Report Keri

7/25/2019 Report Keri

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Honours Project Report

Genetic Algorithms:Colour Image Segmentation

Keri Woods

[email protected]

Supervised by: Audrey Mbogho

Department of Computer Science

University of Cape Town

2007


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Abstract

Image segmentation has great importance in many image processing applications,

and yet no general image segmentation exists. Image segmentation is complicated

task, often with many parameters needing to be tuned to get good results. This

report researches and discusses the concepts of image segmentation, genetic algo-

rithms and segmentation evaluation. Due to the flexibility of genetic algorithms andtheir ability to effectively explore large search spaces, it may be viable to use them

to improve existing image segmentation methods. A region merging algorithm was

implemented and evaluated using quantitative means. These segmentation results

were compared to those of two other image segmentation methods: region growing

and watershed segmentation. Our region merging method was shown to produce

average results. A genetic algorithm was implemented in an attempt to improve

the segmentation results by evolving the segmentation parameters. A fitness func-

tion needing neither human input nor a ground truth segmentation comparison was

proposed. The results on the effect of the genetic algorithm on the performance of

the genetic algorithm are inconclusive. However, even if the genetic algorithm does

offer an improvement, it has the major drawback of running very slowly. There are

many possible way of improving this system, and it seems to be an area where much

research is needed.

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Contents

Abstract i

List of Figures iv

1 Introduction 11.1 Pro ject Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 Project Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.3.1 Limited Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Background and Related Work 4

2.1 General Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Image Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.1 Colour Segmentation . . . . . . . . . . . . . . . . . . . . . . . 5

2.2.2 Methods of Image Segmentation . . . . . . . . . . . . . . . . . 5

2.2.3 Difficulties with Image Segmentation . . . . . . . . . . . . . . 7

2.3 Segmentation Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.4 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4.1 Applications of Genetic Algorithms for Image Segmentation . 9

2.4.2 Fitness Function . . . . . . . . . . . . . . . . . . . . . . . . . 122.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3 System Design and Implementation 14

3.1 Region Merging Image Segmentation . . . . . . . . . . . . . . . . . . 16

3.1.1 Region Merging Module . . . . . . . . . . . . . . . . . . . . . 18

3.2 Genetic Algorithm Module . . . . . . . . . . . . . . . . . . . . . . . . 23

3.2.1 Chromosome Structure . . . . . . . . . . . . . . . . . . . . . . 23

3.2.2 Reproduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.3 Selection and Termination . . . . . . . . . . . . . . . . . . . . 26

3.2.4 Fitness Function . . . . . . . . . . . . . . . . . . . . . . . . . 27

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4 Experimental Design 29

4.1 Evaluation of Region Merging Image Segmentation . . . . . . . . . . 29

4.2 Effect of Genetic Algorithm on Segmentation Quality . . . . . . . . . 30

4.2.1 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Modification of Genetic Algorithm Parameters . . . . . . . . . . . . . 31

4.3.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4.3.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

5 Results 32

5.1 Region Merging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

5.2.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

5.3 Alteration of Genetic Algorithm Parameters . . . . . . . . . . . . . . 36

6 Future Work 38

7 Conclusions 39

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List of Figures

3.1 Module Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

3.2 UML Diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.3 Module Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.4 RegionList Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Region Class . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.6 Genetic Algorithm Module . . . . . . . . . . . . . . . . . . . . . . . . 24

3.7 Parameter Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

3.8 Chromosome Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 26

5.1 Image Segmentation Example . . . . . . . . . . . . . . . . . . . . . . 33

5.2 Comparison of Segmentation Methods using RMSE . . . . . . . . . . 34

5.3 This table shows the comparison of the RMSE values using genetic

algorithms vs. traditional algorithms . . . . . . . . . . . . . . . . . . 34

5.4 The Effect of Scale Parameter on Segmentation Results . . . . . . . . 35

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Chapter 1

Introduction

1.1 Project Description

In this project we review image segmentation methods and look into the use ge-

netic algorithms for colour image segmentation. We base the segmentation part of

our implementation on a region merging method described in Baatz and Schape[8].

For our genetic algorithm, we follow a later improvement by Feitosaet al[22] which

evolves the parameters for region merging to give visibly better results. The key

to this improvement is a well-chosen fitness function, which captures the require-

ments of good segmentation without needing a comparison with a ground truth

segmented image. However, Feitosas fitness function relies on manual (user-based)

segmentation to test the success or failure of the genetic algorithm. Our approach,

in contrast, does not need user feedback, making it useful to real-world, automated

segmentation applications.

1.2 Motivation

Image segmentation is an important process and its results are used in many image

processing applications. However, despite its importance, there doesnt to seem to be

any general method of image segmentation that works well on all images[42]. Image

segmentation involves a lot of uncertainty, often with many parameters that need to

be tuned to provide optimal results. For example, the Phoenix image segmentation

method has 14 adjustable parameters[12]. This large number of parameters create a

very large search space. Colour images have even more information than grey-scale

images, and this information can be used to create higher quality segmentation. It

does, however, increase the complexity of the problem. A way of handling the large

search space is to use a directed search method, such as genetic algorithms.

Genetic algorithms have many qualities that make them well suited to the problem

of image segmentation, such as the ability to forego a local optimum to reach a global

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optimum and the ability to efficiently find an optimal solution from within a large

search space[9].

Genetic algorithms could allow an image segmentation process that usually requires

manual input to become unsupervised.

Genetic algorithms have been used to successfully colour segment images[12]. Dueto their flexibility, it seems feasible to be able to use them to come up with a general

segmentation method.

1.3 Project Scope

The main aims of this investigation are:

1. Research image segmentation

2. Research genetic algorithms, especially those used as part of an image seg-

mentation process

3. Research segmentation evaluation

4. Implement a method of segmenting colour images

5. Implement a genetic algorithm to improve the segmentation algorithm imple-

mented

6. Evaluate whether the use of the genetic algorithm is an improvement over the

original segmentation method

It will be advantageous if the segmentation method using the genetic algorithm is

able to segment general images and enables unsupervised colour image segmentation.

1.3.1 Limited Scope

Due to time limitations, some of the aims mentioned in the project proposal were

not met. These include:

1. Only one segmentation method was implemented and experimented with,

rather than comparing a number of different ones

2. The genetic algorithm implemented wasnt compared with those developed by

others

3. No experimentation on genetic algorithm parameters was done

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The reasons for these aims not being completed include:

1. Difficulties in the implementation of the region merging segmentation, includ-

ing memory leaks

2. Proposal objectives being too ambitious

3. Slow running times of the region merging-genetic algorithm system

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Chapter 2

Background and Related Work

In this section, we start by looking at the concept and importance of image segmen-

tation and mention the requirements for good image segmentation. The implication

of using colour in image segmentation is explored and methods for image segmen-

tation are briefly discussed. Problems with existing image segmentation methods

are mentioned. The evaluation of image segmentation is briefly discussed. Genetic

algorithms are then introduced and their suitability for use in image segmentation

is examined. We explore various applications of genetic algorithms to the problem

of image segmentation. Genetic algorithm fitness functions that have been used by

others with image segmentation as discussed. Finally, the feasibility of the use of

genetic algorithms for general colour image segmentation is considered and designissues for such an algorithm are discussed.

