Image Fusion using Artificial Bee Colony Optimization and Image...

Visual and Infrared Patch-wise DCT based

Image Fusion using Artificial Bee Colony

Optimization and Image Segmentation

Thesis submitted in the partial fulfillment of the requirements for

The award of the degree of

MASTER OF ELECTRICAL ENGINEERING

Submitted By

DEBASIS MAJI

Registration number: 120904 of 12-13

Examination Roll number:M4ELE14-10

Under Guidance of

Prof. Samar Bhattacharya

Electrical Engineering Department

Faculty Council of Engineering and Technology

JADAVPUR UNIVERSITY

KOLKATA-700032

YEAR - 2014

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JADAVPUR UNIVERSITY

KOLKATA-700032

Certificate of Recommendation

This is to certify that Mr. DEBASIS MAJI (M4ELE14-10) has completed his dissertation

entitled An approach towards History based Visual and Infrared patch-wise DCT based image

fusion using Artificial Bee Colony Optimization and image segmentation, underthe direct

supervision and guidance of prof. Samar Bhattacharya, Electrical Engineering Department,

Jadavpur University. We are satisfied with the work, which is being presented for the partial

fulfillment of the degree of Master of Electrical Engineering of Jadavpur University, Kolkata-

700032.

----------------------------------------

Prof. Samar Bhattacharya

Professor, Electrical Engineering Department

Jadavpur University, Kolkata-700032

_______________________________

_______________________________

Prof. Samar Bhattacharya Head of the Department

Department of Electrical Engineering


Prof. Sivaji Bandyopadhyay Dean,



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JADAVPUR UNIVERSITY

KOLKATA-700032

Certificate of Approval *

The foregoing thesis is hereby approved as a creditable study of Master of Electrical Engineering

and presented in a manner satisfactory to warrant its acceptance as a prerequisite to the degree

for which it has been submitted. It is understood that by this approval the undersigned do not

necessarily endorse or approve any statement made, opinion expressed or conclusion therein but

approve thesis only for the purpose it is submitted.

Final Examination for

Evaluation of the Thesis ------------------------------------

--------------------------------------

(Signature of Examiners)

*Only in case the thesis is approved

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Declaration of Originality and Compliance of Academic Ethics

I hereby declare that this thesis contains literature survey and original research work by the

undersigned candidate, as part of his Master of Electrical Engineering.

All information in this document has been obtained and presented in accordance with academic

rules and ethical conduct.

I also declare that, as required by these rules and conduct, I have fully cited and referenced all

material and results that are not original to this work.

Name (Block Letters) : DEBASIS MAJI

Exam Roll Number :M4ELE14-10

Thesis Title :Visual and Infrared patch-wise DCT based image fusion

Using Artificial Bee Colony Optimization and Image

Segmentation.

Signature with Date :

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Dedicated

To

My Parents,

Who have always supported me in all myWho have always supported me in all myWho have always supported me in all myWho have always supported me in all my

Endeavors Endeavors Endeavors Endeavors …….…….…….…….

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ACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTSACKNOWLEDGEMENTS

It is a pleasant task to express my gratitude to all those who have accompanied and helped me in

my thesis.

First and foremost, I really take this opportunity to express my deep sense of gratitude to my

guide, Prof. Samar Bhattacharya, Department of Electrical Engineering, Jadavpur University,

Kolkata, for his invaluable guidance, suggestions encouragement throughout the project which

helped me a lot to improve this project work. It has been very nice to be under his guidance. His

appreciation during the good times has been boosting my morals. I have been extremely lucky to

have him as my guide.

I am also thankful to Prof. Samar Bhattacharya, Smt. MadhubantiMaitra and Dr. R. K. Barai

for their guidance in the seminar classes.

I would also like to convey my gratitude to Prof. AmitavaChatterjee, Gourhari Das and Dr. Smita

Sadhu for their encouragement and valuable suggestions throughout the course of this work.

I am also indebted to Prof. Samar Bhattacharya, the Head of the Department of Electrical

Engineering, and co-operation during this thesis work.

My heart-felt thanks also goes to all my family members for their love and encouragement,

without which, the work would not have been possible.

Last, but not the least, I would like to thank my batch-mates, who have directly or indirectly

helped me in this work.

Date: _______________ ______________________

Jadavpur University, Kolkata DEBASIS MAJI

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CONTENTS

Title PAGE

ACKNOWLEDGEMTS vi

CONTENTS vii

LIST OF TABLES xi

LIST OF FIGURES xii

ACRONYMS

CHAPTER 1: INTRODUCTION

1.1. Introduction 2

1.2. Motivation 3

1.3. Problem Statement 5

1.4. Objectives 5

1.5. Report Organization 6

CHAPTER 2: LITERATURE REVIEW

2.1. Image Fusion 8

2.2. Image Segmentation 14

CHAPTER 3: DESIGN THE PROPOSED IMAGE FUSION AND

SEGMENTATION MODEL

17

CHAPTER 4: IMAGE FUSION

4.1.Introduction 19

4.2. Pixel level Image Fusion 20

4.3. Feature level Image Fusion 21

4.4.Decision level image fusion 22

4.5.Fusion evaluation method 22

4.6. Summary 23

CHAPTER 5: OVERVIW OF PRINIPAL COMPONENT

ANALYSIS BASED IMAGE FUSION

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5.1. Introduction 25

5.2. PCA Details 26

5.3. Properties of PCA 28

5.4. Dimensionality Reduction and Feature Extraction 29

5.5. PCA based Image Fusion 30

5.6. PCA Application in Image Fusion 31

5.7. Summary 31

CHAPTER 6: DCT BASED IMAGE FUSION

6.1. DCT Application in Image Fusion 33

6.2. Simulation Results and Discussion 40

6.3. Conclusion 41

CHAPTER 7: IMAGE STRUCTURAL SIMILARITY-BASED

METRICS

7.1. SSIM Review 43

7.2. Summary 45

CHAPTER 8: ARTIFICIAL BEE COLONY OPTIMIZATION 47

CHAPTER 9: IMPLEMENTED MODEL 53

CHAPTER 10: FUSION RESULTSAND CASE STUDIES

10.1. Comparison between DCT & Optimization Fusion Results 55

10.2. Conclusion 61

CHAPTER 11:OVERVIW OF IMAGE SEGMENTATION

11.1. Challenges for Image Segmentation 63

11.2. Overview of Segmentation Algorithms 64

CHAPTER 12: GSA-K MEANS CLUSTERING CHEN AND VESE

SEGMENTATION

12.1. Chan and vese 66

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12.1.1. Introduction 66

12.1.2. The Chan and Vese Model (Piecewise constant model) for

Image Segmentation

67

12.1.3. Level Set Formulation of the Model 68

12.1.4. The Chan and Vese Algorithm 70

12.1.5. Strengths and Drawbacks of the Chan and Vese Algorithm 71

12.1.6. Extension of Chan Vese algorithm for Vector-valued images 72

12.2. K-means Clustering Algorithm 74

12.3 GSA 74

12.4. Proposed HGSA-k means based Chan and Vese model 75

12.5. Simulation Results and Discussions 77

12.6 Conclusion 82

CHAPTER 13: CONCLUSION

13.1. Conclusion 84

13.2. Future Scope 85

REFERENCES 86

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LIST OF TABLES

Table Title PAGE

5.1 Mutual Information in Fused Image 31

6.1 The Joint-entropy an Mutual Information algorithms, a

measure of quality of the fused image

40

8.1 The basic Artificial Bee Colony Algorithm 49

10.1 Comparing the resultant images of DCTav and DCTopti by

SSIM

56

10.2 Comparing the resultant images of DCTav and DCTopti by

SSIM

58

12.1 K-means clustering Algorithm 74

12.2 GSA K-means approach Algorithm 75

12.3 Timing comparison between the standard C-V model and our

proposed C-V model for segmentation

78

12.4 The segmentation performance of our proposed algorithm 81

LIST OF FIGURES

Figure Title PAGE

3 Proposed Model 17

4.1 Level classification of the various popular image fusion

methods based on computation source

20

4.2.1 A Schematic of Pixel level fusion process 21

4.3.1 Schematic of feature level fusion process 22

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4.4.1 A Schematic of decision level fusion process 22

5.5.1 PCA based image fusion 30

5.6.1 (a) IR image, (b) Visible image, (c) Fused image 31

6.1.1 Block diagram of DCT based image fusion algorithm 35

6.2.1 Results obtained by image fusion using the DCT algorithms 40

7.1 Diagram of the Structural Similarity (SSIM) measurement

system

43

8.1 The flow chart for the Basic Artificial Bee Colony algorithm 48

9 Implemented Model 53

10.1.1 Results obtained after fusion with different schemes 55

10.1.2 Results obtained after fusion with different schemes 57

10.1.3 Results obtained by image fusion using the proposed

DCTopti algorithm

58


DCTopti algorithm

59


DCTopti algorithm

60

12.4.1 Binary tree structure of hierarchical segmentation 76

12.5.1 Sample PCA fused images (a, b, c, d) on which the

experiment has been done

77

12.5.2 Two-class segmentation of the sample images 78

12.5.3 Mean average standard deviation of the GF model 79

12.5.4 Mean average standard deviation value from our proposed

model

80

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ACRONYMS

SYMBOL DESCRIPTION

DCT Discrete Cosine Transform

IR infrared

ABC Artificial Bee Colony

SSIM Structural Similarity Index Measure

PCA Principal Component Analysis

PSNR Peak Signal –to- Noise Ratio

WT Wavelet Transformation

C-V Chan-Vese

NMSD Non-Multi-scale-Decomposition

SPM Segmentation Performance Measure

PET positron emission tomography

MMW millimeter wave

PSO Particle Swarm Optimization

GA Genetic Algorithm

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CHAPTER 1:CHAPTER 1:CHAPTER 1:CHAPTER 1:

INTRODUCTION

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Chapter 1

Introduction

1.1 INTRODUCTION

pplications of advanced surveillance system using multi-modal imagining sensors for

enhancement of vision systems and its performance under challenging environmental conditions,

obstructed view points, and different type of targets has continually been upgraded in many of

the recent research works. Image fusion techniques are gradually increasing as a potential means

of combining two (or more) images for maximizing information content of the resultant image.

Fusion algorithms are applied in a priori image combination for the purpose of object tracking,

recognition, detection, or classification. To perceive minute details from visible images is

difficult due to the presence of shadows, variations in illumination, reflections, and etc. while; on

the other hand, infrared (IR) imaging is to a certain extent unaffected by most of the

aforementioned factors. Image fusion is a technique which combines two or more images into a

single image called the fused image. The content of information stored in the fused image is

greater than that of the constituent input images. Image fusion has recently been, extensively,

implemented in the fusion of Infrared (IR) and visual images.

In this research work a novel Discrete Cosine Transform (DCT) based patch-wise image

fusion technique, using Artificial Bee Colony (ABC) based optimization, has been formulated to

fuse IR and Visible images. For the sake of comparison of quality of the fused images with

respect to other existing algorithms Structural Similarity Index Measure (SSIM) has been used.

A

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The superior result of the proposed algorithm shows that it is highly robust and stable and

provides better results with respect to other existing DCT based algorithms.

1.2 Motivation:

Image fusion techniques usually used for image processing where a single image sensor is not

enough to provide required data. So, fusion is adopted where direct object perception is difficult

and noise prone or expensive.

Two types of images are commonly fused to get grater quality of information.IR sensor will

make complement of image information with visible image range. Visible images offer a rich

content where a detection of people /object can now ever be limited by change in lighting

conditions. IR images generally allow a better contrast which is obtained between a

object/person and the environment, but these images are not as robust to changes in temperature

and wind combination.

So, multi sensor data has become a discipline which demands more general formal solutions to a

number of application cases. Several situations in image processing require both high spatial and

high spectral information in a single image. This is important in remote sensing. However, the

instruments are not capable of providing such information either by design or because of

observational constraints. One possible solution for this is data fusion.

