N : The number of vertexes


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Query

ColorTransform

ColorTransform

k-MeansClustering

{a1, , aM}k-Means

Clusteringb1, , bM

MST of set{a1, , aM,b1, , bM}


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An image inthe database

{ }


N = 2M



ColorTransform

ColorTransform

k-MeansClustering

{a1, , aM}k-Means

Clusteringb1, , bM

MST of set{a1, , aM,b1, , bM}

Query


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{ }IS edges

Approxima-tion

R(I1, I2) =

Mi=1 R(ai) +

Mi=1 R(bi)

An image inthe database

N = 2M


Theoharatoss similarity measure

AC11 , , AC1M,

PC11 ,

, PC1M

AC21 , , AC2M,

PC21 , , PC2M

MST of setAC11 , ,AC1M,

PC11 , ,PC1M,AC21 , ,AC2M,PC21 , ,PC2M

Query


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MWWW (I1, I2) =

RE[R]Var[R|C]


N = 4M

The Performance Comparisons

ImpracticalCBIR

System

Good CBIRSystem

Accuracy


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Bad CBIR System

Computational Time

Study the average precision as a function of N.

The Performance Comparisons

ImpracticalCBIR

System

Good CBIRSystem

AP


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Bad CBIR System

N

Study the average precision as a function of N.

The Resultant Experiments


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Performance Comparison of the Centroid-Based MWW

Runs Test for Three Color Spaces and Color Differences.

AP

Euclidean Distance in RGB

Color SpaceEuclidean Distance in CIE

0.57

0.62

0.67

0.72


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N

L

a

b Color Space

CIE94 Color Difference in

CIE Lab Color Space

20 40 60 80 100 120 140 160 180 200

0.47

0.52

Performance Comparison of the Weighted MWW Runs

Test for Three Color Spaces and Color Differences.

AP



L

b C S

0.62

0.67

0.72

0.77


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N

Lab Color Space


CIE Lab Color Space

20 40 60 80 100 120 140 160 180 200

0.52

0.57

Performance Comparison of Blockwise Sampling-Based

MWW Runs Test for Three Color Spaces and ColorDifferences.

AP

0.62

0.67

0.72


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N



L

a

b Color Space


CIE L

a

b

Color Space

20 40 60 80 100 120 140 160 180 200

0.47

0.52

0.57

Performance Comparison of Three MWW Runs Tests.

AP

C id B d MWW R

0.7418

0.57

0.62

0.67

0.72

0.77


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N

Centroid Based MWW RunsTest

Weighted MWW Runs Test

Theoharatoss MWW Runs

Test

20 40 60 80 100 120 140 160 180 200

0.47

0.52

The First Example of Retrieval Results.

Query Rank = 1 Rank = 2 Rank = 3

Rank = 4 Rank = 5 Rank = 6 Rank = 7


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The Second Example of Retrieval Results.

Query Rank = 1 Rank = 2 Rank = 3

R k R k R k 6 R k


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Conclusions


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Conclusions.

This thesis proposes two similarity measures based on the MWW runs test

1 The centroid-based MWW runs test

2 The weighted MWW runs test


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Conclusions.




The two proposed similarity measures outperform the blockwisesampling-based MWW runs test.


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Conclusions.





The weighted MWW runs test has better performance than thecentroid-based MWW runs test.


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Conclusions.





The weighted MWW runs test has better performance than thecentroid-based MWW runs test.


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In the future work, a more effective method to evaluate the MWW runstest must be investigated.

List of Papers.

T. Leauhatong, K. Atsuta, S. Kondo, A New Content-Based ImageRetrieval Using Color Correlogram and Inner Product Metric, 8thInternational Workshop on Image Analysis for Multimedia InteractiveServices, 2007, pp. 33-33, June 6-8, 2007.

T. Leauhatong, K. Atsuta, S. Kondo, A New Content-based ImageRetrieval Using the Multivariate Generalization of Wald-WolfowitzRuns Test and the k-Means Clustering Algorithm, Proceeding of theSchool of Information and Telecommunication Engineering, vol. 1,no. 1, 2008. (to be appeared)


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List of Papers (continued).

T. Leauhatong, K. Hamamoto, K. Atsuta, S. Kondo, A NewSimilarity Measure for Content-Based Image Retrieval Using theMultivariate Generalization of Wald-Wolfowitz Runs Test,International Symposium on Communications and Information

Technologies 2008, Oct. 21-23, 2008. (to be appeared)T. Leauhatong, K. Hamamoto, K. Atsuta, S. Kondo, A NewContent-based Image Retrieval Using the MultidimensionalGeneralization of Wald-Wolfowitz Runs Test, IEEJ Trans.Electronics, Information and Systems, vol. 129(2009), no. 1. (to be

appeared)


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appeared)

The End

Thank you very much for yourattention.


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thesis defence presentation 4_2

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