2.1 General Overview

Image segmentation is an important process and its results are used in many image

processing applications. However, there is no general way to successfully segment all

images[42]. Colour images have more information than grey-scale images, and this

information can be used to create higher quality segmentation. It does, however,

increase the complexity of the problem. A way of handling this complexity is to use

a directed search method, such as genetic algorithms. Genetic algorithms, which

mimic the process of evolution, have many qualities that make them well suited to

the problem of image segmentation, such as the ability to forego a local optimum

to reach a global optimum[9] and the ability too efficiently find an optimal solution

from within a large search space[6].

The main uses of genetic algorithms in image segmentation are for the modification

of parameters in existing segmentation algorithms and pixel-level segmentation[21].

Various algorithms that successfully apply genetic algorithms to image segmentation

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have been developed. Though these results are promising, none of them solve this

open problem.

2.2 Image Segmentation

Image segmentation is the process of dividing an image into homogeneous regions.

This is equivalent to finding the boundaries between the regions. Segmentation is

the first step for many higher level image processing and computer vision opera-

tions, including shape recognition, medical imaging[24], locating objects in satellite

images[33], face detection[4] and road sign recognition[48].

2.2.1 Colour Segmentation

Until recently, most image segmentation has been performed on grey-scale im-

ages. Processing colour images requires much more computation than the pro-

cessing of grey-scale ones, but now with the increasing speed and decreasing cost

of computation, colour image processing has been much researched in the last

decade[33][19][15][42].

Colour images contain far more information than monochrome images. Each pixel

in a colour image has information about brightness, hue and saturation. There

are many models to represent the colours, including RGB (red, green, blue), CMY

(cyan, magenta, yellow), HSV (hue, saturation, intensity), YIQ, HSI and many

others. Several colour spaces have been used for image segmentation[19] and no

general advantage of one colour space has yet been found[42].

Many of the colour image segmentation algorithms are derived from methods of

grey-scale image segmentation. However, colour creates a more complete represen-

tation of an image and exploiting this fact can result in a more reliable segmenta-

tion. Specialised techniques suited to the nature of colour information have been

devised[33][19].

2.2.2 Methods of Image Segmentation

Image segmentation is an old and important problem, and there are numerous image

segmentation methods. Most of these methods were developed to be used on a

certain class of images and therefore arent general image segmentation methods[9].

Bhanu and Lee[10] divide the image segmentation algorithms into three major

categories:

1. Edge Based

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2. Region Based

3. Clustering Based

4. Model Based1

Edge Based Techniques

Edge detection involves the detection of boundaries between different regions of

the image. These boundaries correspond to discontinuities between pixels of the

chosen feature (eg colour, texture, intensity).

Region Based Techniques

Region splitting is an image segmentation method whereby pixels are classified

into regions. Each region corresponds to a range of feature values, with thresholds

being the delimiters. The choice of these thresholds is very important, as it greatly

affects the quality of the segmentation. This method tends to excessively split

regions, resulting in over segmentation[10].

Region growing joins neighbouring pixels with similar characteristics to form

larger regions. This continues until the termination conditions are met. Most of the

region growing algorithms focus on local information, making it difficult to get good

global results. This method tends to excessively add to regions, resulting in under

segmentation[10].

Region merging recursively merges similar regions. It is similar to region grow-

ing, except that two whole regions are combined, rather than one region combining

with individual pixels[14].

Region splitting and mergingtries to overcome the weaknesses of region grow-

ing and region splitting by combining the two techniques. Initially the image is

divided into arbitrary regions. Region splitting and region merging occur until thetermination conditions are met[10].

The Phoenix image segmentation algorithm is a region splitting method

for segmentation that has been widely used and tested on colour images. It uses

histogram analysis, thresholding and connected component analysis to partially seg-

ment the image. Each region then has the same process applied to it recursively,

until termination conditions are met and the image is fully segmented. The algo-

rithm uses 17 parameters, 14 of which are adjustable[12][30].

1

This isnt discussed here as it is used to match particular objects and so isnt relevant togeneral image segmentation

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Clustering Based Techniques

Clustering separates the image into various classes without any prior knowledge.

This method is based on the assumption that objects within each class should have

a high degree of similarity, while those in different classes should be dissimilar. It is

considered an unsupervised image segmentation technique[33][40].

2.2.3 Difficulties with Image Segmentation

Image segmentation is easy when objects have distinct colours and are well sep-

arated, but can be a problem if there are many complex objects with less dis-

tinct colour. Gradual variation in colour[41], illumination[43], shading[49] and

textures[40] are also possible problems.

A brute force method of dealing with image segmentation would be to enumerate

all possible partitions of the image and evaluate each one. This creates an extremely

large search space, and so this method is not feasible[9].

Even once a segmentation method has been chosen, there are usually many param-

eters that need to be tuned to create high quality segmentation. For most methods,

it is not feasible to perform an exhaustive search of these parameters.

Despite the many methods for image segmentation, there is no general algorithm

that works well for all images. Because of the wide variety of images, a generalalgorithm needs to be adaptable. Only then can a segmentation algorithm cope

with a wide variety of images[10].

Many adaptive methods have been used for image segmentation, including ge-

netic algorithms[11], neural networks[20], self-adaptive regularisation[47], ant colony

optimization[37], fuzzy clustering[2] and simulated annealing[51].

2.3 Segmentation Evaluation

Methods of evaluating image segmentation are divided into two main categories[50]:

1. Analytical Methods

2. Empirical Methods

Analytical methods look at the actual segmentation algorithm itself, rather than

its results, while empirical methods evaluate the segmentation algorithm by lookingat its results. In this case, it is the empirical methods that we are more interested

in. Empirical methods can be further sub divided into:

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1. Goodness Methods

2. Discrepancy Methods

Goodness methods evaluate the quality of the segmentation by looking at its de-

sirable properties, and dont compare it to any other segmentation. It is this type of

method that we wish to use as a fitness function for the genetic algorithm, because

they dont need any prior knowledge of the image segmentation or ground truth

segmented image and so are advantageous for an unsupervised algorithm. Discrep-

ancy methods compare the segmentation results to an ideally segmented image, to

see how much its segmentation differs from the target segmentation. It is this class

of method that we will use to evaluate the results of our segmentation algorithm

during experimentation.

2.4 Genetic Algorithms

Genetic algorithms are an optimization technique that can be used in image segmen-

tation [11]. It mimics natural selection, allowing an algorithm to adapt. Solutions

are represented by a population of individual chromosomes, usually represented as

binary strings. A chromosome is made up of genes, each of which can represent a

particular characteristic. Each individual in the population is evaluated and given

a fitness score based on how well they solve the particular problem. The higher

the individuals fitness score, the greater their probability of breeding. Breeding

creates the next generation through crossover and mutation. Crossover combines

the chromosome of two individuals, creating a new individual which is unlike either

of the parents. Mutation, which occurs only a small percent of the time, randomly

alters a new individuals chromosome. Since the more optimal individuals have a

greater chance of breeding, the population tends to evolve and reach an optimal

solution[45][5][23].

