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OBJECT DETECTION USING WAVELET

TRANSFORM METHOD FOR THREE-WAY

DECOMPOSED IMAGES

PROJECT REPORT

Submitted by

AJU JOHN

Register No: 710011401002

in partial fulfillment for the award of the degree

of

MASTER OF ENGINEERING

in

APPLIED ELECTRONICS

DEPARTMENT OF ELECTRONICS AND COMMUNICATION

ENGINEERING

ANNA UNIVERSITY

REGIONAL CENTRE, COIMBATORE

COIMBATORE - 641 047.

JULY 2013

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ANNA UNIVERSITY

REGIONAL CENTRE, COIMBATORE

COIMBATORE - 641 047

Department of Electronics and Communication Engineering

PROJECT REPORT

JULY 2013

This is to certify that the project entitled

OBJECT DETECTION USING WAVELET TRANSFORM

METHOD FOR THREE-WAY DECOMPOSED IMAGES

is the bonafide record of project work done by

AJU JOHN

Register No: 710011401002

of M.E. (APPLIED ELECTRONICS) during the year 2011-2013.

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

Dr.V.R.VIJAYKUMAR Ph.D., Dr.V.R.VIJAYKUMAR Ph.D.,

Head of the Department Project Guide

Submitted for the project Viva-Voce examination held on _____________

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

Internal Examiner External Examiner

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ABSTRACT

Moving object detection and tracking is often the first step in applications

such as video surveillance. It is hard to detect the object in turbulent medium where

the object is moving also. Three-way decomposition methods which can detect

moving object in turbulent medium. But it suffers to obtain outlier of the object

clearly, final output image is without background.

In this project, it is proposed a novel approach which is used to enhance

target and restrain noise using wavelet transform and image fusion and is applied

for obtaining the object outlier with background. In this method the original

decomposed background and image is fused and it is decomposed and

reconstructed by wavelet and it is separated into a low frequency image and some

high frequency images., secondly, the low frequency image is removed and the

high frequency images are fused into a new image, finally, the fused image is

segmented with threshold and the target is detected and signed by retaining the

background.

The simulated results in Matlab for the PSNR of the obtained frames

determined in the proposed method was found to be 7% less than the three-way

decomposition method.

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ACKNOWLEDGEMENT

First and foremost I place this project work on the feet ofGOD ALMIGHTY who

is the power of strength in each step of progress towards the successful completion ofproject.

I am highly indebted to Dr.V.R.VIJAYKUMAR, M.E., Ph.D., Head of the

Department of ECE for providing invaluable guidance, suggestion and timely supervision

and insights into the subject and helping me wherever possible.

I thankDr. M. SARAVANAKUMAR Ph.D., Regional Director, Anna University

Regional Centre, Coimbatore for his great support with blessings.

I also extend my heartfelt thanks to all staff members of ECE Department who

have rendered their valuable help in making this project successful.

Above all I would like to thank all the members of my family and friends for their

constructive criticism and constant support in making this project a grand success.

AJU JOHN

Reg No.: 710011401002

APPLIED ELECTRONICS

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TABLE OF CONTENTS

CHAPTER NO. TITLE PAGE NO.