We can get some examples in image fusion in different field of application and need for fusion.

One example is medical image fusion where we have to access organs inside the body, which are

not directly accessible. So few no of sensors are used to get measurements of a different tissue

property. Information from a single sensor is fraught with common problems related to sensor

noise, physical constraints and obstruction of view, shadowing, tissue movement and patient

motion among others. Sensor fusion methods are then adopted to parse through the information

from multiple sensors, perform complex deductions and provide consistent conclusions.

Required margins of error from an automated fusion and inference system are required to be at

least as low as that arrived at by the physician herself. An example of the use of fusion is in

radiotherapy treatment, where CT and MRI are employed to provide complimentary soft-tissue

hard-tissue information in the brain and skull. In these medical applications, the sensor and

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sensing technology remains the same but the fusion occurs over data collected at two different

time points.

Second example is artificial intelligence imaging system where multiple environment parameters

are collected by sensors leading to an information overload from the glut of accumulated data.

Automated systems are required to provide reliable decisions in a timely fashion. The amount of

time needed to reach a reliable decision increases rapidly with the amount of information

available. Sensor fusion is necessary to combine information in a way that removes

inconsistencies and presents clearly the best interpretation of measurements input from many

individual sources.

Sensor fusion combines input from many independent sources of limited accuracy and reliability

to give information of known accuracy and proven reliability. Calibration required for accuracy

and reliability. Medical imaging applications use expensive sensors that are calibrated on a

regular basis and are maintained to perform at high standards. Other applications require that

sensors be placed in hostile environments where access is reduced or eliminated, such as in outer

space, deep sea, forests, mountains or river beds. Due to this reason, applications such as

monitoring soil toxicity or water contamination can be addressed by distributing several

hundreds of cheap sensors in the environment.

Lastly, diversity in sensor types allows sensing of a variety of object or environment properties.

Diversity could be achieved by harnessing sensors that focus on different bands in the

electromagnetic spectrum. For example, visible and infrared sensors can be used in security

systems, or visible light and audible sound can be used in a video camera. This diversity leads to

a reduction in the probability of decision error and uncertainty encountered in the measurements

thus making the sensing system more reliable which ultimately benefits the inference-making

procedure.

So as a summary the advantages of sensor fusion over single sensor processing are due to the

redundancy, diversity and complementarily among multiple sensors. When data from multiple

sensors is fused together the resultant observation is expected to have a higher signal to noise

ratio, a reduction in overall measurement variance and a better and more sophisticated picture of

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the environment. Redundancy is caused by the use of multiple sensors to measure the same

entity. It is well known that redundancy reduces uncertainty.

1.3 Problem Statement:

From the survey on the image fusion and segmentation it observed that:

The purpose of advanced surveillance system using multi-mode imaging sensors for

enhancement of vision system and its performance under challenging environmental conditions,

and different type of targets has continually been upgraded in many of the resent research works.

The detection of the moving persons has become more and more important over the past few

years. Various applications in the area of security and surveillance are promising. The objective

of the research work demonstrated in this chapter is to develop a new system which combines an

IR and visible sensor to enable the detection and surveillance of pedestrians over a period of

time. More specifically, we will focus the problems in an environment where pedestrians are

moving in a range of specified distances within an area affected by various lighting and

atmospheric conditions.

1.4 Objectives:

(i) Development of a novel Discrete Cosine Transform (DCT) based patch-wise image

fusion technique, using Artificial Bee Colony (ABC) based optimization.

(ii) Development of Cosine Transform (DCT) image fusion technique using Artificial

Bee Colony (ABC) based optimization, of a method of intelligent fusion which will

enable the robustness of human detected to be improved while reducing false alarms

and the advent of non detected pedestrians.

(iii) For the sake of comparison of quality of the fused images with respect to other

existing algorithms Structural Similarity Index Measure (SSIM) has been used.

(iv) Development and implementation of an improved image fusion technique based on

proposed algorithm shows that it is highly robust and stable and provides better

results with respect to other existing DCT based algorithms.

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1.5 Report Organization:

The thesis report is organized as follows:

In Chapter 2 a Literature Review is presented. Chapter 3 contains the Designe the

proposed image fusion and Segmentation Model of the thesis work. Chapter 4 & Chapter

5&6 briefly describe the Principal Component Analysis and Proposed DCTopti Image

Fusion algorithm. Chapter 7 a Image Structural Similarity-Based Metrics and Chapter 8

Artificial Bee Colony Optimization are briefly describe mathematical and algorithms..Chapter

9 draws the Implemented Model. Chapter 10 several Case studies are described. GSA-K

Means Clustering Chen and Vese Image Segmentation is presented and discusses result in

Chapter 11 and Chapter 12. Finally Chapter 13 gives a Conclusion & describes the Future

Scopes of the implemented image Fusion and image Segmentation algorithms. The References

are given in end.

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CHAPTER 2: CHAPTER 2: CHAPTER 2: CHAPTER 2:

LITERATURE REVIEW

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Chapter 2

Literature Review

2.1 Image Fusion:

Image Fusion is used extensively in image processing systems. Various Image Fusion methods

have been proposed in the literature to reduce blurring effects. Many of these methods are based

on the post-processing idea. In other words, Image fusion enhances the quality of image by

removing the noise and the blurriness of the image. Image fusion takes place at three different

levels i.e. pixel, feature and decision. Its methods can be broadly classified into two that is

special domain fusion and transform domain fusion. Averaging, Bravery method, Principal

Component Analysis (PCA), Discrete Cosine Transform (DCT) based methods are special

domain methods. But special domain methods produce special distortion in the fused image

.This problem can be solved by transform domain approach. The multi-resolution analysis has

become a very useful tool for analyzing images. Therefore, fusion of IR and Visual images is a

potential solution for improvement in person detection, tracking and recognition even under the

presence of challenging situations like: night-time imaging, foggy weather imaging, etc. A brief

summary of the literature is given below:

Toet et al. [4] proposed a cognitive image fusion scheme wherein a study was conducted to

investigate the qualitative relative difference in human visual perception between the component

input images and the visual images. The method proposed is semi-automatic as human subjects

were asked to derive a reference contour image based on semantically meaningful contiguous

regions in a set of component individual images. The reference contour images were used in a

bid to optimize, using a precision-recall framework, so as to enhance the performance of

different image fusion methodologies.

Wang et al. [20] proposed a robust fusion algorithm of infrared and visible images for detecting

person, tracking, recognition, and fusion performance.

Zin et al. [3] proposed an algorithm on person detection using the resultant image of fusion of

thermal and visual image using multi-slit method and movement of Gravity Center (GC)

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Chapter 2 Page 9

patterns. The quality of the fused image can be assessed by using Structural Similarity Index

Measure (SSIM) as proposed by Brooks et al. [6]. In this paper the quality of the fused image

has been determined using the SSIM score.

Extensive use of Principal Component Analysis (PCA) has been found in recent research works,

especially in the field of image fusion. Patil et al. [8] proposed an image fusion strategy using

hierarchical PCA, wherein a study of PCA and pyramid decomposition based image fusion was

performed.

Desale, R.P et al. [33] explained that the Image Fusion is a technique of combining the

appropriate information from a set of images, into a single image, in which the resultant fused

image will be more useful and absolute than any of the input images. This paper discusses the

Formulation, Process Flow Diagrams and algorithms of PCA (principal Component Analysis),

DCT (Discrete Cosine Transform) and DWT based image fusion techniques. The results are also

presented in table & picture format for comparative analysis of above techniques. The DCT &

PCA are conventional fusion techniques with many drawbacks, whereas DWT based techniques

are more favorable as they provides better results for image fusion. In this paper, two algorithms

based on DCTav and DCTopti are proposed.

Prakash, C et al. [34] described that the Image fusion is basically a process where multiple

images (more than one) are combined to form a single resultant fused image. This fused image is

more creative as compared to its original input images. The fusion technique in medical images

is useful for resourceful disease analysis purpose. This paper illustrates different multimodality

medical image fusion techniques and their results assessed with various quantitative metrics.

Firstly two registered images CT (anatomical information) and MRI-T2 (functional information)

are taken as input. Then the fusion techniques are applied onto the input images such as

Mamdani type minimum-sum-mean of maximum(MIN-SUM-MOM) and Redundancy Discrete

Wavelet Transform (RDWT) and the resultant fused image is analyzed with quantitative metrics

namely Over all Cross Entropy(OCE),Peak Signal –to- Noise Ratio (PSNR), Signal to Noise

Ratio(SNR), Structural Similarity Index(SSIM), Mutual Information(MI). From the derived

results it is inferred that Mamdani type MIN-SUM-MOM is more productive than RDWT and

also the proposed fusion techniques provide more information compared to the input images as

justified by all the metrics.

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Mohamed, M et al. [35] has define the Image fusion is a process which combines the data from

two or more source images from the same scene to generate one single image containing more

precise details of the scene than any of the source images. Among many image fusion methods

like averaging, principle component analysis and various types of Pyramid Transforms, Discrete

cosine transform, Discrete Wavelet Transform special frequency and ANN and they are the most

common approaches. In this paper multi-focus image is used as a case study. This paper

addresses these issues in image fusion: Fused two images by different techniques which present

in this research, Quality assessment of fused images with above methods, Comparison of

different techniques to determine the best approach and Implement the best technique by using

Field Programmable Gate Arrays (FPGA). First of these techniques is presented and then each

fusion method is performed on various images. In addition experimental results are

quantitatively evaluated by calculation of root mean square error, entropy; mutual information,

standard deviation and peak signal to noise ratio measures for fused images and a comparison is

accomplished between these methods. Then we chose the best techniques to implement them by

DCT algorithms.

Haghighat, M et al.[36] has explained that the image fusion is a technique to combine

information from multiple images of the same scene in order to deliver only the useful

information. The discrete cosine transformation (DCT) based methods of image fusion are more

suitable and time-saving in real time system. In this paper an efficient approach for fusion of

multi-focus images based on variance calculated in DCT domain is presented. The experimental

result shows the efficiency improvement of our method both in quality and complexity reduction

in comparison with several recent proposed techniques.

Pei, Y et al. [37] explained that this paper proposes an improved discrete wavelet framework

based image fusion algorithm, after studying the principles and characteristics of the discrete

wavelet framework. The improvement is the careful consideration of the high frequency subband

image region characteristic. The algorithms can efficiently synthesis the useful information of

the each source image retrieved from the multi sensor. The multi focus image fusion experiment

and medical image fusion experiment can verify that our proposed algorithm has the

effectiveness in the image fusion. On the other side, this paper studies the quality assessment of

the image fusion, and summarize and quantitatively analysis the performance of algorithms

proposed in the paper.

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Li, H et al. [38] has discussed that in this paper, the wavelet transforms of the input images are

appropriately combined, and the new image is obtained by taking the inverse wavelet transform

of the fused wavelet coefficients. An area-based maximum selection rule and a consistency

verification step are used for feature selection. A performance measure using specially generated

test images is also suggested.

The PCA image fusion method [47] basically uses the pixel values of all source images at each

pixel location, adds a weight factor to each pixel value, and takes an average of the weighted

pixel values to produce the result for the fused image at the same pixel location. The optimal

weighted factors are determined by the PCA technique. The PCA image fusion method reduces

the redundancy of the image data.

Super-resolution (SR) reconstruction [48] is a branch of image fusion for bandwidth

extrapolation beyond the limits of a traditional electronic image system. Katartzis and Petrou

describe the main principles of SR reconstruction and provide an overview of the most

representative methodologies in the domain. The general strategy that characterizes super-

resolution comprises three major processing steps which are low resolution image acquisition,

image registration/motion compensation, and high resolution image reconstruction. Katartzis

and Petrou presented a promising new approach base on Normalized Convolution and a robust

Bayesian estimation, and perform quantitative and qualitative comparisons using real video

sequences.