Genetic algorithms have been used to solve a wide variety of problems, including

numerical and combinatorial optimisation, circuit design and cellular automata rule

design[23]. In image processing, genetic algorithms have successfully been used for

feature extraction, object recognition[44], knowledge based segmentation[36] and

image classification[18].

Image segmentation is easily and naturally formulated as on optimisation problem.

It can either be seen as finding the optimal segmentation amongst all candidate seg-

mentations, or as finding the optimal parameters for an existing image segmentation

algorithm. In both cases, this creates an extremely large search space, indicating

the use of genetic algorithms[6].

Genetic algorithms are advantageous in that they are able to forego local optima

in an attempt to reach the global optimum[9]. This makes them far less likely to

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get caught in a local optimum than deterministic optimization techniques, such as

local hill-climbing and gradient descent. Though more computationally expensive

than these methods, genetic algorithms are less computationally expensive than ex-

haustive searches and other adaptive techniques, such as simulated annealing, which

is theoretically guaranteed to find a global optimum[35]. While, genetic algorithms

cannot guarantee finding a global optimum, they usually give a good approximation.

This makes genetic algorithms a good compromise between accuracy and computa-

tional intensity.

Many image segmentation problems have large search spaces but need only an

approximate global optimum. In this case, genetic algorithms using a directed search

have proven useful[10]. A disadvantage of genetic algorithms is that they can take

a long time to converge. Though this is the case, they are still much more efficient

than performing an exhaustive search[23] [51].

Many images, particularly natural scenes, are complex and noisy. A characteristic

of genetic algorithms is their effectiveness and robustness in dealing with uncertainty,

insufficient information and noise. Combined with the fact that no matter how it is

posed, the image segmentation problem involves a very large search space, making

genetic algorithms well suited to the problem[10][3].

One of the major challenges for designing genetic algorithms is defining a fitness

function. The only information available to the population of chromosomes is the re-

sult of the fitness function evaluated every generation. This makes an appropriatelydefined fitness function essential for successful genetic algorithms. In the context of

image segmentation, the fitness function should evaluate the resulting segmentation.

There is, however, no generally accepted unsupervised method of evaluating image

segmentation[44].

2.4.1 Applications of Genetic Algorithms for Image Segmen-

tation

Farmer and Shugars[21] divide the genetic algorithms used for image segmentation

into two major classes:

1. Parameter selection, where genetic algorithms are used to modify the param-

eters of an existing image segmentation method to improve its output.

2. Pixel-level segmentation, where genetic algorithms are used to perform region

labelling.

Most image segmentation methods have many parameters that need to be opti-

mised, and therefore the first method is used more often[11]. Many such methods are

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discussed, as well as a few methods employing pixel-level segmentation. Modified

genetic algorithms and hybrid genetic algorithms have also been used for segmenta-

tion.

Parameter Modification

Most image segmentation methods have many parameters, constants and thresholds

that need to be adjusted to produce optimal segmentation results. This creates a

very large search space. Since the parameters typically interact in complex and non-

linear ways, an analytic solution is not generally possible. With a reasonable amount

of computation, genetic algorithms are able to find good approximations of a global

optimum within a large search space. They are therefore well suited to problems

involving parameter optimization. Most of the applications of genetic algorithms to

image segmentation involve the optimisation of various parameters[44][11][42][40].

Bhanu et al[11] pose image segmentation as an optimisation problem. They de-

fine a general segmentation method, whereby genetic algorithms are applied to the

parameters of various well known image segmentation methods. They advocate the

use of genetic algorithms to adapting the parameters of knows segmentation meth-

ods in order to be applicable to general images. They used outdoor colour imagery

and adapted 4 parameters of the Phoenix segmentation algorithm with genetic al-

gorithms. They had successful results, producing high quality image segmentation

with a reasonable amount of computation. Even though they perform well on out-door scenes, these algorithms have not been proved to be able to cope with general

images. The fact that these algorithms can be modified to adapt the parameters of

other segmentation methods makes this method very promising.

Feitosa et al[22] adopt a very similar approach and use genetic algorithms to modify

the parameters of a region merging segmentation algorithm. They use a fitness

function that measures the similarity of resulting segments to a target segmentation

provided by a user. Though computation is straight forward and intuitive, manual

segmentation is still necessary beforehand. This method can easily be adapted to

modify parameters of other segmentation methods.

Zingaretti el al[52] propose using genetic algorithms in unsupervised colour image

segmentation. This is another case of parameters of an existing image segmentation

method being tuned by genetic algorithms. A key difference in this method is

that it performs multi-pass thresholding. Different thresholds are adapted during

each pass of genetic algorithms. An important advantage of this method over the

previous one is that segmentation is performed totally unsupervised, without any

manual segmentation. It also doesnt rely on any prior information regarding the

type of image that is being processed or the task for which the segmentation results

will be used. This approach successfully segmented a wide variety of images, with

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the exception of images that were highly textured.

Pignalberi et al[39] use genetic algorithms for the optimisation of parameters in an

image segmentation algorithm. In this case, they focused on range images, where a

pixel is coloured depending on the distance between the object and a sensor. This

method segments out surfaces of 3D objects, but could be applied to segmentation

of 2D images.

Pixel-Level Segmentation

In pixel-level segmentation, genetic algorithms are used for region labelling. A pixel

is classed in a particular region depending on its characteristics[21]. Peng el al[38]

take this approach. Each pixel in the image is represented by a chromosome, which

is a region label.

Ramos and Muge[40] reformulate image segmentation as a clustering problem and

use genetic algorithms to find the optimal clusters. The chromosomes encode which

pixels are members of which regions. The major disadvantage of this method is that

the number of clusters must be given as an input, and so cant be an unsupervised,

general approach. Chun and Yang[16] take a similar approach, but use a fuzzy

fitness function.

Modified Genetic Algorithms

Gong and Yang[25] represent the image and the segmentation results by quadtrees.

In a similar way to Zingaretti el al[52], they define a two pass system, genetic

algorithms being used for optimization in both passes. In the first pass, genetic

algorithms are used to minimise an energy function. In the optional second pass,

a parameter defining how coarse or fine the segmentation is modified by genetic

algorithms to obtain optimal segmentation results. The chromosomes encode the

quadtrees, making it inefficient to apply the usual crossover and mutation operations.

To cope with this, a new crossover method and three mutation methods are defined.Aoyagi and Tsuji[7] use modified genetic algorithms for pixel-level segmentation.

They approach image segmentation as a feature clustering problem and like Gong

and Yang[25] use an energy function as a fitness function. They found it difficult to

get ideal segmentation using traditional genetic algorithms, and so introduced four

special types of mutation. They also propose a new method for creating individuals

of the population.

Hybrid Genetic Algorithms

Grenfenstette[26] mentions that genetic algorithms can be combined with local

search techniques, creating a high performance search algorithm. The following

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are examples of successful implementation of hybrid genetic algorithms for image

segmentation.