ABSTRACT iii

LIST OF TABLES viii

LIST OF FIGURES ix

LIST OF ABBREVIATIONS AND SYMBOLS x

1 INTRODUCTION 1

1.1 MOTIVATION OF THE WORK 3

1.2 OBJECTIVE OF THE WORK 3

1.3 CHAPTER ORGANISATION 4

2 LITERATURE REVIEW 5

2.1 ROBUST VIDEO DENOISING USING

LOW RANK MATRIX COMPLETION

5

2.2 RASL:DECOMPOSITIONFOR

LINEARLY CORRELATED IMAGES 6

2.3 A BAYESIAN COMPUTER VISIONSYSTEM FOR MODELLING HUMAN

INTERACTIONS

6

2.4 BAYESIAN MODELING OF

DYNAMIC SCENES FOR OBJECT

DETECTION

7

2.5 IMAGE RECONSTRUCTION OF VIDEO

DISTORTED BY ATMOSPHERIC

TURBULENCE

8

2.6 TWO-STAGE RECONSTRUCTION

FOR SEEING THROUGH WATER 8

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TABLE OF CONTENTS


2.7 STABILIZING AND DEBLURRING

ATMOSPHERIC TURBULENCE9

2.8 A HIGH-QUALITY VIDEO

DENOISING ALGORITHM BASED

ON RELIABLE MOTION ESTIMATION

10

2.9 AN INFRARED SMALL AND DIM

TARGET DETECTION ALGORITHM

BASED ON THE MASK IMAGE

10

2.10 A NEW FUSION ALGORITHM FOR

DIM TARGET DETECTION BASED

DUAL-WAVE INFRARED IMAGES

11

2.11 AN ALGORITHM OF DIM AND

SMALL TARGET DETECTION

BASED ON WAVELET

TRANSFORM AND IMAGE FUSION

11

2.12 SIMULTANEOUS VIDEO

STABILIZATION AND MOVING

OBJECT DETECTION IN

TURBULENCE

12

2.13 SUMMARY 13

3 THREE-WAY DECOMPOSITION AND TWO

DIMENSIONAL IMAGE WAVELET

TRANSFORM

15

3.1 THREE-WAY DECOMPOSITION 15

3.1.1 Three-Term Decomposition 18

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TABLE OF CONTENTS


3.1.2 Turbulence Model 20

3.1.3 Restoring Force 22

3.2 TWO-DIMENSIONAL WAVELET

TRANSFORM

24

3.3 SUMMARY 26

4 OBJECT DETECTION USING WAVELET

TRANSFORM METHOD FOR THREE-WAY

DECOMPOSED IMAGES

27

4.1 SUMMARY 29

5 RESULTS AND DISCUSSION 30

5.1 SIMULATION RESULTS FOR

THREE-WAY DECOMPOSITION30

5.2 SIMULATION RESULTS FOR

PROPOSED METHOD

35

5.3 PERFORMANCE ANALYSIS 48

6 CONCLUSION 50

6.1 FUTURE WORK 50

APPENDIX

REFERENCES

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LIST OF TABLES

TABLE NO TITLE PAGE NO

5.1 Comparison based on performance 48

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LIST OF FIGURES

FIGURE NO. TITLE PAGE NO.

3.1 The various steps of the three-way

decomposition algorithm

17

3.2 Schematic diagram of two-dimensional

wavelet decomposition

25

4.1 Flow chart of the proposed algorithm 28

5.1 Three-term decomposition results for two

example frames from testing Sequence 1. 31







5.5 Proposed method results for one frame from

testing sequence 1. 37

5.6 Proposed method results for second frame

from testing sequence 1. 39







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5.11 Proposed method results for one frame fromtesting sequence 4. 46



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LIST OF ABBREVIATIONS AND SYMBOLS

ALM Augmented Lagrange Multiplier

BTV Bilateral Total Variation

MSE Mean Square Error

NLM Non-local means

PSNR Peak Signal-to-Noise Ratio

RASL

SVD

Robust Alignment by Sparse and Low-Rank

Singular Value Decomposition

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CHAPTER 1

INTRODUCTION

In recent years, video surveillance systems for the purpose of security have been

developed rapidly. Video surveillance of human activity usually requires people to be

tracked. It is important to security purpose and traffic control which is also used to take

necessary step for avoid undesired interaction. But the refraction index of the air varies

based on several atmospheric characteristics, including the airs temperature, humidity,

pressure, carbon dioxide level, and dust density. Such conditions are typically not

homogeneous; for instance, a non-uniform temperature distribution might be observed

above a surface receiving sunlight. While considering this certain conditions in

atmosphere like light rays traveling through the air with non-uniform changes in its

relative refraction index will go through a complex series of refraction and reflection,

causing extreme spatially and temporally varying deformations to the captured images

and cause turbulence in the captured images. It is somewhat like noises and cause difficult

if the objects of interest are additionally moving in the scene, their motion will be mixed

up with the turbulence deformation in the captured images, rendering the problem of

detecting the moving objects.In three-way decomposition method each image frames are decomposed into the

background, the turbulence and the moving object. In this method, first apply a

preprocessing step to improve the contrast of the sequence and reduce the spurious and

random noise. Consequently, obtained an object confidence map using a turbulence

model which utilizes both the intensity and the motion cues. Finally, decomposed the

sequence into its components using three-term rank minimization. The obtained output

decomposed result contains turbulence frame, object frame without background and the

background. So the problem in this method is the obtained outlier of the object is not

much clear. The final output image is without background so it is hard with content

provided without background for the human interpretation of the image and also need a

large storage space.

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Wavelet methods for detection and enhancement tasks have received considerable

attention within the fields of dim and small target detection [1]. The general approach is

to:

1) Original image is decomposed and reconstructed by wavelet and it is separated into alow frequency image and some high frequency images

2) The low frequency image is removed and the high frequency images are fused into a

new image

3) The fused image is segmented with threshold and the target is detected and signed.