Mitianoudis and Stathaki demonstrate the efficiency of a transform constructed using

Independent component Analysis (ICA) and Topographic Independent Component Analysis

based for image fusion in this study [49]. The bases are trained offline using images of similar

context to the observed scene .The images are fused in the transform domain using novel pixel-

based or region-based rules .An unsupervised adaption ICA-based fusion scheme is also

introduced. The proposed schemes feature improved performance when compared to approaches

based on the wavelet transform and a slightly increased computational complexity. The authors

introduced the use of ICA and topographical ICA based for image fusion applications .These

bases seem to construct very efficient tools, which can complement common techniques used in

image fusion, such as the Dual-Tree Wavelet TRANSFORM. The proposed method can

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outperform the wavelet approaches. The Topographical ICA based method offers a more

accurate directional, thus capturing the salient features of the image more accurately.

He, D et al. [39] explained that the main objective of image fusion is to create a new image

regrouping the complementary information of the original images. The challenge is thus to fuse

these two types of images by forming new images integrating both the spectral aspects of the low

resolution images and the spatial aspects of the high resolution images. The most commonly

used image fusion techniques are: Principal Components Analysis (PCA), Intensity-Hue-

Saturation Transformation (IHS), High Pass Filter (HPF) and Wavelet Transformation (WT).

The PCA and IHS, are simple to use but they are highly criticized because the resulting image

does not preserve faithfully the colors found in the original images. The HPF method is sensitive

to the filtering used (filtering type, filter window size, etc.) and the mathematical operations

used.

Y-T, K et al. [40] has discussed in this paper the Histogram equalization is widely used for

contrast enhancement in a variety of applications due to its simple function and effectiveness.

Examples include medical image processing and radar signal processing. One drawback of the

histogram equalization can be found on the fact that the brightness of an image can be changed

after the histogram equalization, which is mainly due to the flattening property of the histogram

equalization.

T.Zaveri, M et al. [41] explained that the Image fusion is a process of combining multiple input

images of the same scene into a single fused image, which preserves relevant information and

also retains the important features from each of the original images and makes it more suitable

for human and machine perception. In this paper, a novel region based image fusion method is

proposed. In literature shows that region based image fusion algorithm performs better than pixel

based fusion method. Proposed algorithm is applied on large number of registered images and

results are compared using standard reference and no reference based fusion parameters.

O, R et al. [42] has discussed a novel approach for the fusion of spatially registered images and

image sequences. The fusion method incorporates a shift invariant extension of the discrete

wavelet transform, which yields an over complete signal representation. The advantage of the

proposed method is the improved temporal stability and consistency of the fused sequence

compared to other existing fusion methods. We further introduce information theoretic quality

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measure based on mutual information to quantify the stability and consistency of the fused image

sequence.

Ghimire, D et al. [43] has discussed that the main objective of image enhancement is to improve

some characteristic of an image to make it visually better one. This paper proposes a method for

enhancing the color images based on nonlinear transfer function and pixel neighborhood by

preserving details. In the proposed method, the image enhancement is applied only on the V

(luminance value) component of the HSV color image and H and S component are kept

unchanged to prevent the degradation of color balance between HSV components. The V

channel is enhanced in two steps. First the V component image is divided into smaller

overlapping blocks and for each pixel inside the block the luminance enhancement is carried out

using nonlinear transfer function. In the second step, each pixel is further enhanced for the

adjustment of the image contrast depending upon the center pixel value and its neighborhood

pixel values. Finally, original H and S component image and enhanced V component image are

converted back to RGB image.

Sruthy, S et al. [44] has focused on the development of an image fusion method using Dual Tree

Complex Wavelet Transform. The results show the proposed algorithm has a better visual quality

than the base methods. Also the quality of the fused image has been evaluated using a set of

quality metrics.

Patil, U et al. [45] has focused on image fusion algorithm using hierarchical PCA. Authors

described that the Image fusion is a process of combining two or more images (which are

registered) of the same scene to get the more informative image. Hierarchical multi scale and

Multiresolution image processing techniques, pyramid decomposition are the basis for the

majority of image fusion algorithms. Principal Component analysis (PCA) is a well-known

scheme for feature extraction and dimension reduction and is used for image fusion. We propose

image fusion algorithm by combining pyramid and PCA techniques and carryout the quality

analysis of proposed fusion algorithm without reference image.

Aribi, W et al. [46] explained that the quality of the medical image can be evaluated by several

subjective techniques. However the objective technical assessments of the quality of medical

imaging have been recently proposed. The fusion of information from different imaging

modalities allows a more accurate analysis. We have developed new techniques based on DCT

opti fusion. MRI and PET images have been fused with eight multi resolution techniques. The

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results proved that DCTav and DCTopti techniques to offer the best results.

2.2 Image Segmentation:

Image segmentation, i.e. partitioning an image into homogeneous areas, is one of the most

fundamental problems in a variety of applications, including but not limited to remote sensing,

optical imaging, and medical image analysis. It have been made toward a general segmentation

scheme, many difficult challenges still exist for many problems, especially on medical images.

For example, poor image contrast and noise are very common for many modalities, such as

ultrasound, positron emission tomography (PET) .Chan-Vese (C-V) model is a very standard

active contour based approach in image segmentation. This model uses region-based information

in its level set based formulation and tries to minimize an energy fitting functional associated

with it by solving an Partial Differential Equation. Though this model can segment internal

objects very well, it still suffers from the problem of getting stuck at local minimum due to the

fitness functional being a non-convex and non-unique one.

In this work, a method to predetermine the mean value of intensity within and outside the active

contour is proposed which significantly improves the computation time of the C-V model. In

addition the model is less sensitive to contour initializations and is found to converge to the

global minimum in almost all cases. A brief summary of the literature is given below:

A unique method developed by Gibou and Fedkiw [50] was developed that solves the C-V

model by using the k_means clustering algorithm. Although this method [51] was found to be

much faster than the standard C-V model and did not require the need for level sets, it still

suffers from the problem of getting stuck at local minimum if the initial cluster points are not

appropriately selected. This error increases as the number of classes into which the image has to

be segmented increases.

In this work, evolutionary algorithms have been used in conjunction with the k_means algorithm

to take care of this problem. Successful implementations have been done using the Gravitational

Search Algorithm (GSA) [52] to segment images into two-class, three-class and four-class

effectively. Our model is seen to outperform the model suggested by Gibou and Fedkiw[50].

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Active region based image segmentation is generally carried out by Chan-Vese (C-V) model [53]

by wrapping around [53][54], an initial active contour [55] along the steepest descent direction

of energy employing gradient descent search (GDS) method [56]. The Chan-Vese model for

image segmentation is well developed and well-cited enough. The formulation of Chan-Vese

model usually comes up with the requirement of solving the partial differential equation (PDE)

for obtaining the route of contours evolved during the process of computation employing level

set formulation [53][54].Consequently, the associated energy gradients are derived by using the

Euler-Lagrange equations. In this respect, the GDS method is a convenient tool as they can be

utilized for minimization of non-convex functional and easy to implement as they involve

calculation of first order derivatives. But it generally converges to the first local minimum it

encounters and its rate of convergence is often very slow. For the sake of brevity, in this work we

presume the findings of the related previous works to be truthful i.e. the C-V energy fitting

functional [53] is non-convex and non-unique in nature and may also have many local minima.

Thus to alleviate the

problem of getting stuck to local minima, this work proposes a modified gradient search

technique that guarantees better and faster convergence of the C-V algorithm towards its global

minimum to get accurate segmentation results compared to the wellestablished heuristic

searches. The present work mainly rests on the efficacy of a variant of GDS, namely, the Delta-

Bar-Delta rule (DBR), proposed by Jacobs [57],which utilizes a learning parameter update rule,

in each iteration, in addition to the weight update rule. This method bears similarity with the

RPROP [56] method, although the update rules are quite distinct in nature. In this work, we

propose a modified version of DBR algorithm, namely MDBR algorithm, which utilizes a

modified version of DBR algorithm to update learning rate parameters and momentum method to

update weights, to achieve even faster convergence. The proposed Chan-Vese-MDBR algorithm

has been utilized to segment both scalar and vector valued images and its superiority has been

firmly established in comparison with other popular search methods used for level set based

image segmentation algorithms e.g. the well established basic GDS model and recently proposed

momentum (MOMENTUM),resilient backpropagation (RPROP) and conjugate gradient

(CONJUGATE) based learning methods.

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CHAPTER 3:CHAPTER 3:CHAPTER 3:CHAPTER 3:

Design the proposed image fusion and

segmentation Model

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Chapter 3 Page 17

Chapter 3

Design the proposed image fusion and

Segmentation Model

3. Proposed image fusion and Segmentation Model:

Proposed image fusion and Segmentation Model

Pre - Processing

Image Fusion Domain

Developed a new

Fusion algorithm

Post - Processing

Segmentation using

Modified or developed

Chan – Vese

Segmentation

Image Enhancement

Or fused image quality

measurement

Performance Evaluation

Segmentation

Result Display

Fusion

Result Display

Raw image

Infrared

image

Visual image

Back

Ground

subtraction

Object detection

Analysis

Fig.3. Proposed Model

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CHAPTER 4CHAPTER 4CHAPTER 4CHAPTER 4::::

IMAGE FUSION

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Chapter 4

Image Fusion

4.1. Introduction:

The fast modern development of the technique of sensors, micro-electronics, and multi-

sensor systems, fusion algorithms appreciably reduce the amount of raw data that needs to be

presented or processed without loss of information content as well as provide an effective way of

information integration. Day by day numerous image fusion algorithms are developed to address

the growing need for image fusion. The algorithms developed into two groups; Multi-scale-

Decomposition (MSD)-based fusion methods, and Non-Multi-scale-Decomposition (NMSD)-

based fusion methods [3]. All NMSD are not based on multi-scale transforms. Most common

NMSD fusion methods includes, Principal Component Analysis (PCA), DCT.

Image fusion techniques can also be classified based on the level of Processing where the fusion

takes place (Hall, 2001) [3]. There are three main levels where image fusion may take place and

they include.

Pixel Level

Feature Level and

Decision Level.

Level classification of the various popular image fusion methods based on computation source

that illustrates them is shown in Fig.3.1.

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Image Fusion

Pixel-level image

fusion

Averaging

DCT

PCA

WaveletTransform

Intensity Hue Saturation (IHS) Transform

Feature-level image fusion Decision-level image fusion

Neural Networks

Region-BasedSegmentation

K-means Clustering

Similarity Matching to Content-Based image Retrieval

Fusion Based on Fuzzy andUnsupervised FCM

Fusion Based on SupportVector Machine

Fusion Based on Information Level in the Regions of Images

Fig4.1. Level classification of the various popular image fusion methods based on computation

source

4.2. Pixel level image fusion:

Pixel level image fusion is the lowest processing level referring to the merging of the physical

parameters of the source images. Figure 4.2.1 illustrates schematic of pixel level fusion process.

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Infrared image

Visible image

Pixel Fusion Validation Fused image

Fig.4.2.1. A Schematic of Pixel level fusion process [3].

To perform Pixel level fusion all input images need to be spatially registered exactly to all other

input images, so that all Pixel positions of all the input images correspond to the same location in

the real world.

4.3. Feature level image fusion:

Feature level methods are the next stage of processing where image fusion may take place. It

have required to extraction of object (features) from the input images. Since, one of the

important goals of fusion is to conserve the image features, feature level, feature level methods

have the ability to capitulate subjectively better fused images than pixel based techniques. Figure

4.3.1.illustrates a schematic of feature level fusion process.

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Chapter 4 Page 22

Fig.4.3.1. Schematic of feature level fusion process [3].

4.4. Decision level image fusion:

Decision level techniques are the highest level of processing where image fusion can take

place. Fusion at the Decision level takes Feature level fusion one step further by declaring

identities to the objects recognized, by the individual input images, and then assigning a quality

measure to the extracted features-see figure 4.4.1.