Genetic algorithms have been combined with other evolutionary methods to tackle

the image segmentation problem. Bhandarkar and Zhang[9] combine genetic algo-

rithms with simulated annealing based techniques - which mimic the physical pro-cess of cooling - to approach the problem of grey-scale image segmentation. They

do this is an attempt to get rid of the weaknesses of each class. This resulted in

better performance than traditional genetic algorithms. Zhijun et al[51] combined

genetic algorithms and simulated annealing to evolve a neural network, resulting in

less computation than if genetic algorithms were used on there own. Melkemi et

al[35] combine genetic algorithms with extremal optimization to perform pixel-level

segmentation.

2.4.2 Fitness Function

As mentioned previously, the choice of an appropriate fitness function is very im-

portant. It is the fitness function that is largely responsible for the quality of the

image segmentation obtained. The fitness function is what the algorithm "aims" to

optimise. When dealing with image segmentation, one needs a fitness function that

indicates how well the image has been segmented.

Feitosaet al[22] calculate fitness by quantifying the difference between the segmen-tation obtained using the individuals parameters and a target segmentation. The

target segmentation is obtained by manual segmentation, making this a discrepancy

method of evaluation. This works fine for experimental purposes - it shows that

genetic algorithms can be used to improve the quality of segmentation. However,

this fitness function makes the segmentation program of little practical use. If one

needs to segment the image beforehand, no benefit is obtained from the program.

Many other implementations also used discrepancy methods for calculating fitness,

including [29][39]. These methods arent relevant for use as a fitness function in this

implementation, as we need an unsupervised method of image segmentation.

Instead of using comparing the segmentation to a target segmentation, Zingaretti

el al[52] compare it to an edge map obtained by applying a Roberts edge operator

to the image. This makes the application more useful, but using an edge map as

"perfect" segmentation means that their program tries to obtain this segmentation.

It doesnt seem that segmentation better than that obtained with the edge operator

can be obtained, and using an edge filter is much more efficient.

As discussed previously, good image segmentation meets certain requirements:[33][9][10][27]

1. Every pixel in the image belongs to a region

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2. A region is connected: any two pixels in a particular region can be connected

by a line that doesnt leave the region

3. Each region is homogeneous with respect to a chosen characteristic. The char-

acteristic could be syntactic (for example, colour, intensity or texture) or based

on semantic interpretation

4. Adjacent regions cant be merged into a single homogeneous region

5. No regions overlap

One needs a fitness function that quantifies the quality of segmentation and it

would be ideal if a fitness function could evaluate the segmentation based on the

above segmentation requirements.

2.5 Conclusion

The use of genetic algorithms in image segmentation shows promising results. Ge-

netic algorithms are a commonly used approach to optimising the parameters of

existing image segmentation algorithms The major decisions are choosing a method

of segmentation to which genetic algorithms will be applied, finding a fitness func-

tion that is a good measure of the quality of image segmentation and finding a

meaningful way to represent the chromosomes.

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Chapter 3

System Design and Implementation

This system is composed of two modules:

1. Region Merging Module

2. Genetic Algorithm Module

The Region Merging Module performs a region merging method of image segmen-

tation on the input image. The Genetic Algorithm Module optimises the region

merging parameters. varies the region merging parameters, in an attempt to im-

prove the segmentation.

The Region Merging Module can be totally independent of the Genetic Algorithm

Module, with the parameters being set manually rather than letting them be altered

by the genetic algorithm. The Genetic Algorithm Module only calls the Region

Merging Module to calculate the fitness value. The interaction between the modules

is shown below in Figure 3.1:

The Region Merging Module receives and stores the input image. Whenever the

Genetic Algorithm Module requires a fitness value, it sends the segmentation pa-

rameters that it is currently working with to the Region Merging Module, requestinga fitness value. The Region Merging Module uses these parameters, segments the

image, evaluates the fitness and sends the fitness value to the Genetic Algorithm

Module. This process is repeated until the genetic algorithm terminates. The Ge-

netic Algorithm Module then sends the parameters that corresponded to the best

fitness value to the Region Merging Module. The Region Merging Modules uses

these parameters to segment the image and outputs the results of this segmenta-

tion.

These modules are loosely coupled, with the region merging module being able tobe replaced with a different segmentation method that needs its parameters tuned.

The fitness function can also be easily replace with different fitness function. This

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Region Merging

Module

Genetic Algorithm

Module

Input Image

Output Result

Send Parameters

(Request Fitness)

Return Fitness

Final Parameters

Figure 3.1: Module Interaction

allows the system to be more adaptable when experimenting with the use of genetic

algorithms for image segmentation.

This system was implemented in C++, using Microsoft Visual Studio 2005. Image

handling was done using the CImg Library[46], which is an open source C++ toolkit

for image processing. This library is very easy to set up, is well documented and

easy to use. It also offers much useful functionality for image processing.

A genetic algorithm library, GALib[1] was used for the implementation of the

Genetic Algorithm Module. It is well-documented, is very easy to use and offers

many different options for customising and configuring your genetic algorithm.

This implementation uses genetic algorithms modify the parameters of a region

merging algorithm. This particular region merging method was designed by Baatz

and Schape[8]. Feitosaet al[22] used genetic algorithms to modify the parameters of

this algorithm in order to optimise the segmentation obtained. This implementation

follows Feitosa et als ideas, except uses a different fitness function. The problemwith the fitness function used by them is that it relies on manual segmentation as

measure of good segmentation, which makes the segmentation method only useful

to prove that a genetic algorithm can be used to improve segmentation. This means

that their implementation isnt useful as a segmentation application.

The article[22] didnt mention key implementation details, leaving implementation

open to interpretation.

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3.1 Region Merging Image Segmentation

The idea behind region merging[8][22] is to divide the image up into many small

regions. Adjacent regions can be merged together, based on whether certain criteria

are met. This continues until no regions meet the merging criteria.

This particular method of region merging looks at the heterogeneity of the various

regions in the image when deciding whether or not regions will be merged. The

goal of the merging procedure is to minimise the weighted heterogeneity. There are

two main classes of heterogeneity: spectral heterogeneity and spatial heterogeneity.

The spectral heterogeneity measures how varied the colour within the region is.

The spatial heterogeneity measures the deviation of the region from a compact,

smooth shape. This is separated into compactness and smoothness components.

Compactness looks at the ratio of the perimeter to the square root of the area,

while smoothness looks at the ratio of the perimeter to the length of a bounding

box of the region, parallel to the image borders.

Initially, each pixel is initialised as a region. Regions are then visited in turn,

to decide whether that region will merge with another region. The order in which

regions are visited is discussed later.