Since the moving objects are sparse in the sequence. This means that the number of

pixels occupied by the moving objects is small (or can be considered as outliers)

compared to the total number of pixels in the frames. This is a reasonable assumption for

most realistic surveillance videos. So it can be compare with dim and small target

detection where the number of pixels occupied by the target is small compared to the

number of pixels in the frames.

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1.1MOTIVATION OF THE WORKSmall target detection has been a hot research field of image processing and guidance.

In order to make the weapon system and video surveillance in high security areas like

border region and desert region have a greater attention is needed, the target would be

detected in the far distance. At this point, the target in the imaging plane is a bright spot

with only one or a few pixels that is the moving objects are sparse in the sequence. This

means that the number of pixels occupied by the moving object is small (or can be

considered as outliers) compared to the total number of pixels in the frames. This is a

reasonable assumption for most realistic surveillance videos, which cannot reflect the

shape, contour and texture features. What's more, due to the complex environment

containing turbulence and the noise of detector and background, the ratio of signal to

noise is very low, so the traditional image processing algorithms cannot detect small

target.

1.2OBJECTIVE OF THE WORK

This project consist of two parts, in the first the input frames which are distorted

with turbulence are decomposed into object, frame and turbulence, that is three-way

decomposition of input frames. In the next step the decomposed images are fused except

turbulence and two-dimensional wavelet decomposition and data fusion of high

frequency components and marking the centroid. In this paper, a new detection algorithm

based on wavelet transform and image fusion used in three-way decomposed images

since the decomposed images contain noises and outlier of the decomposed object is not

clear and some of the images are not fully decomposed. The algorithm makes full use ofthe multi-resolution analysis feature of wavelet transform and fuses different resolution

images to enhance target and restrain noise. It has a strong engineering applicability.

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1.3 CHAPTER ORGANISATION

Rest of the work is divided into chapters and is organized as follows:

Chapter 2 discusses about various literatures Three-way decomposition and wavelettransform.

Chapter 3 presents the background of Three-way decomposition and wavelettransform.

Chapter 4 derive and discuss the proposed method. Chapter 5 presents the simulation result and discussion on the performance

parameter.

Chapter 6 concludes the report by describing various observation and scope offuture work.

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CHAPTER 2

LITERATURE REVIEW

Literature survey has been done in the area of three-way decomposition and two-

dimensional wavelet transform. The research done by various authors are studied and

some of them are discussed in the following section.

2.1 ROBUST VIDEO DENOISING USING LOW RANK MATRIX

COMPLETION

Liu C. et.al, proposed [6] about Robust video denoising using low rank matrix

completion. The give most existing video denoising algorithms assume a single statistical

model of image noise, e.g. additive Gaussian white noise, which often is violated in

practice. In this paper, they presented a new patch-based video denoising algorithm

capable of removing serious mixed noise from the video data. By grouping similar

patches in both spatial and temporal domain, they formulated the problem of removing

mixed noise as a low-rank matrix completion problem, which leads to a denoising scheme

without strong assumptions on the statistical properties of noise. The resulting nuclear

norm related minimization problem can be efficiently solved by many recent developedmethods. The robustness and effectiveness of our proposed denoising algorithm on

removing mixed noise, e.g. heavy Gaussian noise mixed with impulsive noise, is

validated in the experiments and proposed approach compares favorably against a few

state-of-art denoising algorithms. The proposed video denoising method is built upon the

same methodology grouping and collaboratively filtering as many patch-based methods

do. Different from existing methods, the proposed algorithm is derived with minimal

assumptions on the statistical properties of image noise. The basic idea is to convert the

problem of removing noise from the stack of matched patches to a low rank matrix

completion problem, which can be efficiently solved by minimizing the nuclear norm (1

norm of all singular values) of the matrix with linear constraints. It is shown in the

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experiments that our low rank matrix completion based approach can efficiently remove

complex noise mixed from multiple statistical distributions

2.2 RASL: DECOMPOSITION FOR LINEARLY CORRELATED IMAGES

Arvind Ganesh et.al, proposed [1] about RASL: Robust Alignment by Sparse and

Low-Rank Decomposition for Linearly Correlated Images. In this paper, they studied the

problem of simultaneously aligning a batch of linearly correlated images despite gross

corruption (such as occlusion). The method seeks an optimal set of image domain

transformations such that the matrix of transformed images can be decomposed as the

sum of a sparse matrix of errors and a low-rank matrix of recovered aligned images. They

reduced the extremely challenging optimization problem to a sequence of convex

programs that minimize the sum of 1-norm and nuclear norm of the two component

matrices, which can be efficiently solved by scalable convex optimization techniques with

guaranteed fast convergence. Then they verified the efficacy of the proposed robust

alignment algorithm with extensive experiments with both controlled and uncontrolled

real data, demonstrating higher accuracy and efficiency than existing methods over a wide

range of realistic misalignments and corruptions.