Infrared image

Visible image

Feature

extraction

Feature

extraction

object recognition

Decision level

fusion

object recognition

Results

Fig.4.4.1. A Schematic of decision level fusion process [3].

4.5. Fusion evaluation methods:

The target of image fusion is to create a realistic and combined image that retains the

important information from the source images while minimizing the noise caused by fusing the

images. For the application, these images will be typically viewed and interpreted by an operator.

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A number of evaluation approaches and metrics have been proposed to quantify image fusion

performance.

4.6. Summary:

For image fusion research is mainly due to the contemporary developments in the fields of

multi-spectral, high resolution and cost effective image sensor design technology. Pixel-level

image fusion algorithms represent an efficient solution of operator related information overload.

Fusion effectively reduces the amount of data that needs to be processed without any significant

loss of useful information and also integrates information from multi-spectral sensors.

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OVERVIEW OF PRINCIPAL COMPONENT

ANALYSIS BASED IMAGE FUSION

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Chapter 5

Overview of Principal Component Analysis

5.1. Introduction:

Sometimes, the original data representation will be redundant for some reasons, i.e. some

variables will have a variation smaller than the measurement noise and thus will be irrelevant,

sometimes the original data is too big that it cannot be expressed because of lack of time.

Principal Component Analysis is a way to reduce features to some extent. It was introduced by

Karl Pearson in the year of 1901 [79] is a powerful process for extracting structure from possibly

high dimensional data sets. It is a statistical technique which uses orthogonal transformation to

convert a set of observations of possibly correlated variables called principal component. The

number of original variables is greater than or equal to the number of principal components. The

analysis is such a way that the first principal component always has the largest possible variance

and the second principal component always having the second largest possible variance, and so

on. If the data set is jointly normally distributed, it is guaranteed that principal components

should be independent. Depending on the field of signal processing application, it is also called

the discrete Karhunen-Loeve transform (KLT). It is readily performed by solving an Eigen value

problem or by using iterative algorithms which estimate principal components. PCA can produce

with lower-dimensional picture, a projection of this object when viewed from its most

informative point of view.

5.2. PCA Details:

PCA finds the linear projection of high dimensional data into a lower dimensional

subspace such as:

1. The variance retained is maximized.

2. The least square reconstruction error is minimized.

It is an orthogonal transformation of the coordinate system in which we describe our data. This

technique transforms the data to a new coordinate system such that the greatest variance by some

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projection of the data comes to lie on the first coordinate, which is called first principal

component and the second greatest variance lies on the second coordinate, which is called

second principal component and so on.

Mathematically this transform can be defined as a set of p-dimensional vectors of weights

)(21)( ),.......,,( kpk wwwW = that map each row vector )(iX of X to a new vector of principal

component scores ,),.....,( )(21)( ipi tttt = given by )()()( . kiik WXt = in such a way that all the

individual variables of t considered over the data set successfully inherit the maximum possible

variance from x, with each leading vector W constrained to be a unit vector.

First Component:

The first principal component )1(W can be stated as:

2

)(

2

)(1)1( ).(1

maxarg)(

1

maxarg∑∑

==

==

i

i

i

i WXW

tW

W

Equivalently, the equation can be written in matrix form as:

1

maxarg

1

maxarg 2

)1( XWXWW

XWW

W TT

==

==

Since )1(W has been defined to be a unit vector,

maxarg)1(WW

XWXWW

T

TT

=

)1(W Found, the first component of a data vector )(lX can then be given as a score )1()()(1 .WXt ll = in the

transformed coordinates, or as the corresponding vector in the original variables, .. )1()1()( WWX l

Further components:

The thK component can be found by discarding the first 1−k principal components from X:

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T

S

k

S

Sk WXWXX )(

1

1

)(1ˆ ∑

−

=

−−=

Loading vector,

ˆˆ

1

maxargˆ

1

maxarg11

2

1)(WW

WXXW

WWX

WW

T

k

T

k

T

kk

−−

−=

==

=

The full principal components decomposition of X can therefore be given as:

XWT =

Where W is a p-by-p matrix whose columns are the eigenvectors of .XX T

Covariance:

Empirical sample covariance matrix of dataset X is proportional to XX T

The sample covariance Q between two of the differential principal components over the dataset

can be given as:

)).((),( )()()()( kjkj XWXWPCPCQ α

)()( k

TT

j XWXW=

)()()( kk

T

j WW λ=

)()()( k

T

jk WWλ=

Where the Eigen value property of )(kW has been used to move from line 2 to line 3.

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Other way to characterize the principal components transformation is therefore as the

transformation to coordinates which diagonals the empirical sample covariance matrix as:

TT WWXXQ Λ=α

Λ=Λ WWWWQWW TTT α

Where, Λ is the diagonal matrix of Eigen values )(kλ of XX T

5.3. Properties of PCA:

Property 1: qp ≤≤1 , where p is an integer, the orthogonal linear transformation xBy `= where y

is the p-element vector and B` is a (qxq) matrix, assume that, ∑∑ = BBy ` be the variance

covariance matrix for y. Where, B` is the transposition of B. Trace of ∑y

denoted by ∑

ytr )(

maximized by taking pAB = , here pA consists of the first p columns of A.

Property 2: For that orthogonal transformation xBy `= , with x, B, A and ∑y

defined as earlier,

then ∑

ytr )( can considered to be minimum by taking *

pAB = where *pA consists of the last p

columns of A.

The mathematical implication of this second property is that the last few PCs are not

simply unstructured left-over after removing the important PCs. Because these last PCs have

variances as small as possible they are useful in their own right. They can help to detect

unsuspected near-constant linear relationships between the elements of x, and they may also be

useful in regression, in selecting a subset of variables from x, and in outlier detection.

Property 3: ''222

'111 ..... qqq ααλααλααλ +++=∑

Diagonal elements, ∑

=

=Q

kkjkjx

1

2)var( αλ

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Then, perhaps the implication of the result is that not only can we decompose the combined

variances of all the elements of x into decreasing contributions due to each PC, but we can also

decompose the whole covariance matrix into contributions 'kkk ααλ from each PC. Although not

strictly decreasing, the elements of 'kkk ααλ will tend to become smaller as k increases,

as 'kkk ααλ decreases for increasing k, whereas the elements of kα tend to stay 'about the same

size because of the normalization constraints: qkkk ,....,2,1,1'

==αα

5.4. Dimensionality Reduction and Feature Extraction:

Principal Component Analysis allows the extraction of a number of principal components

which can exceeds the input dimensionality. Suppose that the number of observations M exceeds

the input dimension N. PCA even when it is based on the M x M dot product matrix, can find at

most N nonzero Eigen values. They are identical to the nonzero Eigen values of the N x N

covariance matrix.

In this method, computation of the largest Eigen value and the corresponding rescaled

eigenvectors corresponding with the principal components in the feature space. After this we are

getting a column matrix of Eigen values and a matrix of eigenvectors according to the dimension

of the given matrix.

Suppose a matrix having the dimension 200 x 250 has been given as a input to PCA.

Then output of two matrix is obtained. In that one is containing column data of Eigen values

(200 x 1) and another one is having same dimension of input matrix containing rescaled Eigen

vectors (200 x 250) corresponding with the principal components in feature space.

These column data of Eigen values in descending order has been given as a input feature vectors

for classification task. PCA Based Image Fusion.

5.5. PCA Based Image Fusion:

The basic concept of PCA is to transform number of uncorrelated variables (which are

called Principal Components) from number of correlated variables [77].

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By Solving Eigenvalue problem, PCA is performed. This is an orthogonal linear

transformation, which transforms data to a new coordinate system. The greatest variance

occupies the first coordinate. In the second coordinate, the second greatest variance lies

[78]. First coordinate is termed as first principal component and so on. Covariance matrix

(C) of data ( tD ) is diagonalizable and defined as: [79]

C = ∑=mi

TiDiD

m1

1 (5.5.1)

Where, tDn

ℜ∈ t = [1, 2, m] and ∑ =mi tD1 = 0.

To spot on the features and reduce the noise, SVD based PCA fusion algorithm is applied

both on VI and IR images.

Figure 5.5.1: PCA based image fusion

5.6. PCA Application in Image Fusion:

Figure 5.5.1 demonstrates the fusing algorithm using PCA. Figure 5.6. 2 show that VI and

IR image is fused and it can be shown that the fused image carries maximum information

than these two inputs [80]. Table 1 shows about the mutual information between fused

image and input images.

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(a) (b) (c)

Figure 5.6.1: (a) IR image, (b) Visible image, (c) Fused image

TABLE5.1. Mutual Information in Fused Image

Mutual Information between Visible image and

Fused image (100X100)

100%

Mutual Information between IR image and Fused image

(100X100)

82.85%

5.7. Summary:

The PCA image fusion method simply uses the pixel values of source images at each pixel

location. The PCA technique is useful for image encoding, image data compression, image

enhancement, pattern recognition and image fusion.IR and visible image fusion result compare

with Mutual Information 82.85%.

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CHAPTER 6CHAPTER 6CHAPTER 6CHAPTER 6: : : :

DISCRETE COSINE TRANSFORMATION

BASED IMAGE FUSION

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Chapter 6

Discrete Cosine Transformation Based Image Fusion

6.1. DCT Application in Image Fusion:

DCT has recently, found extensive use in the field of digital image processing. One of the

significant applications of DCT in that field is image fusion. A large number of DCT coefficients

are known to be concentrated in the low frequency region resulting in effective energy

compactness properties [9] [10]. The 2D Discrete Cosine Transform ),( 21 ffX of an image or

2D signal 21)2

,1

(NN

nnX×

ℜ∈ is defined using the following expression (6.1.1).

)2

()1

()2

,1

( ffffX φφ=

)

22

2)1

22(

cos()

12

1)1

12(

cos(

11

01

12

02

)2

,1

(N

fn

N

fnN

n

N

nnnx

++∑−

=∑−

=

ππ (6.1.1)

∀1

220

111

0

−≤≤

−≤≤

Nf

Nf

≤≤

=

=

111,

1

2

01

if,

1

1

)1

(,where

NfN

fN

fφ

−≤≤

=

=

122

1,

2

2

02

if ,

2

1

)1

(

NfN

fN

fφ

21 & ff discrete frequency variables ),( 21 nn pixel index.

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Similarly,2D inverse DCT is defined by the following mathematical expression (6.1.2).

( )2

()1

)2

,1

( ffnnx φφ=

)

22

2)1

22(

cos()

12

1)1

12(

cos(

11

01

12

02

)2

,1

()2

()1

(N

fn

N

fnN

n

N

nffXff

++∑−

=∑−

=

ππφφ (6.1.2)

111

0, −≤≤ Nnwhere

122

0 −≤≤ Nn

Image fusion have different categories [19], i.e. (a) Multiview fusion (b) Multimodal fusion (c)

Multitemporal fusion (d) Multifocus fusion (e) Fusion for image restoration. In this section , we

describe six types of DCT image fusion techniques. Fused images are divided into non-

overlaping blocks of size N×N. Here we computed for dct coe fficients rule are implment to get

fused DCT coefficients. The fused image is produced by IDCT fused coefficients. This process is

shown in the figure.6.1.1[2].

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Fig.6.1.1. Block diagram of DCT based image fusion algorithm

Therefore, let DCT coefficient matrix is 1X from image patch

1l of image 1 and DCT coefficient

is 2X from image patch

1l of image 2. Suppose cX be the fused DCT coefficients and size of

image patch is pNpN × [2]. The different image fusion techniques proposed in [2] are

discussed as follows:-

a) DCTav:

In this technique each and every one DCT coefficients from mutual image blocks of the

two component images are averaged to get DCT coefficients corresponding to the fused

image. Finally, the inverse DCT of the coefficient matrix gives us the fused image. cX is

defined using the following expression (6.1.3).