When considering whether a region is going to be merged, each of the regions ad-

jacent to the region are considered. A fusion factor between the region and each

particular adjacent region is calculated. The fusion factor takes into account thevarious heterogeneity components:

Fusionfactor= wcolour hcolour+ (1 wcolour) hshape

where:

hcolour is the spectral heterogeneity component

hshape is the spatial heterogeneity component

wcolour is the weight given to the spectral heterogeneity component, which gives its

relative importance in comparison to the spatial heterogeneity component

A colour heterogeneity of each of the colour channels (red, green and blue) is calcu-

lated separately, and added to get the spectral heterogeneity component (modified

from the version presented in the paper):

hcolour = cwc(nObj3 cObj3 nObj1 cObj1 nObj2 cObj2)

where:

Obj1 is the region selected for merging

Obj2 is the region adjacent to Obj1

Obj3 is the result of merging Obj1 and Obj2

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c is the particular colour channel being considered

c is the standard deviation of the pixels in the colour channel c 1

The spatial heterogeneity component is a combination of compactness and smooth-

ness components:hshape=wcompact hcompact+ (1 wcompact hsmooth)

where:

wcompact is the weight given to the compactness component relative to the smooth-

ness component

hcompact is the compactness component

hsmooth is the smoothness component

The formula for the compactness component is:

hcompact=nObj3 lObj3nObj3 (nObj1 lObj1

nObj1

+ nObj2 lObj2nObj2 )where: l is the perimeter of the region

The formula for the smoothness component is:

hsmooth= nObj3 lObj3bObj3 (nObj1 lObj1bObj1

+ nObj2 lObj2bObj2 )where: b is the perimeter of the regions bounding box

Once the fusion factor for each adjacent region has been calculated, the region with

the minimum fusion factor is considered. If its fusion factor is less than a certain

threshold, then that adjacent region will be merged to the region being initially

considered. The threshold value used here to the square of a scale parameter. This

is known as a scale parameter, as adjusting this will result in differences in the

resulting region size. The larger the scale parameter, the more merges that will

happen, resulting in larger regions.

This process is then repeated, with another region being selected and the fusionfactor between it and its neighbouring regions being calculated. This process is

repeated until no more regions can be merged.

Baatz[8] mentions that one of the problems with their method of region merging

is that the order in which regions are visited in an attempt to merge them makes

a difference in the segmentation results. They recommend that when choosing a

sequence of starting regions that sequential merges should be distributed as far

from each other as possible.

1In this case, =

1

N1N

i=1x2i xbar2 =

1

N1N

i=1(xi x)2 where N is the number of

pixels, xi is the pixel value and xis the average value of the pixels

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They mention that an approximate solution is to handle each region in a random

sequence, but this isnt optimal. They didnt give details of the method they actually

used.

We tried to select random regions and process them, but found that processing

regions in order

2

was more successful. This also provides a deterministic result,which makes it easier for a genetic algorithm to work out. If the fitness generated by

the segmentation algorithm isnt deterministic, it is difficult for the genetic algorithm

to optimise it.

3.1.1 Region Merging Module

The system only depends on the CImg[46] class, with its accompanies cimg_library

namespace, as well as standard C++ templates and functions.We make broad use of the Standard Template Library (STL) to create containers

for the point, edge and region data structures. In each case, we use the container

that minimises the segmentation algorithms running time.

The system is composed of:

1. classRegion

2. classRegionList

3. structPoint

Their interactions can be seen in the UML diagram, shown below in Figure 3.2.

RegionList and Region are the two main classes, with Point being just a simple

struct. Along with this, various typedefs were defined:

typedef unsigned long int Label

typedef std::map < Label, Region >RMaptypedef cimg_library::CImg < Label >RImage

typedef cimg_library::CImg < Label >Image

typedef std::multimap < Label, Region >EdgeMaptypedef std::pair < Label, Region >EdgePairtypedef std::list < Point >PointList

2Initially, the pixels are given region labels left to right, top to bottom. Region ordering is anordering of these regions, with regions that no longer exist being ignored

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RegionList( );~RegionList();

getSize();mergeAll ();mergeRandom();saveResults();saveRegionMap();

addRegion();getRegion();removeRegion();getFusionFactor ();getHCompact ();getHSmooth();getHColour();getHShape();tryMerge ( );coordToLabel ();

RImage rimage;Image image;RMap* regions;unsigned int imageWidth;unsigned int imageHeight;float wRed;float wGreen;float wBlue;float wColour;float scale;float wCompact;

RegionList

...

...std::list

...

...std::multimap

Region();~Region();

void addEdge();unsigned int getArea();Label getLabel();float getAverageR();float getAverageG();float getAverageB();unsigned int getPerimeter();

unsigned int getPerimeterCombined();unsigned int getPerimeterBB();unsigned int getPerimeterBBCombined();float getStdDev();float getStdDevCombined();void splice( );

EdgeMap* getEdges();PointList* getPixels();void removeAllEdgesTo ( );void changeAllEdgesTo ( );

RImage* rimage;Image* image;PointList* pixels;EdgeMap* edges;Label label;unsigned int maxX;unsigned int maxY;unsigned int minX;unsigned int minY;Label sumR;Label sumG;Label sumB;float averageR;float averageG;float averageB;unsigned int area;unsigned int perimeter;

Region

...

...std::map

...

...

cimg_library::cimg

Point( int a, int b)

int xint y

Point

Figure 3.2: UML Diagram

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Region Merging

Module

Genetic Algorithm

Module

Input Image

Output Result

Send Parameters

(Request Fitness)

Return Fitness

Final Parameters

Figure 3.3: Module Interaction

RegionList Class

The RegionList class represents the collection of all the regions in the segmented

or partially segmented image. The structure of the class is shown in Figure 3.4.

The main components of this class are:

1. RImage rimage

2. Image image

3. RMap* regions

The Image object, represents the original image, represented in RGB colour space.

Image is a type of CImg object and allows access to the red, green and blue compo-

nents of each pixel. The RImage object (region map) is also a type of CImg image

object, with the same dimensions as the original image.

The segmentation algorithm working on a collection of regions must often select

and adjust a specific region. In this case, the STL map data structure is the natural

choice (RMap). As a container, a map has the advantage of a logarithmic size

complexity for key-based insertions, deletions, and searching. To allow keyed access

to our collection of regions, we assign a unique integer (Label) to each region based

on its initial position in the starting image. Subsequently, when merging two regions,

the target region will keeps its key and adjusts all neighbouring regions to reflect

this change. In this way, all possible changes to the region collection, like adding,removing, or altering region contents, and searching for a region, run in logarithmic

complexity in the size of collection.

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RegionList( const char* filename, float r, float g, float b, float col, float s, float com );~RegionList();

int getSize();void mergeAll ();

bool mergeRandom();void saveResults( const char* filename );void saveRegionMap( const char* filename );void addRegion( const Label& label, const Point& p );Region* getRegion( const Label& label );void removeRegion( const Label& label );float getFusionFactor ( Region* region1, Region* region2 );float getHCompact ( Region* region1, Region* region2 );float getHSmooth( Region* region1, Region* region2 );float getHColour( Region* region1, Region* region2 );float getHShape( float hCompact, float hSmooth );bool tryMerge ( Region* r );Label coordToLabel ( unsigned int x, unsigned int y );

RImage rimage;Image image;RMap* regions;unsigned int imageWidth;

unsigned int imageHeight;float wRed;float wGreen;float wBlue;float wColour;float scale;float wCompact;

RegionList

Figure 3.4: RegionList Class

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Region( Label lbl, const Point& p, RImage* regionImage, Image* originalImage );

~Region();

void addEdge( Label lbl, Region* otherRegion );unsigned int getArea();Label getLabel();float getAverageR();float getAverageG();float getAverageB();unsigned int getPerimeter();unsigned int getPerimeterCombined( const Region* otherRegion );unsigned int getPerimeterBB();unsigned int getPerimeterBBCombined ( const Region* otherRegion );float getStdDev( unsigned int channel );float getStdDevCombined( const Region* otherRegion, unsigned int channel );

void splice( Region* otherRegion );EdgeMap* getEdges();PointList* getPixels();void removeAllEdgesTo ( Label lbl );void changeAllEdgesTo ( Label lblOldRegion, Region* newRegion );

RImage* rimage;Image* image;PointList* pixels;EdgeMap* edges;Label label;unsigned int maxX;unsigned int maxY;unsigned int minX;unsigned int minY;Label sumR;Label sumG;Label sumB;float averageR;float averageG;float averageB;unsigned int area;unsigned int perimeter;

Region

Figure 3.5: Region Class

The image height and width are stored, as they are accessed very frequently and

their storage prevents numerous function calls to the Image and RImage objects. Allthe other attributes are segmentation parameters and are passed in as arguments to

the constructor. These are either set manually or are set by the genetic algorithm.