2.3 A BAYESIAN COMPUTER VISION SYSTEM FOR MODELLING HUMANINTERACTIONS

Rosario B. et.al, proposed [10] a Bayesian Computer Vision System for Modeling

Human Interactions. In this work, they described a real-time computer vision and machine

learning system for modeling and recognizing human behaviors in a visual surveillance

task. The system is particularly concerned with detecting when interactions between

people occur and classifying the type of interaction. Examples of interesting interaction

behaviors include following another person, altering one's path to meet another, and so

forth. Our system combines top-down with bottom-up information in a closed feedback

loop, with both components employing a statistical Bayesian approach. They proposed

and compare two different state-based learning architectures, namely, HMMs and

CHMMs for modeling behaviors and interactions. The CHMM model is shown to work

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much more efficiently and accurately. Finally, to deal with the problem of limited training

data, a synthetic and a life-style training system is used to develop flexible prior models

for recognizing human interactions. They demonstrated the ability to use these a priori

models to accurately classify real human behaviors and interactions with no additionaltuning or training.

2.4 BAYESIAN MODELING OF DYNAMIC SCENES FOR OBJECT

DETECTION

Shah M. and Sheikh Y. proposed [11] the Bayesian Modelling of dynamic scenes

for object detection. In this work, they proposed an accurate detection of moving objects

is an important precursor to stable tracking or recognition. They presented an objectdetection scheme that has three innovations over existing approaches. First, the model of

the intensities of image pixels as independent random variables is challenged and it is

asserted that useful correlation exists in intensities of spatially proximal pixels. This

correlation is exploited to sustain high levels of detection accuracy in the presence of

dynamic backgrounds. By using a Non-parametric density estimation method over a joint

domain-range representation of image pixels, multimodal spatial uncertainties and

complex dependencies between the domains (location) and range (colour) are directly

modelled. They proposed a model of the background as a single probability density.

Second, temporal persistence is proposed as a detection criterion. Unlike previous

approaches to object detection which detect objects by building adaptive models of the

background, the foreground is modelled to augment the detection of objects (without

explicit tracking) since objects detected in the preceding frame contain substantial

evidence for detection in the current frame. Finally, the background and foreground

models are used competitively in a MAP-MRF decision framework, stressing spatial

context as a condition of detecting interesting objects and the posterior function is

maximized efficiently by finding the minimum cut of a capacitated graph. Experimental

validation of the proposed method is performed and presented on diverse set of dynamic

scenes.

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2.5 IMAGE RECONSTRUCTION OF VIDEO DISTORTED BY

ATMOSPHERIC TURBULENCE

Milanfar P. and Zhu X. proposed [7] how to reconstructed image from distorted

video by atmospheric turbulence. In this work they give how to correct geometric

distortion and reduce blur in videos that suffer from atmospheric turbulence, a multi-

frame image reconstruction approach is proposed in this paper. This approach contains

two major steps. In the first step, a B-spline based non-rigid image registration algorithm

is employed to register each observed frame with respect to a reference image. To

improve the registration accuracy, a symmetry constraint is introduced, which penalizes

inconsistency between the forward and backward deformation parameters during the

estimation process. A fast Gauss-Newton implementation method is also developed to

reduce the computational cost of the registration algorithm. In the second step, a high

quality image is restored from the registered observed frames under a Bayesian

reconstruction framework, where we use L1 norm minimization and a bilateral total

variation (BTV) regularization prior, to make the algorithm more robust to noise and

estimation error. Experiments show that the proposed approach can effectively reduce the

influence of atmospheric turbulence even for noisy video with relatively long exposuretime.