)]2

,1

(1

)2

,1

(1

[5.0)2

,1

( ffXffXffcX += (6.1.3)

where, 1,......2,1,02,1 −= pNff

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b) DCTma:

All the DC elements corresponding to the two image patches of the component images

are averaged. The AC coefficients with the large magnitude are chosen since these are

those coefficients that correspond to the brightness changes, edges and object boundaries

in the component images. The technique is expressed mathematically by (6.1.4) and

(6.1.5). The aforementioned components do tend to fluctuate in and around zero. Finally,

the inverse DCT of the coefficient matrix gives us the fused image.

)]0,0(1

)0,0(1

[5.0)0,0( XXcX += (6.1.4)

1 ,.......,2,12

,1

,

)2

,1

(2

)2

,1

(1

,),2

,1

(2

)2

,1

(2

)2

,1

(1

,),2

,1

(1

)2

,1

(

−=

⟨

≥=

pNffwhere

ffXffXwhereffX

ffXffXwhereffXffcX

(6.1.5)

c) DCTah:

In this fusion rule, DC coefficients and AC components with the small magnitude are

averaged and the remaining high magnitude AC components are chosen based on their

magnitude, as given by (6.1.6) and (6.1.7).

15.0,.....,1,02

,1

,

)]2

,1

(2

)2

,1

(1

[*5.0)2

,1

(

−=

+=

pNffwhere

ffXffXffcX (6.1.6)

1,.......,25.0,15.0,5.0,,

)2

,1

(2

)2

,1

(1

,),2

,1

(2

)2

,1

(2

)2

,1

(1

,),2

,1

(1

)2

,1

(

21 −++=

⟨

≥=

NNNffwhere

ffXffXwhereffX

ffXffXwhereffXffcX

(6.1.7)

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d) DCTcm:

The DC coefficients of the two image patches corresponding to the two component images

are averaged and the AC coefficients are selected based on the larger contrast measure, as

given by mathematical expression (6.1.8) and (6.1.9).

)0,0()0,0(5.0)0,0( 21 XXX c += (6.1.8)

measurecontrast ,

1,.....,2,1,,

),(),(,),,(

),(),(,),,(),(

21

21

212211212

212211211

21

=

−=

⟨

≥=

ηη

ηη

ηη

Nffwhere

ffffwhereffX

ffffwhereffXffX c

(6.1.9)

e) DCTch:

Hence, DCTch fusion is very much similar to DCTah. The lowest magnitude AC

components along with the DC components are averaged and the remaining coefficents

are chosen based on largest contrast measures, as given by expressions (6.1.10) and

(6.1.11).

15.0,.....,2,1,02

,1

,

)]2

,1

(2

)2

,1

(1

[5.0)2

,1

(

−=

+=

Nffwhere

ffXffXffcX (6.1.10)

⟨

≥=

)2

,1

(2

)2

,1

(1

,),2

,1

(2

)2

,1

(2

)2

,1

(1

,),2

,1

(1

)2

,1

(ffffwhereffX

ffffwhereffXffcX ηη

ηη (6.1.11)

1,.....,25.0,15.0,5.02

,1

, −++= NNNffwhere

f) DCTe:

This technique is similar to DCTcm. It has been shown DC components are averaged

together. Those AC components that correspond to the largest energy in the frequency

band are selected, as given by mathematical expression (6.1.12) and (6.1.13).

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)]0,0(2

)0,0(1

[5.0)0,0( XXcX += (6.1.12)

≥

≥=

21,),

2,1

(2

21,),

2,1

(1

)2

,1

(

jjwhereffX

jjwhereffX

ffcX ψψ

ψψ (6.1.13)

band

spectralthj aover amplitude avarage2

,1

21

1,.....,2,12

,1

,

=

+=

−=

jj

ffj

Nffwhere

ψψ

DCTopti:

However, we have proposed an image fusion algorithm in this paper that addresses the

problem of weighted combination as a metaheuristic optimization problem as represented

by the following mathematical expressions (6.1.14) and (6.1.15).

)]2

,1

(22

ˆ)2

,1

(11

ˆ[)2

,1

( ffXffXffcX αα += (6.1.14)

where, f

gmin

2,1

arg]2ˆ,

1ˆ[

αααα = (6.1.15)

∑−

=∑−

=−

=1

01

1

02

2)]2,1(2)2,1(1[ )2/1(

2))2,1(1max(10log10

pN

f

pN

f

ffXffXpN

ffXg

∑−

=∑−

=+∑

−

=∑−

=

∑−

=∑−

=−

=1

01

1

02

2)]2

,1

(2

[

1

01

1

02

2)]2

,1

(1

[

1

01

1

02

)]2

,1

(2

)2

,1

(1

[

pN

f

pN

fffX

pN

f

pN

fffX

pN

f

pN

fffXffX

f

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The cost function (6.1.15) has been developed as a hybrid formulation of the Peak Signal-to-

Noise Ratio and the Correlation coefficient. The optimization or global minimization of the

objective function given by expression (6.1.15) has been done by the well-known Artificial Bee

Colony optimization which is a recent swarm optimization algorithm for non-convex problems

like that of the formulation of the cost function in our case.

It is most of the spatial domain image fusion methods are complex and time consuming which

are hard to be performed on real-time applications. Moreover, when the source images are coded

in Joint Photographic Experts Group (JPEG) standard or when the fused image will be saved or

transmitted in JPEG format, the fusion approaches which are applied in DCT domain will be

very efficient. To perform the JPEG coding, an image (in color or grey scales) is first subdivided

into blocks of 8x8 pixels. The Discrete Cosine Transform (DCT) is then performed on each

block. This generates 64 coefficients which are then quantized to reduce their magnitude.

The coefficients are then reordered into a one-dimensional array in a zigzag manner before

further entropy encoding. The compression is achieved in two stages; the first is during

quantization and the second during the entropy coding process. JPEG decoding is the reverse

process of coding. We denote A and B as the output images of two cameras that have been

compressed in JPEG coding standard in the sensor agent and further transmitted to fusion agent

of VSN. In the case of using spatial domain method these images must be decoded and

transferred to spatial domain. Then after applying fusion procedure, the fused image must be

coded again in order to be stored or transmitted to an upper node. Tang[36] has considered the

above mention issue of complexity reduction and proposed two image fusion techniques in DCT

domain, namely, DCT + Average and DCT+ Contrast. DCT +Average is calculated by simply

taking the average of all the DCT coefficients of all the input images. This simple method of

averaging leads to undesirable side effects including blurring.

In order to reduce the complication for the real-time applications and also enhance the quality of

the output image, an image fusion technique in DCT domain. Here, the variance of 8×8 blocks

calculated from DCT coefficients is used as a contrast criterion for the activity measure. Then, a

consistency verification (CV) stage increases the quality of output image. Simulation results and

comparisons show the considerable improvement in the quality of the output image and

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reduction of computation complexity.

6.2. Simulation result and Discussion:

We test our DCT algorithms on Thermal and visual images as shown in the following fig. 6.2.1

and the resultant fused image obtained is quite satisfactory.

Fig. 6.2.1.Results obtained by image fusion using the DCT algorithms

However, on comparing a thermal image and its corresponding visual images of DCT by the

Joint-entropy an Mutual Information algorithms, a measure of quality of the fused image. We

obtain the following results, as given in table results TABLE 6.1.

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TABLE6.1.

Type of

image fusion

Joint-entropy

(Infrared

image)

Joint-entropy

(Visual

image)

Mutual

Information(Infrared

image)

Mutual

Information(Visual

image)

DCTav 8.2756 8.3105 1.187 1.1522

DCTma 8.6732 8.8402 1.4476 1.2807

DCTah 8.4214 8.4656 1.1517 1.1075

DCTe 8.6785 8.8029 1.4796 1.3551

DCTch 8.4208 8.4680 1.1516 1.1044

DCTcm 8.6507 8.8800 1.4772 1.2479

DCTopti 8.2597 8.3956 1.2114 1.0756

6.3 Conclusion:

Six different types of image fusion algorithms based on discrete cosine transform (DCT) and

DCTopti was developed and fused image quality was evaluated using Joint-entropy and Mutual

Information algorithms. DCTopti based image fusion algorithms performed well and these

algorithms are very suitable for real time applications.

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IMAGE STRUCTURAL SIMILARITY INDEX

MEASURE

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Chapter 7

Image Structural Similarity Index Measure

7.1. Image Structural Similarity Index Measure Review:

An effective process to judge the quality of the fused image is measuring the loss of structural

information. The image quality measurement, as proposed by Wang et al. [1], is based on

Structural Similarity Index Measure (SSIM). Hence, the structural philosophy can be proposed

for set of equation defining the structural similarity (SSIM) quality metric in image space [6].

For the comparison of two images X and Y, luminance is calculated as the mean of each image

[5] [1].

Fig.7.1. Diagram of the Structural Similarity (SSIM) measurement system [5].

The system diagram of the proposed quality assessment system is shown in fig.7.1. Here, x and y

are two nonnegative image signals, which have been aligned with each other. If we consider one

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Chapter 7 Page 44

of the signals to have perfect quality, then the similarity measure can serve as quantitative

measurement of the quality of the second signal.

Two images (or image patches) X and Y to be compared, luminance is estimated as the mean

intensity ( xµ ) , given by equitation (7.1).

∑=

=N

nnx

Nx

1

1µ (7.1)

Standard deviation ( xσ ) is estimated for contrast as given by expression (7.2).

∑=

−−

=N

nxnx

Nx

1

2)(1

1µσ (7.2)

Now, the estimated structure for the image vector X by removing the mean and normalized by

the stander deviation, given by (7.3).

x

xxx

σ

µς

−= (7.3)

Hence, we have used a structural similarity index measure(SSIM) for images added using a

luminance comparison function ),( YXl , the contrast comparison function ),( YXc and structure

comparison function ),( YXs to get a composite measurement using the following expression

(7.4).

γβα )],([)],([)],([),( YXsYXcYXlYXSSIM = (7.4)

where α, β and γ positive constants are used to adjust of three components.

and, the component functions are given by

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122

12

),(

kyx

kyxYXl

++

+=

µµ

µµ (7.5)

222

22

),(

kyx

kyxYXc

++

+=

σσ

σσ (7.6)

3

3

3

3,

),(kyx

kxy

kyx

kyxYXs

+

+=

+

+⟩⟨=

σσ

σ

σσ

ςς (7.7)

where <X,Y> is the correlation between the structure of two images.

Now, 2

,,1 23

kkand === βα to get the following mathematical expression(7.8).

)2

22)(1

22(

)2

2)(1

2(),(

kyx

kyx

kyxkyxyxSSIM

++++

++=

σσµµ

σµµ (7.8)

Once the universal image quality index (UIQI) by the following mathematical expression and is

written as [31].

)22

)(22

(

4

22

2.

22

2.),(

yxyx

yxxy

yx

yx

yx

yx

yx

xyyxQ

µµσσ

µµσ

σσ

σσ

µµ

µµ

σσ

σ

++=

++= (7.9)

6.2. Summary:

We have summarized the traditional approach to image quality assessment based on error-

sensitivity, and have enumerated its limitation. We use of structural similarity as an alternative

motivating principle for the design of image quality measures. However, the effectiveness of

these models degrades significantly when applied to a IR and VI images from including a variety

of different types of distortions.

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ARTIFICIAL BEE COLONY OPTIMIZATION

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Chapter 8

Artificial Bee Colony Optimization

8. Artificial Bee Colony Optimization:

The basic Artificial Bee Colony (ABC) algorithm, for global optimization of high dimensional

numerical problems, was proposed by Karaboga [22]. In comparison to Genetic Algorithm (GA)

and Particle Swarm Optimization (PSO), ABC is characterized with lower computational

complexity, and easier programming [23-24]. The ABC algorithm and its variants have been

used for optimization in a wide spectrum of real world problems like image clustering [25], edge

enhancement [26], multi-level threshold image segmentation [27], training neural networks [28],

path planning of free-flying space robot [29], harmonic estimation [30], and a multitude of other

problems.