Region Class

TheRegionclass represents a region in a segmented or partially segmented image.

The structure of the class is shown in Figure 3.5.

The main components of the Regionclass are:

1. PointList* pixels

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2. EdgeMap* edges

3. Label label

Pixels represent the pixels making up the image. They are Points, stored as a list

(PointList). A list was used because insertion by pushing on to the front of thelist runs in constant time. Deletion of pixels only occurs when all the pixels in the

region are deleted3 are deleted, so at each pixel delete takes constant time. (Deletion

runs in linear time if the algorithm wasnt already iterating through the list.)

Edges are stored as a multimap (EdgeMap). A boundary pixel in a region can

point to one or more other regions. However, edges are stored separately from pixels,

since actual pixel positions are unimportant when using edges to check connectivity.

Insertion and find are both logarithmic time operations on a multimap. When

erasing, all the elements with the same key are deleted. This is an logarithmic timeoperation, plus linear time is required for deleting nequal elements.

Regions are assigned unique integer values (Label) based on their initial positions

in the image.

Pointers to both the original image and the region map are included as this class

needs access to them. All the other attributes are stored, and updated every time

the region is altered. These values are needed for the fusion factor calculation. It

is worth using a little extra memory to store these values and save the numerous

computations that would be required otherwise.

3.2 Genetic Algorithm Module

The Genetic Algorithm Module is a simple module, with much of the functionality

being provided by the GALib library[1]. Its basic behaviour and interaction with

the Region Merging Module is shown in Figure 3.6.

The genetic algorithm is represented by a GASimpleGA object, provided by GALib.This class is used for genetic algorithms with non-overlapping populations, and in-

herits from the general GAGeneticAlgorithm class.

3.2.1 Chromosome Structure

Each chromosome is represented by a GABin2DecGenome object (again provided

by GALib) and inherits from the general GAGenome class. This type of genome

stores its genes in binary, but converts them into decimal values to be used in thefitness calculation.

3Regions are only every merged or destroyed

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Region Merging Module

InitializePopulation

Mutate Offspring

Insert Offspringinto Population

Are stoppingcriteria satisfied

Select Indiviualsfor Mating

Select Indiviualsfor Mating

Mate individulalto produce offspring

Genetic Algorithm Module

request fitnes

return fitness

Figure 3.6: Genetic Algorithm Module

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0.1 410wBlue 0-1

0-1 40.1 10wGreen0-1 4wRed 0.1 10

7

No. ofBits

10

7

1000

100

No. ofValues

1000.01

0.01

0.1

Precision

0-100

Range

0-1

0-1

wColourscale

wCompact

Figure 3.7: Parameter Details

In the Genetic Algorithm Module, a chromosome represents the various segmenta-

tion parameters of the region merging algorithm. These are:

1. Scale parameter

2. Weight given to the spectral heterogeneity

3. Weight given to the compactness component relative to the smoothness com-

ponent

4. Weight of the red channel

5. Weight of the green channel

6. Weight of the blue channel

Each of these is encoded in binary, as a separate gene. The scale parameter canvary from 0 to 100, while all the other parameters are vary from 0 to 1. The scale

parameter and the weight of the various colour bands each have a precision of0.1,

while spectral and compactness weights have a precision of 0.01. All the weight

parameters are encoded as positive integers, with the maximum value of1 divided

by the particular precision factor (0.01 0r 0.1). To access the actual fractional

values of the weights, one converts the parameter from binary to decimal and then

multiplies it by the precision factor.

To encode each gene in binary, one looks at the number of possible values thatparameter can take on. For example, the scale parameter can take on(10010)+1 =1001 different values. The binary representation of that gene therefore has to be

able to encode 1001 different values. 1001 is then encoded using the same number

of bits that would be used to encoded the smallest power of2 greater than 1001.

This is 1024 = 210, and so log21024 = 10 bits is used to encode this.

As can be see from figure, there are about1000100100101010 = 1010 differentparameter combinations! It would be infeasible to try each of these combinations to

find the ideal combination of them, indicating the use of a genetic algorithm.

The only other complication is that the sum of the weights of the colour bands

needs to add up to 1, so their values are normalised. To get the normalised value

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Scale wColour wCompact wRed wGreen wBlue

10 bits 7 bits 7 bits 4 bits 4 bits 4 bits

Figure 3.8: Chromosome Structure

of of band i, one takes the weight of band i and divides it by the sum of all three

band weights.

3.2.2 Reproduction

In this implementation, one point crossover is used. In one point crossover, a random

position on the chromosome is select and the two individuals exchange the genes

on one side of that point. The mutation used is flip mutation, which is the typicalmutation operation used on binary strings: bits in the chromosome are flipped with

a given probability.

Elitism is used, with the best individual in each generation being carried over to

the next generation.

3.2.3 Selection and Termination

Roulette wheel selection is used to select individuals to take part in reproduction. Inroulette wheel selection, an individuals probability of taking part in reproduction

is proportional to their fitness. In this case, the fitness values are normalised: in

this fitness evaluation (see the following section later), a low fitness corresponds to a

good quality segmentation. The fitness values values are adjusted so that individuals

with low fitness value end up with a high adjusted fitness, which corresponds to a

high probability of taking place in reproduction.

Termination takes place when the maximum number of generations is reached.

This was chosen to be the termination criterion because then one can be sure thatthe genetic algorithm will terminate. On the other hand, if convergence was used

as the termination criterion, it could continue for very many generations with the

population never converging. Also, because of the large amount of computation

required for each fitness computation - an image has to be both segmented and

evaluated - one wants to make sure not too many generations are evolved. The

image segmentation parameters dont have to be exact to get a good segmentation

result, so it isnt worth waiting for the population to converge.

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3.2.4 Fitness Function

As mentioned previously, one would like a fitness function that evaluates the follow-

ing requirements of good image segmentation:

1. Every pixel in the image belongs to a region

2. A region is connected

3. Each region is homogeneous

4. Adjacent regions cant be merged into a single homogeneous region

5. No regions overlap

Requirements 1, 2 and 5 are always obtained when using this region merging tech-nique, therefore the important characteristics to quantify is that each region is ho-

mogeneous and that adjacent regions cant be merged into one homogeneous region.