2.6 TWO-STAGE RECONSTRUCTION APPROACH FOR SEEING

THROUGH WATER

Omar Oreifej et.al, proposed [9] the way to reconstruct the image distorted by

water. Several attempts have been lately proposed to tackle the problem of recovering the

original image of an underwater scene using a sequence distorted by water waves. The

main drawback of the state of the art is that it heavily depends on modelling the waves,

which in fact is ill-posed since the actual behavior of the waves along with the imaging

process are complicated and include several noise components; therefore, their results are

not satisfactory. In this paper, they revisited the problem by proposing a data-driven two-

stage approach, each stage is targeted toward a certain type of noise. The first stage

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leverages the temporal mean of the sequence to overcome the structured turbulence of the

waves through an iterative robust registration algorithm. The result of the first stage is a

high quality mean and a better structured sequence; however, the sequence still contains

unstructured sparse noise. Thus, we employ a second stage at which we extract the sparseerrors from the sequence through rank minimization. Their method converges faster, and

drastically outperforms state of the art on all testing sequences even only after the first

stage.

2.7 STABILIZING AND DEBLURRING ATMOSPHERIC TURBULENCE

Zhu X. and Milanfar P. proposed [13] the method to stabilizing and Deblurring

atmospheric turbulence. In this paper, a new approach is proposed to correct geometric

distortion and reduce space and time-variant blur in videos that suffer from atmospheric

turbulence. They first register the frames to suppress geometric deformation using a B-

spline based non-rigid registration method. Next, a fusion process is carried out to

produce an image from the registered frames, which can be viewed as being convolved

with a space invariant near-diffraction-limited blur. Finally, a blind deconvolution

algorithm is implemented to deblur the fused image. Experiments using real data illustrate

that this approach is capable of alleviating blur and geometric deformation caused byturbulence, recovering details of the scene and significantly improving visual quality.

2.8 A HIGH-QUALITY VIDEO DENOISING ALGORITHM BASED ON

RELIABLE MOTION ESTIMATION

Freeman W. and Liu C. proposed [2] a High-Quality Video Denoising Algorithm

Based on Reliable Motion Estimation. Although the recent advances in the sparse

representations of images have achieved outstanding denoising results, removing real,structured noise in digital videos remains a challenging problem. They showed the utility

of reliable motion estimation to establish temporal correspondence across frames in order

to achieve high-quality video denoising. In this paper, they proposed an adaptive video

denoising framework that integrates robust optical flow into a non-local means (NLM)

framework with noise level estimation. The spatial regularization in optical flow is the

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key to ensure temporal coherence in removing structured noise. Furthermore, we

introduce approximate K-nearest neighbor matching to significantly reduce the

complexity of classical NLM methods. Experimental results show that the system is

comparable with the state of the art in removing AWGN, and significantly outperformsthe state of the art in removing real, structured noise.

2.9 AN INFRARED SMALL AND DIM TARGET DETECTION ALGORITHM

BASED ON THE MASK IMAGE

Yao Yunping and Zhang Weiproposed [12] a method for detecting infrared small

and dim target. To overcome the affection of heavy clutter and dim target intensity on

small target detection, a novel background prediction method is proposed. By combining

the mask image and morphological filters, this method can predict the background more

precisely and reduce background processing time. Finally, in terms of target detection

rates and the procession time per frame, the performance comparison between the

proposed method and the Top-hat filtering method is given. The experimental results

indicate that this method can enhance the predicted accuracy of background, even in the

low SNR (signal-to-noise rate), and is a more preferable and effective way to detect

infrared small and dim targets.

2.10 A NEW FUSION ALGORITHM FOR DIM TARGET DETECTION BASED

ON DUAL-WAVE INFRARED IMAGES

Shao-Hua Wang et.al, proposed [5] the method of new fusion algorithm for dim

target detection based on dual-wave infrared images. In this paper, a new approach to dim

targets detection based on dual-wave infrared images is proposed. Based on the salient

features and regional relativity of dual-wave infrared images, the algorithm gives relative

fusion detection for target. Firstly, the source dual-wave infrared images are decomposed

by wavelet transform, and the salient features of the images of each band are used to

determine the potential target area. Secondly, based on the relativity of dual-wave images,

the resulted wavelet coefficients are weighted. Finally, a threshold segmentation method
http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Yao%20Yunping.QT.&searchWithin=p_Author_Ids:37394468400&newsearch=truehttp://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Zhang%20Wei.QT.&searchWithin=p_Author_Ids:37271991400&newsearch=truehttp://link.springer.com/search?facet-author=%22Shao-Hua+Wang%22http://link.springer.com/search?facet-author=%22Shao-Hua+Wang%22http://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Zhang%20Wei.QT.&searchWithin=p_Author_Ids:37271991400&newsearch=truehttp://ieeexplore.ieee.org/search/searchresult.jsp?searchWithin=p_Authors:.QT.Yao%20Yunping.QT.&searchWithin=p_Author_Ids:37394468400&newsearch=true

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is used for dim target detection in the restructured fusion image. Compared with

traditional algorithms, the experimental results show that the proposed algorithm makes

full use of the dual-wave infrared images, inhibits the background carrier and improves

the SNR and detects dim target in higher probability.