The collective intelligent behavior of insect or animal group in nature such as flocks of birds,

Colonies of ants, schools of fish, swarms of bees and termites have attracted the attention of

researchers. The aggregate behavior of insects or animals is called swarm behavior.

Entomologists have studied this collective behavior to model biological swarms, and engineers

applied these models as a framework for solving complex real-world problems [22].

Bee swarms exhibit many intelligent behaviors in their tasks such as nest site building, marriage.

foraging, navigation and task selection. There is an efficient task selection mechanism in a bee

swarm that can be adaptively changed by the state of the hive and the environment. Swarm

intelligence is a research field that models the collective intelligence in swarms of insects or

animals [24].

The flow chart for the basic Artificial Bee Colony (ABC) algorithm is shown in the following

figure8.1.

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Fig. 8.1. The flow chart for the Basic Artificial Bee Colony algorithm

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The swarm of bee consists of three essential components, food sources, employed foragers, and

unemployed foragers. There are three types of bees in the swarm: employed bees, unemployed

bees, and scouts. There is one employed bee for every food source. The employed bee whose

food source is exhausted by the employed and onlooker bees becomes a scout. The pseuocode

for the ABC algorithm is given as follows.

TABLE 8.1

The basic Artificial Bee Colony Algorithm

BEGIN

- Initialize ABC control parameters.

i) Maximum Cycle Number, MCN , for which the ABC algorithm is iterated.

ii) Number of Employed Bees = Number of Onlooker Bees = SN .

iii) The number of trials, limit , to improve a food source after which it is abandoned.

iv) The dimension of each food source, Dim ,

v) Randomly Create an initial population, ),.....,1;,......,1(, DimjSNijix .

- WHILE ( MCNiter )

i) 1 iteriter

ii) % Employed Bee Phase %

a) FOR ( SNi :1 )

o Produce a new candidate from the existing food source using the

following expression (16).

ikSNkjk

xjixjijixjiv and ,...,2,1 ),,(,,, (8.1)

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o Evaluate the quality of the new candidate food source, )( ifit v .

o A Greedy selection algorithm is employed to select one and

discard the other among ix and iv based on their corresponding

fitness values )( ifit x and )( ifit v respectively.

o IF )( ifit v is not better than )( ifit x then the trial counter is

incremented by unity according to the following mathematical

expression (17).

(8.2) 1+= ii trialtrial

END IF

END FOR

iii) % Probability value assignment to each food source %

An onlooker bee chooses a food source depending on the probability value, ip ,

associated with that food source, ix , computed using the following expression

(7.3).

(8.3)

1)(

)(

i

∑=

=SN

nnfit

ifitp

x

x

iv) % Onlooker Bee Phase %

a) 1;1 == iitr

b) WHILE )( SNitr ≤

• 1+= itritr

• Generate a random number )1,0(∈rand

• IF ( iprand < )

o Produce a new candidate from the existing food source using the

following expression (16).

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ikSNkjk

xjixjijixjiv ≠∈∀−+= and ,...,2,1 ),,(,,, φ

o Evaluate the quality of the new candidate food source, )( ifit v .

o A Greedy selection algorithm is employed to select one and

discard the other among ix and iv based on their corresponding

fitness values )( ifit x and )( ifit v respectively.

o IF )( ifit v is not better than )( ifit x then the trial counter is

incremented by unity according

1+= ii trialtrial

END IF

END WHILE

c) 1+= ii

d) IF )( SNi >

1=i

END IF

v) % Determine Scout %

a) IF imitltriali >)max(

Replace ix with a new randomly produced solution/food source

END IF

vi) Memorize the global best solution so far

vii) 1+= iteriter

END WHILE

END

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IMPLEMENTED MODEL

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Chapter 9

Implemented Model

9. Implemented model:

Fig. 9. Implemented Model

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FUSION RESULTS AND CASE STUDIES

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Chapter 10

Fusion Results and Case Studies

10.1. Results and Case Studies:

Now that we have discussed elaborately the algorithm for image fusion we need to implement it

on different component images and prove the stability and robustness of the algorithm. The

results and inferences obtained after extensive experimentation are discussed in detail in this

section.

Case study 1: A thermal image and its corresponding visual image were taken from the

database [7] and, subsequently, the results obtained after implementing the aforementioned

fusion schemes are shown in the following fig. 10.1.1.

Fig. 10.1.1.Results obtained after fusion with different schemes

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Now, on closely observing the obtained results as represented by fig. 10.1.1 we can conclude that

by human visual perception the two fused images that are not corrupted with noise and with have

quality edge preservation is obtained by DCTav (1st row, 3

rd column) and by DCTopti (3

rd row,

3rd column). However, on comparing the resultant images of DCTav and DCTopti by SSIM, as a

measure of quality of the fused image, we obtain the following result, as given in TABLE 10.1.

TABLE 10.1

Reference (component) Image SSIM (with DCTav fused

image)

SSIM (with DCTopti fused

image)

Visual 0.54274 0.55721

One can easily infer from the results tabulated in the preceding table 10.1 that the fused image by

DCTopti, the image fusion methodology proposed by us, is far more superior than that obtained

by DCTav [2]. Therefore, the superiority of the image fusion algorithm over one of the

contemporary existing algorithms is proved.

Case study 2: Similarly, another thermal image and its corresponding visual image were taken

from the database [7] and, subsequently, the results obtained after implementing the

aforementioned fusion schemes are shown in the following fig. 10.1.2.

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Fig. 10.1.2. Results obtained after fusion with different schemes

Now, on closely noticing the resultant fused images as represented by fig. 10.1.2 one can easily

infer, by human visual perception, that the two fused images that are not corrupted with noise

and have high quality edge preservation is obtained by DCTav (1st row, 3

rd column) and by

DCTopti (3rd row, 3

rd column). However, on comparing the resultant images of DCTav and

DCTopti by SSIM, as a measure of quality of the fused image, we obtain the following result, as

given in TABLE 10.2.

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TABLE 10.2

Reference (component) Image SSIM (with DCTav fused

image)

SSIM (with DCTopti fused

image)

Visual 0.61132 0.61836

One can easily infer from the results tabulated in the preceding table 10.2 that the fused image by

DCTopti, the image fusion methodology proposed by us, is far more superior than that obtained

by DCTav [2]. Therefore, again the superiority of the image fusion algorithm over one of the

contemporary existing algorithms is proved.

Case study 3: Now, we need to prove that our algorithm is not domain constrained only to IR

and visual image fusion but also it can result in the fusion of various types of images. One such

example is given here. The input images are taken from the database provided here [32]. The

resultant fused image is shown in the following fig. 8.1.3.

Fig .10.1.3 Results obtained by image fusion using the proposed DCTopti algorithm

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On closely observing the two component images, image 1 and image 2, as shown in fig. 10.1.3

we see that in image 1 the camera was focused on the table clock during image acquisition and in

image 2 the camera was focused on the boy during image acquisition. Finally, by the fusion of

the two images image 1 and image 2 using DCTopti, the algorithm proposed by us, we obtain a

fused image where it appears as if the camera was focused both on the table clock and the boy.

Therefore, we can proclaim that the DCTopti image fusion algorithm, proposed by us, performs

well on not only IR and Visual images but also on other types of images.

Case study 4: Now, we use the DCTopti image fusion algorithm, proposed by us, for the

fusion of a visual image, image 1, with a millimeter wave (MMW) image, obtained from the

database in [32], as shown in the following fig. 10.1.4.

Fig.10.1.4. Results obtained by image fusion using the proposed DCTopti algorithm

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One can easily infer from the resultant fused image shown in the preceding fig. 1 that our

proposed algorithm can also perform the image fusion of a visual image with a MMW image.

Case study 5: Finally, we test our DCTopti algorithm on two visual images as shown in the

following fig. 8.1.5 and the resultant fused image obtained is quite satisfactory.

Fig.10.1.5. Results obtained by image fusion using the proposed DCTopti algorithm

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10.2 .Conclusion:

This research work demonstrates a novel image fusion algorithm for the fusion of Infrared and

Visual image. However, through extensive experimentation it has been proven that this algorithm

can also perform the operation of image fusion over other different types of images. One of the

salient aspects of this research work is that it uses the renowned Artificial Bee Colony algorithm

for optimization of a novel cost function for determining the fusion weights for the DCT

coefficient matrix of two different image patches. Not only by human visual perception but also

by the SSIM score it has been proven that the algorithm proposed by us outperforms most of its

other contemporary competitors. The authors intend to undertake the segmentation of desired

objects from the fused images as a future prospect of research work.

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OVERVIEW OF IMAGE SEGMENTATION

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Chapter 11

Overview of Image Segmentation

11.1. Challenges for Image Segmentation:

Image segmentation, i.e. partitioning an image into homogeneous areas, is one of the most

fundamental problems in a variety of applications, including but not limited to remote sensing,

optical imaging, and medical image analysis. The level set based Chan-Vese algorithm primarily

uses region information for successive evolutions of active contours of concern towards the

object of interest and, in the process, aims to minimize the fitness energy functional associated

with. Orthodox gradient descent methods have been popular in solving such optimization

problems but they suffer from the lacuna of getting stuck in local minima and often demand a

prohibited time to converge. Although great strides have been made toward a general

segmentation scheme, many difficult challenges still exit for this problem, especially on medical

images. For example, poor image contrast and noise are very common for many modalities, such

as ultrasound, positron emission tomography (PET) and single photon emission computed

tomography (SPECT). Patient movement and partial volume effect in imaging process can easily

further deteriorate the image quality by blurring tissue boundaries. It is because of this weakness

in the current technology that leads us to propose a new segmentation method that does not stand

alone, but relies on prior information about the shape of interest. This reliance on previous

knowledge of generate acceptable results in segmentation is especially applicable in the domain

of medical images because it is most often the goal of the physician to obtain the segmentation of

a particular region or object. Combining the knowledge of what items are to be found with the

knowledge of what shape those items have possessed in the past allows our method to accurately

and efficiently and segment images that would otherwise be impossible to do without

intervention.

In computer vision, segmentation is the process of partitioning a digital image into multiple

segments. The goal of segmentation is to simplify and change the representation of an image into

something that is more meaningful and easier to analyze. Image segmentation is typically used

to locate objects and boundaries in images.

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11.2. Overview of Segmentation Algorithms:

Image Segmentation is the process of finding a mapping σ such that:

,2: iΡ→Ζσ ( )Ν≤≤ i1 (11.2.1)

Here 1Ρ , ,......,

2Ρ

NΡ are the Ν Classes to which a pixel can belong. Then we can define a

few useful notions for Segmentation. W e denote the original image as .Ι

Ι=Ρ=i

N

iU1

(11.2.2)

( ) Φ=Ρ∩Ρ→≠∀ jijiji, (11.2.3)

Equation 11.2.2 signifies that every pixel is contained in at least one class such that the union of

all the sets yields the entirety of the original image. Next stipulation, which found in equation

11.2.3, says that no pixel can belong to more than one class and consequently, the intersection of

any two different classes is necessarily the empty setϕ .

There are many different methods for arriving at segmentation and of determining the worth of

Segmentation. The Segmentation algorithms can be classified into three categories:

(a) Pixel-based Algorithms

(b) Edge-based Algorithms

(c) Region-based Algorithms

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CHAPTER 12:

GSA-K MEANS CLUSTERING CHEN AND VESE

SEGMENTATION

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Chapter 12 Page 66

Chapter 12

GSA-K Means Clustering Chen and Vese

segmentation

12.1 Chan and Vese

12.1.1. Introduction:

Active Contour Models [58, 66, 77] also called snakes are used for detecting an object outline

from an image. Very often the active contour models employ energy based segmentation

techniques [68], where the basic idea is to minimize the energy associated with the active

contour, as the curve evolves to fit around the desired objects. The energy associated with an

active contour generally consists of internal energy and external energy. The internal energy

deals with the properties of the contour such as area enclosed, length of the contour and its

smoothness. The external energy depends upon the image structure and the user imposed

constraints.