Various different fitness function were. Liu[31] proposed goodness method to be

used for the quantitative evaluation of the performance of image segmentation, which

could be used as a fitness measure. The evaluation function Fon segmented image

I is defined as:

F(I) = 11000N2RRi=1 e2

iAi

where: N2 is the size of the image R is the total number of regions Ai is the area

of region i ei is the colour error, Euclidean distances in colour space between the

values of the pixels in region i in the original image and the values of the pixels in

the segmented image, defined as:

ei= Aij=1

(C1jR C2

jR)

2 + (C1jG C2jG)

2 + (C1jB C2jB)

2

where: R, G and B are the colour channels C1j is the colour of pixel j in the

original image C2j is the assigned colour of the same pixel in the segmented image

Lower values ofF(I) correspond to better segmentation. Fevaluates the results

both locally and globally.

R is global measure and penalises over-segmentation.

The e2

iAi

portion is a local measure which penalises small regions or regions with a

large colour error.

Borsottiet al[13] propose an improvement, which was implemented:

Q(I) = 11000N2

RRi=1[

e2i

1+logAi+ (R(Ai)

Ai)2]

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We propose an alternative fitness function4, aiming to minimise weighted colour

heterogeneity. The colour heterogeneity is based on Feitosas[22] concept.

E(I) = ((Ri=1Hi) + 1) R

where:

E(I) is the fitness evaluation of segmented image I

R is the number of regions in the image

Hi is the colour heterogeneity of the ith region:

Hi=Ai (R+ G+ B)

where: Ai is the area of region i

j is the standard deviation of colour channel j

Hiis the weighted colour heterogeneity of region i. It is weighted by the size of the

region so that larger regions contribute more to the overall heterogeneity. The colour

heterogeneity of all the regions are added together to get the total heterogeneity of

the image. 1 is added to this as when each region has area of 1, the standard

deviation of that image is zero. When the regions are initialised, they are have

an area of1 pixel, and so would each have a standard deviation of zero. If the 1

wasnt added, the fitness of the initial segmentation would be 0, meaning its the

ideal segmentation, which of course isnt the case.

The sum of the colour heterogeneities as multiplied by R to penalise small regions.

This is done because smaller regions tend to have a smaller standard deviation, for

example a single pixel has a standard deviation of1.

When evaluating this method against the segmentation requirements, one can seethat it is a good measure of the fact that each region is homogeneous. The fact

that adjacent regions cant be merged isnt evaluated directly in this measure, but

multiplying by the number of regions indirectly evaluates this: if two adjacent regions

are very similar and are merged, their combined standard deviation doesnt increase

much (ie Ai i +Aj j) is not much greater than (Ai +Aj) (i +j)), thetotal colour heterogeneity is multiplied by 1 less5. This results in a lower fitness

value. This indirectly implies that if fitness is at a minimum, adjacent regions cant

be merged into a homogeneous regions, otherwise the fitness value would decrease -

which is not possible if the fitness value is the minimum one.

4Once again, a low fitness value corresponds to good segmentation5Because the number of regions decreases

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Chapter 4

Experimental Design

The main areas that need to be tested are:

1. Evaluation of region merging image segmentation

2. Segmentation improvement provided by genetic algorithms

3. Improvement of genetic algorithm by altering genetic algorithm parameters

4.1 Evaluation of Region Merging Image Segmen-

tation

Various images from the Berkeley Image Dataset[34] will be chosen to be segmented.

These represent a wide range of images, from those that are easy to segment to

those that are much more difficult to segment, such as a camouflaged animal. These

results will be evaluated subjectively. For example, it can be seen whether or not a

camouflaged animal is segmented out.

Dorin Comaniciu[17] has images on his website with the corresponding successfully

segmented images. These segmented images will be used as ground truths when

evaluating our system. It would have been better if images manually segmented

by humans were used as the ground truth, as they represent "ideal" segmentation.

However, no manually segmented images in the correct format were found. The

region merging algorithm will be run on each of the images to produce the resulting

segmented images. One needs to find an objective way of evaluating the performance

of this segmentation in comparison to the ground truth images.

This evaluation will be done using ImageMagicks[32] compare function, using the

MSE (mean squared error) option. The difference between the values of each pixel of

the ground truth segmentation and the corresponding pixel in the segmented image

that is being evaluated. This value is then squared, to get rid of negative values

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and penalise more heavily where the pixel value difference is large. These values are

then summed over the whole image to get the MSE. The root of this is taken to get

, the RMSE (root mean squared error). This value is then divided by the number

of pixels in the image to obtain the normalised RMSE, an evaluation measure that

is size independent.

This same procedure will be repeated with the region growing and watershed al-

gorithms implemented by Marco Gallotta. The results of all three of these image

segmentation algorithms will be compared.

4.2 Effect of Genetic Algorithm on Segmentation

Quality

4.2.1 Hypothesis

The use of the genetic algorithm will improve the quality of the image segmentation.

4.2.2 Method

Each image to be evaluated will be segmented using the region merging algorithm.

The segmentation parameters will be tweaked to attempt to obtain the best results.The best results will be evaluated using a normalised RMSE, as discussed above,

and recorded. Due to the fact that the results from genetic algorithms arent deter-

ministic, the images will be segmented five number times1 by the genetic algorithm

version. Each run will be evaluated and the average score for each image recorded.

The average score for each algorithm type will calculated and the results will be

compared.

The population size used in the genetic algorithm should be made as large as

computation time allows. The other genetic algorithm parameters should be tweakedto try and obtain the best possible results. Note of the values used should be made,

so that the experiment can be repeated2.

15 was an arbitrary choice. The more times the segmentation is run, the more accurate theresults, so it should be repeated as many times as is feasible

2It may be preferable to perform the next part of the experimentation first, examining the effectof modifying the parameters of the genetic algorithm, to determine the optimal parameters

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4.3 Modification of Genetic Algorithm Parameters

4.3.1 Purpose

The main purpose of this section of the experimentation is to see what effect changing

the genetic algorithm parameters and other factors - such as reproduction operators

and termination criteria - will have on the quality of the segmentation results. This

knowledge can then be used to find the optimal settings for the genetic algorithm.

4.3.2 Method

Various settings can be modified, such as:

1. Population size

2. Chance of mutation taking place

3. Termination criteria

4. Number of individuals passing unchanged to the next generation

5. Crossover operators used

6. Mutation operators used

7. Selection method

8. Whether elitism is used and how many individuals are passed unchanged to

the next generation

The setting to be examined is chosen. If it is a numerical value, it will be tested

at equally spaced intervals throughout its range or part of its range, otherwise the

various options are tried. It is very important that only one of these factors is

changed at a time, so that one knows what is causing the change in the segmentation

quality (if any change).

The segmentation will be performed 53 times will each option or value, and the....

measure calculated. The average of these values will be taken as the result at that

particular value or option. If the parameter being set is numerical, the results will

be graphed and analysed, if not the various options will be compared. Conclusions

will be made about what options produce the best segmentation results.

3again an arbitrary choice

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Chapter 5

Results

5.1 Region Merging

The segmentation program outputs two result images. The first is the segmented

image, with each region being shown in the average colour of all its pixels. The

second is the region map, where each region is given a different value, and therefore

a different shade in the image. This is done to make the distinction between regions

clearer. If two adjacent regions have the same or very similar average values, the

fact that they werent merged (and probably should have been) wouldnt show up

in the segmented image. An example of the results are shown in Figure 5.1.