2.11 AN ALGORITHM OF DIM AND SMALL TARGET DETECTION BASED

ON WAVELET TRANSFORM AND IMAGE FUSION

Jie Zhao et.al, proposed [4] a method for detecting dim and small targets based on

wavelet transform and image fusion. According to the needs of dim and small target

detection, a new detection algorithm based on wavelet transform and image fusion is put

forward in the paper. In this algorithm, firstly, the original image is decomposed and

reconstructed by wavelet and it is separated into a low frequency image and some high

frequency images, secondly, the low frequency image is removed and the high frequency

images are fused into a new image, finally, the fused image is segmented with threshold

and the target is detected and signed. After the flight test validation, this algorithm has

better accuracy and stability.

2.12 SIMULTANEOUS VIDEO STABILIZATION AND MOVING OBJECT

DETECTION IN TURBULENCE

Omar Oreifej et.al, [8] proposed a new method for object detection by

simultaneously video stabilization and object detection in turbulent medium. Turbulence

mitigation refers to the stabilization of videos with non-uniform deformations due to the

influence of optical turbulence. Typical approaches for turbulence mitigation follow

averaging or dewarping techniques. Although these methods can reduce the turbulence,

they distort the independently moving objects, which can often be of great interest. In this

paper, they addressed the novel problem of simultaneous turbulence mitigation and

moving object detection. Here proposed a novel three-term low-rank matrix

decomposition approach in which they decomposed the turbulence sequence into three

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components: the background, the turbulence, and the object. They simplified this

extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and l

norm. Our method is based on two observations: First, the turbulence causes dense and

Gaussian noise and therefore can be captured by Frobenius norm, while the movingobjects are sparse and thus can be captured by l norm. Second, since the objects motion

is linear and intrinsically different from the Gaussian-like turbulence, a Gaussian-based

turbulence model can be employed to enforce an additional constraint on the search space

of the minimization. They demonstrated the robustness of our approach on challenging

sequences which are significantly distorted with atmospheric turbulence and include

extremely tiny moving objects.

2.13 SUMMARY

There are so many papers that are related to this project are considered in literature

survey. Rank optimization-based video denoising has recently flourished with several

successful works reported, from which here will only discuss the most related articles.

Robust PCA was proposed where a low rank matrix was recovered from a small set of

corrupted observations. The various steps of the proposed algorithm through convex

programming. Similar concepts were later employed in [1] for video denoising, where

serious mixed noise was extracted by grouping similar patches in both the spatial and

temporal domains, and solving a low-rank matrix completion problem. In [10], linear rank

optimization was employed to align faces with rigid transformations, and concurrently

detect noise and occlusions.

Moving object detection is a widely investigated problem. When the scene is static,

moving objects can be easily detected using frame differencing. A better approach would

be to use the mean, the median, or the running average as the background. The so-called

Eigen background [6] can also be obtained using PCA. Additionally, the correlation

between spatially proximal pixels could also be employed to improve the background

modeling using a joint domain (location) and range (intensity) representation of image

pixels such as in [11].

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Approaches for turbulence mitigation focused mainly on registration-based

techniques. In [7] and [13] both the turbulence deformation parameters and a super-

resolution image were recovered using area-based B-Spline registration. More recently,

in [9], turbulence caused by water was overcome by iteratively registering the sequenceto its mean followed by RPCA to extract the sparse errors. Averaging based techniques

are also popular for video denoising and turbulence mitigation, including pixel-wise

mean/median, nonlocal means (NLM) [2]. In reference papers [4], [5] and [12] provide

details about the dim and small target detection techniques in various fields like infrared,

turbulent medium etc. using wavelet transform and image fusion. The algorithm which

aims at the characteristics of dim and small target and the background detects the dim

target in combination with the multi-definition ability of the wavelet transform and the

comprehensive analysis ability of the image fusion to overcome defects of low signal-to-

noise ratio of the dim and small target images. The reference paper mentioned in [18] is

target detection by three-way decomposition by turbulence mitigation is the existing

method for object detection in infrared sequences significantly distorted by atmospheric

turbulence and also containing a moving human. But applying three-way decomposition

the outlier of the decomposed object is not clear. The existing method suffers from clear

object outlier and still facing noise in the image. In order to overcome the problem of

existing method a new algorithm is put forward which uses the three-way decomposed

images. The proposed algorithm makes full use of the multi-resolution analysis feature of

wavelet transform and fuses different resolution images to enhance target and restrain

noise. Thus taking the advantages of wavelet transform and image fusion the outlier of

the object can be made clearly.