Chan-Vese (C-V) model is a very standard active contour based approach in image

Segmentation. This model uses region-based information in its level set based formulation and

tries to minimize an energy fitting functional associated with it by solving an Partial Differential

Equation. Though this model can segment internal objects very well, it still suffers from the

problem of getting stuck at local minimum due to the fitness functional being a non-convex and

non-unique one. Often different initial contours give varied segmentation results.

A unique method developed by Gibou and Fedkiw [59] was developed that solves the C-V

model by using the k_means clustering algorithm. Although this method [58] was found to be

much faster than the standard C-V model and did not require the need for level sets, it still

suffers from the problem of getting stuck at local minimum if the initial cluster points are not

appropriately selected. This error increases as the number of classes into which the image has to

be segmented increases.

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In this work, evolutionary algorithms have been used in conjunction with the k_means algorithm

to take care of this problem. Successful implementations have been done using the Gravitational

Search Algorithm (GSA) [60] to segment images into two-class, three-class and four-class

effectively. Our model is seen to outperform the model suggested by Gibou and Fedkiw [62].

12.1.2. The Chan and Vese Model (Piecewise constant model) for Image

Segmentation:

As mentioned before, Chan and Vese [61] proposed a piecewise-constant model for image

segmentation. An evolving curve C in Ω , is defined as the boundary of an open subset ω of Ω (i.e. Ω⊂ω , and ω∂=C ). Then )(Cinside denotes the regionω , and )(Coutside denotes the

region ω/Ω [61]. The image 0u is assumed to be formed by two regions of piecewise-constant

intensities having distinct values i

ou and ou0 . i

ou represents the intensity of the object to be

detected and ou0 the intensity of the background of the object. The object is assumed to have a

boundary or bounding contour 0C . Then the intensity inside 0C is i

ou and the intensity outside

0C is ou0 . Thus the energy fitting term can be defined as [61]:

dxdycyxu

dxdycyxu

CinsideAreaCLengthCccF

Coutside

Cinside

2

)(202

2

)(101

21

),(

),(

))((.)(.),,(

∫∫

−+

−+

+=

λ

λ

µν

(12.1.2.1)

where C is any curve that is being iteratively evolved, and the constants 21 and cc denote the

average intensity of the image inside and outside the evolving curve C . The free parameters of

the equation in (12.1.2.1) must all be positive. The fitting energy (12.1.2.1) also contains some

penalizing terms such as the length of the evolving curve C and the area of the region inside the

curve C . These two terms helps to smoothen the evolving contourC . It is quite evident from the

above equation (12.1.2.1) that the energy associated with the contour C becomes minimum

when 0CC ≈ i.e., the evolving contour sits exactly on the object boundary.

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The above functional in (12.1.2.1) is quite similar to that as the Mumford-Shah Functional [63].

The Mumford-Shah Functional (MSF ) tries to segment an image into its various sub-regions by

using region-based information. The Chan and Vese model tries to represent each region or

connected component iR of C/Ω using a constant intensity ic . This ic represents the average

intensity of the region i.e. )( 0uaverageci = on each connected component iR [61, 63]. This

reduced case is called the minimal partition problem. Here the values of the constants are:

))((

))((

2

1

Coutsidemeanc

Cinsidemeanc

=

=

(12.1.2.2)

12.1.3. Level Set Formulation of the Model:

In level set methods [61, 69], a contour Ω⊂C is represented by the zero level set of a Lipschitz

function R→Ω:φ . This is also called a level set function and it is defined in such a way that

<Ω∈=Ω=

>Ω∈==

=Ω∈=∂=

0),(:),(/)(

0),(:),()(

0),(:),(

yxyxCoutside

yxyxCinside

yxyxC

ωφω

φω

(12.1.3.1)

Using the level set function φ and also the Heaviside function H and the one-dimensional

Dirac measure δ0 so as to use one-dimensional calculations, the energy fitting terms ),,( 21 CccF

can be reformulated as [61]:

dxdyyxHcyxu

dxdyyxHcyxu

dxdyyxHdxdyyxyxccF

))),((1(),(

)),((),(

)),((),()),((),,(

2

202

2

101

21

φλ

φλ

φµφφδνφ

−−−−−−−−++++

−−−−++++

++++∇∇∇∇====

∫∫∫∫∫∫∫∫

∫∫∫∫∫∫∫∫

Ω

Ω

ΩΩ

(12.1.3.2)

Now, one can determine the constants c1 and c2 by keeping φ fixed and minimizing the energy

functional ),,( 21 φccF with respect to c1 and c2. Hence c1 and c2 can be expressed in terms of φ ,

given as [61]:

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Chapter 12 Page 69

∫

∫

Ω

Ω=dxdyyxH

dxdyyxHyxu

c)),((

)),((),(

)(

0

1φ

φφ

(12.1.3.3)

∫

∫

Ω

Ω

−

−

=dxdyyxH

dxdyyxHyxu

c))),((1(

))),((1)(,(

)(

0

2

φ

φφ

(12.1.3.4)

Here, (12.1.3.3) can be utilized, provided 0)),(( >∫Ω

dxdyyxH φ , and (12.1.3.4) can be utilized,

provided 0))),((1( >−∫Ω

dxdyyxH φ . In [61], regularized (smooth) versions of the Heaviside

function H and the one-dimensional Dirac function 0δ , called εH and εδ respectively, are

utilized to compute the Euler-Lagrange equations associated with the computation of φ and they

are defined as:

22

' 1)()(arctan

21

2

1)(

xxHx

xxH

+==

+=ε

επ

δεπ εεε

(12.1.3.5)

Keeping the constants 21 ,cc fixed, and minimizing F with respect to φ , the associated Euler-

Lagrange equation for φ is deduced. This finally gives the following equations for the curve

evolution which must be solved iteratively:

( ) ( ) 0)(2

202

2

101 =

−+−−−

∇∇

=∂∂

cucudivt

λλµφφ

νφδφ

ε

(12.1.3.6)

Ω= in),(),,0( 0 yxyx φφ

(12.1.3.7)

Ω∂=∂

∂

∇on0.

)(

nrφ

φφδε

(12.1.3.8)

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It is also very important to remember that as the evolving curve can develop shocks and degrade

with time, it is necessary to periodically reinitialize the zero level curve of φ to the signed

distance function [59, 67, and 71]. The convention is to solve the following equation periodically

so as to re-initialize the level set, where φ the function to be re-initialized is and )(φsign is the sign

function.

( )φφφ

∇−=∂∂

1)(signt (12.1.3.9)

However, it should be remarked in this context that, often the step of re-initialization introduces

further complications like moving the zero level set away from its original location or increasing

the computation time. In fact, it is not really well established yet, when and how such a re-

initialization step should be implemented [71]. Algorithm 1 presents the basic Chan and Vese

algorithm.

12.1.4 The Chan and Vese Algorithm:

The st.eps of the basic Chan and Vese algorithm [61] can be summarized as given in algorithm.

12.1.4.1

______________________________________________________________________________

______________

Step 1. Construct the initial level set function 0φ for iteration n = 0.

Step 2. Calculate the values of the average intensities inside and outside the evolving contour

by computing

)(1nc φ and nc )(2 φ , using (12.1.3.3) and (12.1.3.4) respectively, at iteration = n.

Step 3. Solve the Partial Differential Equation in φ (12.1.3.6), (12.1.3.7), (12.1.3.8) to obtain

the new level set function 1+nφ for

iteration = n+1.

Step 4. The level set function φ may have to be reinitialized locally using (12.1.3.9). This step is optional and, if

Employed, is generally repeated after every few iterations of the curve evolution.

Step 5. Compare the level set functions ( nφ , 1+nφ ). If the solution is not stationary, Then make

n = n+1 and

go to Step 2, Otherwise go to Step 6.

Step 6. Stop contour evolution and report segmentation result.

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______________________________________________________________________________

_______________

Algo. 12.1.4.1. The Chan and Vese algorithm for image segmentation using level set approach.

12.1.5. The Strengths and Drawbacks of the Chan and Vese Algorithm:

The inherent strength of the above mentioned method is that interior contours within the image

can be automatically detected using this method [61]. However, sometimes, if an initial contour

is placed far away from the final segmented result, it may be so that this method will not be able

to converge to the final result within the desired number of iterations. Also, the energy fitting

functional term is non-convex in nature [64, 65] and contains several local minimum points.

Since this method utilizes a gradient descent based adaptation procedure, good initial choices of

the contour are essential as, otherwise, the system may get locked at the first local minimum of

the functional. So if the initial contour can be placed in a near optimal position, it will be able to

achieve the final segmented result quickly, within a small number of iterations. The optimal

placement of the initial contour will also be able to avoid the local minimum and converge closer

to the global minimum point. As mentioned previously, to overcome this initialization problem

of the Chan and Vese algorithm, we propose a metaheuristic optimization based robust

initialization procedure that can finally achieve optimum or near optimum contour(s),

irrespective of the choices of the initial contour.

Another feature of the Chan and Vese algorithm that requires discussion is the (optional) re-

initialization step. This re-initialization step is computationally expensive and a better way to

evolve the curve is to force the evolving contour to be as close to a signed distance function as

possible. Using the property of the signed distance function [71], a metric as in (12.1.5.1) can be

added to the energy fitting term in (12.1.2.1). By adding this term, now (12.1.5.3) can be solved

iteratively without the need for any re-initialization of level set function. Under these

circumstances, there will be no need to implement step 4 in algo. 12.1.4.1. The mathematical

formulation can then be described as [71]:

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( ) dxdyP ∫ −∇=2

12

1)( φφ

(12.1.5.1)

)(),2

,1

()2

,1

,( φφφ PccFccE +=

(12.1.5.2)

( ) ( )

−+−−−

∇∇

+

∇∇

−∇=∂∂ 2

202

2

101

2 )( cucudivdivt

λλµφφ

νφδφφ

φφ

ε

(12.1.5.3)

12.1.6 Extension of Chan Vese algorithm for Vector-valued images:

The Chan and Vese model can be extended to cater to the vector-valued images (such as RGB or

multi-spectral images) [70]. The model is similar to the scalar model of the Chan Vese

algorithm. The only difference is that the model minimizes the fitting energy over each

component of the vector-valued images. This model also has very strong de-noising capabilities.

Let i

u,0 be the i th channel of an image onΩ , with Ni ,....,3,2,1= channels and C be the

evolving curve. The constant vectors are defined as ),......,2

,1

( +++=+N

cccc and

),......,2

,1

(−−−=−N

cccc [70]. Then similar to (12.1.2.1), for the vector-valued case, the energy

functional can be given as [70]:

∫ ∑

∫ ∑

=

−−

=

++

−+

−

−+

+=

)( 1

2

,0

)( 1

2

,0

),(1

),(1

))((.)(.),,(

Coutside

N

i

iii

Cinside

N

i

iii

dxdycyxuN

dxdycyxuN

CinsideAreaCLengthCF

λ

λ

µνcc

(12.1.6.1)

Where +iλ and −

iλ are the parameters for the ith channel and must be positive.

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The constant +c and −

c vectors represent the average image intensities, inside and outside the

evolving contourC , for each channel of the vector-valued image. Similar to the scalar case, it is

prudent to use level set formulation for minimizing the above functional for the vector valued

case too. Also as given before, regularized (smooth) version of the Heaviside function εH and

the one-dimensional Dirac function εδ are used in the formulation.