The results of the comparison of the region merging implementation with the region

growing and watershed algorithms is shown in Figure 5.2.

As can by seen, this implementation had rather average results. The watershed

method performed the best, and ran much faster than either of the other algorithms.

5.2 Genetic Algorithm

Two different fitness functions were implemented. Q(I), as defined previously, could

be subjectively seen to perform badly, appearing to produce worse segmentation

results than the original region merging algorithm. No further evaluation using this

fitness function was performed.

E(I) subjectively seemed to perform better than the original region merging algo-

rithm. To confirm or refute this, further evaluation was performed. This evaluation

was objective, being deterministic and calculated by the computer.

The results obtained are shown below in Figure 5.3:

As can be seen, the genetic algorithm only showed an improvement over the original

region merging implementation for one of the images. Reasons for this could include

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(a)

(b)

(c)

Figure 5.1: Image Segmentation Example(a)Original Image

(b)Segmented Image(c)Image Map

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Hand

4959

Woman5597

House3095

RegionGrowing

3558

5076 3324.65

4296

3699

RegionMerging

Watershed

4622

Figure 5.2: Comparison of Segmentation Methods using RMSE

4959Woman

4938

5172

5437

6575

5067

5437

3324Hand

GA avg 4947

3613

3435

GA5

House

4655

3472

GA3

GA1

GA2

3490

Non GA

4852 3414

5195 3408

GA4

4787

5249

5076

Figure 5.3: This table shows the comparison of the RMSE values using geneticalgorithms vs. traditional algorithms

a poorly chosen fitness function, using a population size that is too small to offer

enough variation for the individuals to evolve or not running the genetic algorithm

for enough generations for the population to evolve sufficiently.

It may seem totally infeasible to find the ideal parameter combination for the

region merging algorithm. However, the fact that there are1010, different parameter

combinations is deceptive. From experimenting with varying the parameters, it

was found1 that the only parameter that made a significant different was the scale

parameter. Even the scale parameter only had any great effect on the segmentation

when altered by a large amount. A feasible solution would be to give each colour

channel an equal weighting, setting wRed, wGreen and wBlue all to 0.33; letting

compactness and smoothness have the same influence, setting wCompact to 0.5.

The effect of changing the scale parameter is shown below in Figure 5.4.

The effect of changing the scale parameter by 10 isnt that great. Suppose, to be

on the safe side, we allow the scale parameter to vary by increments of 5. This

means that there are only 20 different combinations of parameters to try - which

should be slightly faster than running 2 generations of a genetic algorithm with a

population size of10.

With a bit of prior knowledge, one doesnt even have to try all of this limited range

of scale factor. If the various objects in the image appear distinct (such as the flowers

shown below), one can set the scale parameter high. This high scale parameter will

mean that more region merging occurs. This means that small colour variations,

such as shadows or reflections, within an object hopefully wont be recognised as

separate objects, while the separate objects are distinct enough from each other not

to be merged together. However, if one is looking to distinguish objects of similar

1These are just general observations, and havent been formally tested

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(a)

(b)

(c)

Figure 5.4: The Effect of Scale Parameter on Segmentation Results(a)Original Image

(b)Scale parameter 30(c)Scale parameter 70

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colour, such as the camouflaged crocodile, one needs to set the scale parameter

much lower. The negative aspect of doing this, however, is that it means that the

segmentation isnt unsupervised and does require user interaction.

A major problem in using this region merging- genetic algorithm system is that

it is very slow to run. When processing a 481 by 321 pixel image, using a geneticalgorithm with a population size of 10 and running 20 generations, the take taken is

about an hour2. This makes getting results a rather tedious process, especially since

because of the random nature of genetic algorithms, one needs to take the average

performance over a few trials when evaluating the performance of the segmentation.

Marco Gallotta came up with a solution to this problem and ran this algorithm on

a grid.

5.2.1 Conclusion

It can be concluded that we are unable to reject the hypothesis that the use of

a genetic algorithm would improve the quality of the image segmentation. The

genetic algorithm could provide an improvement in segmentation quality, though

this hasnt been shown. Because of the time taken to run the genetic algorithm, its

full potential hasnt been explored.

Although there is a chance it could offer an improvement in segmentation quality,

the major drawback is that running the genetic algorithm is extremely slow. Thiscan be improved by running it on a grid, but not many people have access to a grid,

and so in most cases this isnt a feasible solution. Other options would be to limit

the range through which the parameters are allowed two vary or to provide a totally

different underlying image segmentation algorithm. An example of an algorithm that

could be used would by the watershed segmentation algorithm. In the experiments

done with Marco Gallottas implementation of this algorithm, it was found to run

far quicker than either the region growing or region merging methods.

5.3 Alteration of Genetic Algorithm Parameters

It was not feasible to run these experiments due to the extremely long execution

time of the region merging segmentation with the genetic algorithm3. Not only does

one have to wait a long time to get results for the performance of various parameter

settings, but it makes it totally infeasible to increase the maximum number of gener-

ations or increase the population size. This is unfortunate, as one predicts that the

segmentation performance would increase the as the number of generations increase2Running on a laptop with a Core Duo 1.8 GHz with 1gig RAM3It takes exactly an hour to run the algorithm for 20 generations, each with ten individuals

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(because there is more time to evolve) and also increase with increasing population

size (a larger population provides larger variation, which makes finding an optimum

solution more likely).

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Chapter 6

Future Work

Improvements on the system could include using different merging criteria (instead

of the fusion factor) or using a different colour space. As mentioned the fitness

function is very important to a genetic algorithm. Various fitness functions were

suggested, though only one was experimented with. These fitness functions, as

well as others could be experimented with. A fitness function is just a function,

so there is the possibility that genetic programming1 could be used to evolve a

fitness function. Manually segmented images could be used as ground truths and a

discrepancy measure could be used as a fitness function. If this training set of images

is a good representation of the type of images that one wishes to segment, this could

be successful. The evolved fitness function could be used in a program, such as theone implemented in this paper to provide unsupervised image segmentation. The

main challenge of doing this would be to provide suitable terminal and function sets.

1for a description of genetic programming see [28]

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Chapter 7

Conclusions

We successfully implemented region merging segmentation method. We improved

on this by using a genetic algorithm to modify the segmentation parameters. In

the process of doing this, we discovered the importance of a well chosen fitness

function and a novel fitness function was defined. A major advantage of this fitness

function is that it requires no comparison with a manually segmented image. This

has a major advantage over many other fitness functions requiring such input, this

method useful to real-world, automated segmentation applications.

The effect of the genetic algorithm on the image segmentation results is inconclu-

sive, its major drawback is that it is extremely slow to run. This means that the

small improvement in segmentation quality probably isnt worth the extra compu-

tation time. A way of getting around this drawback is to run the genetic algorithm

on a grid.

A major problem with the development of a general image segmentation method

is that different applications and different users require different results from image

segmentation. In reality, there is no ideal segmentation and the quality of the

segmentation depends on required use of the output.

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