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CHAPTER 3

THREE-WAY DECOMPOSITION AND TWO-DIMENSIONAL IMAGE

WAVELET TRANSFORM

In this section, the necessary basics of three-way decomposition and two-

dimensional wavelet transform are summarized. First we will discuss about three-way

decomposition and then 2D wavelet transform concepts along with data diffusion method.

Using this we get the knowledge about to apply the wavelet transform method for three-

way decomposed images for object detection.

3.1 THREE-WAY DECOMPOSITION

Given a sequence of frames{I I} acquired from a stationary cameraresiding in a turbulent medium while observing relatively tiny moving objects,

decompose the sequence into background, turbulence, and object components. More

precisely, consider the frames matrix F {vecIvecI} for IKR k

1,2,.T where WxH denotes the frame resolution (width by height) and vec:R

R is the operator which stacks the image pixels as a column vector. We formulate our

decomposition

mn RankAs . t . F A O E ,

O s, E (3.1)

where F, A, O, and E are the matrices of frames, background, object, and error

(turbulence), respectively. Here, the . norm counts the number of nonzero entries,

. norm is the Frobenius norm which is equal to the square root of the sum of squared

elements in the matrix, s represents an upper bound of the total number of moving objects

pixels across all images, and is a constant which reflects our knowledge of the

maximum total variance due to corrupted pixels across all images. The decomposition is

based on the intrinsic properties of each of the components.

First the background of the frame. The scene in the background is presumably

static; thus, the corresponding component in the frames of the sequence has linearly

correlated elements. Therefore, the background component is expected to be the part of

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the matrix which is of low rank. Minimizing the rank of the low-rank component of the

frames matrix F emphasizes the structure of the linear subspace containing the column

space of the background, which reveals the background.

The turbulence is the fluctuations of fluids (for instance air and water) attainGaussian-like characteristics such as being unimodal, symmetric, and locally repetitive;

therefore, the projected deformations in the captured sequence often approach a Gaussian

distribution. For this reason, the turbulence component can be captured by minimizing its

Frobenius norm. The Frobenius norm of a matrix is the same as the Euclidean norm of

the vector obtained from the matrix by stacking its columns. Therefore, as in the well-

known vector case, constraining the error in the Euclidean norm is equivalent to

controlling the sample variance of the error. Furthermore, theoretically, the estimate

obtained by the Frobenius norm has several desirable statistical properties.

The moving objects, here assume that the moving objects are sparse in the

sequence. This means that the number of pixels occupied by the moving objects is small

(or can be considered as outliers) compared to the total number of pixels in the frames.

This is a reasonable assumption for most realistic surveillance videos. For this reason, the

moving objects are best captured by restricting the number of nonzero entries (denoted

by the 0 norm of the matrix), which is desirable for finding outliers.

In practice, parts of the turbulence could also appear as sparse errors in the object

matrix O. Therefore, an additional constraint needs to be enforced on the moving objects.

Here employ a simple turbulence model to compute an object confidence map which is

used to encourage the sparse solutions to be located on regions exhibiting linear motion

that is dissimilar from the fluctuations of the turbulence. Under the new constraint, the

optimization problem (3.1) must be reformulated as

minA,O,ERankA) s.t. F=A+O+E,

O s, E (3.2)

where : R Ris the object confidence map, which is a linear operator that

weights the entries of O according to their confidence of corresponding to a moving object

such that the most probable elements are unchanged and the least are set to zero.

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Figure 3.1 shows a diagram of the three-way decomposition approach. First apply a pre-

processing step to improve the contrast of the sequence and reduce the spurious and

random noise. Consequently, an object confidence map using a turbulence model which

utilizes both the intensity and the motion cues. Finally, decompose the sequence into itscomponents using three-term rank minimization.

Figure 3.1 The various steps of the three-way decomposition algorithm

Here, decompose the matrix which contains the frames of the turbulence video into

its components: the background, the turbulence, and the objects. The decomposition is

performed by solving the rank optimization in (3.2), which enforces relevant constraints

on each component. In the next section, we describe the details of the decomposition

approach.