Minimizing the energy in (12.1.6.2) with respect to the constants +c and −

c , for Ni ,....,3,2,1= ,

we obtain [70]:

∫

∫

Ω

Ω+ =dxdyyxH

dxdyyxHyxu

c

i

i

)),((

)),((),(

)(

,0

φ

φφ

∫Ω

−

∫Ω

−=−

dxdyyxH

dxdyyxHyxi

u

ic ))),((1(

))),((1)(,(,0

)(φ

φφ

(12.1.6.2)

The extra regularizing term in (12.1.5.1) is added as in the scalar case to (112.1.6.2) to avoid the

necessity of the additional re-initialization phase. Similarly the energy functional in (12.1.6.2.)

can be minimized by the gradient descent search, with respect to φ by keeping the vectors +c and

−c constant. The following Euler-Lagrange equation has been derived that needs to be solved iteratively

so as to evolve the curve [70]:

∑=

−−−+∑=

+−+−−∇

∇+

∇

∇−∇=

∂

∂ N

iicyxiui

N

N

iicyxiui

Ndivdiv

t 1

2),(,0

1

1

2),(,0

1)(

2 λλµφ

φνφεδ

φ

φφ

φ

(12.1.6.3)

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Chapter 12 Page 74

12.2 K-means Clustering Algorithm

The main concept of clustering is to make a group of similar data in to cluster that

comprises of almost similar members [73]. All the members in a group are different in

comparison with other members in that group. K indicates the number of clusters and the

value of K is positive. In this work, the value of K is set to 2. The training of this algorithm

completes, when there is no such change in any cluster.

TABLE 12.1. K-means clustering Algorithm [74]

1. Inputs: number of K and dataset for intrusion detection.

2. Outputs: Set of clusters K whish minimize square-error criterion

3. Initialization: Select K elements for data randomly and initialize K clusters.

4. Repeat step 2, when number of cluster structure changes.

5. Cluster determination: To which source data belongs. Add element to the cluster

with minimum (Using Euclidean distance) Distance ( iQiP , )

6. Mean calculation: Mean of cluster. Using step 3, change in cluster centroid to mean

obtained.

12.3. GSA:

GSA optimization algorithm is based on law of gravity [75]. Newton defined it as, “Every

particle in the universe attracts every other particle with a force that is directly proportional

to the product of the masses of the particles and inversely proportional to the square of the

distance between them.”

System having G masses in which the j thmass’s position is defined as:

S Gjgjs

djsjsjsj ,....,2,1),,.....,,......,2,1( ==

(12.3.1)

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where, d

js is jth mass’s position in d th dimension and in the search space, g is total

numbers of dimensions. The calculated mass of each agent:

∑ = −

−=

Gk

tworsttkfit

tworsttjfittj

O

1)()(

)()( (12.3.2)

Where, tj

O is the mass and )(tj

fit is fitness value of agent j at t.

and ,...,1),(max)( Gktk

fittworst ∈=

(12.2.1)

TABLE.12.2. GSA K-means approach Algorithm [76]

1. Scaled dataset

2. For K =2.

Using Euclidean distance

Centroid determination of each cluster

3. For producing 2 centroids

4. Determine number of agents

Define G’ constant

Compute fitness function

Stopping condition is [0,100]

5. Resultant GSA K-means

12.4. Proposed HGSA_K-means based CV model:

Proposed GSA-K-means based CV model is presented here. In this approach, the fitting

functional energy of the CV model is used to assign masses to the agents in the search

space. The algorithm is described below:

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The basic method is as follows: Suppose the motive is to segment the image into three-

parts. After the first step, the image has been divided into two clusters – one object and its

complementary background. The intensity variation across the captured object and its

complementary background is compared, and the one having the larger variation becomes

the target for the next step of the hierarchy. The intensity with the smaller intensity

variation is not used for the next step of segmentation. Thus the image will be divided into

three distinct parts using the modified proposed CV model. Figure 12.4.1 describes the

Binary tree structure of hierarchical segmentation algorithm.

Figure 12.4.1. Binary tree structure of hierarchical segmentation

The procedure is represented as a binary tree with the regions being represented as nodes

and children of each node being created by a single step of the two-cluster GSA_K

algorithm. The set of the leaves of this tree constitutes the final segmentation of the

original image into a number of clusters equal to the number of leaves.

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12.5. Simulation Results and Discussions:

This proposed method is implemented in Mat lab (version R2013a, using Core 2 Duo CPU, 2.66

GHz, 3GB RAM). In this work, hierarchical setup is used to continuously segment the images

following the Chan-Vese Image segmentation model. For this approach, HGSA_k-means

clustering based CV model is used for image segmentation. To illustrate the effectiveness of our

method we use the PCA fused images for segmentation as their segmentation results are required

to be accurate. We use four sample images to segment them into two, three and four class

respectively. For each image, we have given five test runs of both the standard k_means based C-

V model (G-F) and our proposed GSA-k_means based C-V model (GSA-k) and noted down the

results.

(a) (b) (C) (d)

Fig.12.5.1. Sample PCA fused images (a, b, c, d) on which the experiment has been done

Finally, Figure 12.5.2.Gives the segmentation result of this HGSA_K-means proposed

algorithm when applied on the sample images of figure 4 in its 2-class implementation. All

of the images are of size256x256.

Here, it is also reported about the progression of error while detecting the clusters in the

image for segmentation.As it is evident from the above observation that the percentage of

error increases as the number of clusters to be increased.

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Fig12.5.2: Two-class segmentation of the sample images [7] of figure: 10.5.1 by this

proposed algorithm. Here, k-mean-iteration=5, max-it=5; and N=5.

TABLE 12.3.Timing comparison between the standard C-V model and our proposed C-V

model for segmentation of some gray-scale images of size 256x256(as present in fig

.12.5.2).

Images C-V Model(in

seconds)

Our Proposed C-V

Model(in seconds)

(a) 3.21 0.79

(b) 3.11 0.28

(c) 2.42 0.56

(d) 2.39 0.21

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Here, we also report the progression of error while detecting the clusters in the image for

segmentation. As it is quite evident from the above observations,the error percentage increases as

the number of clusters to be detected increases.

Cluster Value

Mean average standard deviation GF model

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Image (a) Image (b) Image (c) Image (d)

2 class

3 class

4 class

Images 4 class 3 class 2 class

Image (a) 30.45768 13.67835 18.67457

Image (b) 13.45631 1.899138 32.85679

Image (c) 20.36278 3.435678 34.78345

Image (d) 18.42367 1.823498 37.38236

Fig.12.5.3. Mean average standard deviation of the GF model. Here the deviation from the

nominal value is quite high which shows that this method often diverges from the global

minimum value.

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Cluster Value

Mean average standard deviation GSA_K model

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Image (a) Image (b) Image (c) Image (d)

2 class

3 class

4 class

Images 4 class 3 class 2 class

Image (a) 0.149071 0 0.341267

Image (b) 1.452897 0.798327 0

Image (c) 0 0.182574 2.365891

Image (d) 0 15.36159 0

Fig.12.5.4. Mean average standard deviation value from our proposed model. The deviation is

relatively kept under check for all the class divisions for image (a)-(b)-(d). However, for the

image (c), the deviation is quite high for the 2-class image segmentation by our proposed model.

As we can see from the above observations that the clustering algorithm’s performance

decreases steadily as the number of clusters is increased. In proposed HGSA_K method,

the error percentage is very low for the 2 class cases. So it seems prudent enough to

convert the multi-cluster problem into a subsequent iterative based 2-cluster problem so as

to decrease this error.

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The advantages of proposed method are as follows:

1. No need for level sets.

2. Good convergence towards the global minimum.

3. Faster method than the normal CV model.

4. At each step, only the relevant parts of the image is being used for clustering based

segmentation, thereby, preventing lots of redundant calculations and saving

computation time

Performance:

The segmentation performance is also evaluated quantitatively where the automatically

segmented image is compared with the manually segmented image and the similarity is

expressed in terms of Segmentation Performance Measure (SPM), expressed in percentage.

Table 12.4 shows this performance for our proposed system, for each of the four independent

runs of our algorithm with different initial choices, as mentioned before. Ideally the SPM should

be as high as possible with its maximum possible value being 100%. It can be seen that, in each

case, our proposed algorithm could achieve an SPM of more than 99.925%, which should be

considered as a highly encouraging performance.

TABLE 12.4:The segmentation performance of our proposed algorithm for fig. 12.5.2.

a 99.8298

b 99.9175

c 99.9662

d 99.9865

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12.6. Conclusions:

Our proposed GSA-k_means algorithm is successful in segmenting images by using the C-

V model. Due to the coupling of the standard k_means clustering algorithm along-with the GSA

algorithm, the convergence of the cluster values to the global minimum is almost always

guaranteed. It is also necessary to point out that this implementation does not need the use of

level sets and is much quicker than the standard level set implementation of the C-V model.

Extensive experiments in two-class image segmentations have been performed and it has been

observed that our method outperforms both the standard C-V model and the k_means G-F

model. Our proposed C-V model is much faster than the standard C-V model and is also

insensitive to the contour initializations. Experiments done on some fused images validate our

claim. For future work, our model can be extended towards multi-phase level set segmentation

and also for vector valued images. Proposed HGSA_K-means CV algorithm is successful in

segmenting images by using the CV model. Due to the coupling of the standard K-means

clustering algorithm along-with the GSA algorithm, the convergence of the cluster values to the

global minimum is almost always guaranteed.

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CONCLUSION & FUTURE SCOPE

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Chapter 13

Conclusion & Future Scope

13. Conclusion:

This chapter describes the conclusion about the research work and gives the suggestion for

future work.

13.1 Conclusion:

In this research work, attention was drawn towards the current trend of the use of Infrared and

Visual image fusion techniques, especially approaches based on Discrete Cosine Transforms.

This research work demonstrates a novel image fusion algorithm for the fusion of Infrared and

Visual image. However, through extensive experimentation it has been proven that this algorithm

can also perform the operation of image fusion over other different types of images. One of the

salient aspects of this research work is that it uses the renowned Artificial Bee Colony algorithm

for optimization of a novel cost function for determining the fusion weights for the DCT

coefficient matrix of two different image patches. Not only by human visual perception but also

by the SSIM score it has been proven that the algorithm proposed by us outperforms most of its

other contemporary competitors. The authors intend to undertake the segmentation of desired

objects from the fused images as a future prospect of research work.

Our proposed C-V model is much faster than the standard C-V model and is also insensitive to

the contour initializations. Experiments done on some fused images validate our claim. For

future work, our model can be extended towards multi-phase level set segmentation and also for

vector valued images. Proposed HGSA_K-means CV algorithm is successful in segmenting

images by using the CV model. Due to the coupling of the standard K-means clustering

algorithm along-with the GSA algorithm, the convergence of the cluster values to the global

minimum is almost always guaranteed. Our proposed GSA-k_means algorithm is successful in

segmenting images by using the C-V model. Due to the coupling of the standard k_means

clustering algorithm along-with the GSA algorithm, the convergence of the cluster values to the

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Chapter 13 Page 85

global minimum is almost always guaranteed. It is also necessary to point out that this

implementation does not need the use of level sets and is much quicker than the standard level

set implementation of the C-V model.

13.2 Future Scope:

As a future work we intend to consider the use of the second order partial derivatives of the

cost function for faster and better convergence of the active contour model. For future work, our

model can be extended towards multi-phase level set segmentation and also for vector valued

images. Proposed HGSA_K-means CV algorithm is successful in segmenting images by using

the CV model in its both two-phase and multi-phase implementation. Due to the coupling of the

standard K-means clustering algorithm along-with the GSA algorithm, the convergence of the

cluster values to the global minimum is almost always guaranteed. From segmentation to image

imprinting and denoising problems and beyond, such methods will no doubt play an important

role in future image analysis research work and try to implement it by hardware. The final aspect

in future development and improvement is how to estimate and evaluate the quality of a fused

image. As we have discussed in previous and it develop by hardware applications. A few, right

to use methods without reference image are significant for our concern in Infrared and Visual

imaging system.

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REFERENCES

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References Page 87

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