I ...I

Frames

Pre-Processi

ng

Processed

Frames

Three-Term

Low Rank

Background

Object

Turbulence

Intensity

Model

Motion

Model

ObjectConfidence

map

Turbulence Noise

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3.1.1 Three-Term Decomposition

When solving (3.2), it is more convenient to consider the Lagrange form of the

problem.min

A,O,ERankA) + O E

s.t. F=A+O+E, (3.3)

where and are weighting parameters. The optimization of (3) is not directly tractable

since the matrix rank and the 0 norm are non-convex and extremely difficult to optimize.

However, it was recently shown that when recovering low-rank matrices from sparse

errors, if the rank of the matrix A to be recovered is not too high and the number of

nonzero entries in O is not too large, then minimizing the nuclear norm of A and the

l norm of O can recover the exact matrices. Therefore, the nuclear norm and the

l norm are the natural convex surrogates for the rank function and the 0-norm,

respectively. Applying this relaxation, our new optimization becomes

minA,O,E

A O E s.t. F=A+O+E, (3.4)

where Adenotes the nuclear norm of matrix A. We adopt the Augmented Lagrange

Multiplier method (ALM) to solve the optimization problem (3.4). Define the augmented

Lagrange function for the problem as

LA,O,E,Y A O E Y . F A O E

F A O E (3.5)

where Y Ris a Lagrange multiplier matrix, is a positive scalar, and . denotes the

matrix inner product (traceAB). Minimizing the function in (3.5) can be used to solve

the constrained optimization problem in (3.4). Here use the ALM algorithm to iteratively

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estimate both the Lagrange multiplier and the optimal solution by iteratively minimizing

the augmented Lagrangian function:

A+. O+. E+ argmin

A,O,E LA,O,E,Yk.

Y+ Y F+ A+ O+ E+ (3.6)

When is a monotonically increasing positive sequence, the iterations converge

to the optimal solution of problem (3.4). However, solving (3.6) directly is difficult;

therefore, the solution is approximated using an alternating strategy minimizing the

augmented Lagrange function with respect to each component separately:

A+ argmin

A,O,E LA, O, E, Y.

O+ argmin

A,O,E LA,O ,E, Y.

E+ argmin

A,O,E LA, O,E ,Y. (3.7)

Following the idea of the singular value thresholding algorithm derive the solutions for

the update steps in (3.7) for each of the nuclear, Frobenius, and l norms. Consequently,

a closed form solution for each of the minimization problem is found:

UWV

svdF O E

YA+ US

WV

O+ S

F A+ E Y

E+ 1

Y F A+ O+ (3.8)

where svd(M) denotes a full singular value decomposition of matrix M and S. is the

soft-thresholding operator defined for a scalar x as

Sx signx.max{|x| , 0}, (3.9)

and, for two matrices A= (aj)and B= (bj) of the same size, SB applies the soft-

thresholding entry-wise outputting a matrix with entriesS(bj).

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3.1.2 Turbulence Model

A turbulence model to enforce an additional constraint on the rank minimization

such that moving objects are encouraged to be detected in locations with non- Gaussian

deformations. Exact modelling of the turbulence is in fact ill-posed as it follows a non-

uniform distribution which varies significantly in time, besides having an additional

complexity introduced during the imaging process, thus rendering the problem of

modelling turbulence extremely difficult. Although the refraction index of the turbulent

medium is often randomly changing, it is also statistically stationary thus, the

deformations caused by turbulence are generally repetitive and locally centred this

encourages the use of Gaussian-based models as approximate distributions that are

general enough to avoid over-fitting, but rather capture significant portion of the turbulent

characteristics. So it is used a Gaussian function to model the intensity distribution of a

pixel going through turbulence. This is similar to which employs a mixture of Gaussians;

however, it is found that a single Gaussian worked better since more complicated models

often require a period of training which is not available in our sequences. Therefore, the

intensity of a pixel at location x is modelled using a Gaussian distribution:

Ix~N, (3.10)

where and are the mean and the standard deviation at x, respectively. On the other

hand, the deformation caused by turbulence can be captured in the motion domain besides

the intensity. Therefore, we combine the intensity and the motion features to obtain a

better model of turbulence. In order to capture the ensemble motion in the scene, so it is

used the concept of a particle in a Lagrangian particle trajectory acquisition approach

and assumed that a grid of particles is overlaid onto a scene where each particle

corresponds to a single pixel (the granularity is controllable). The basic idea is to quantify

the scenes motion in terms of the motion of the particles which are driven by dense

optical flow. A so-called particle advection procedure is applied to produce the particle

trajectories.

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Given a video clip R,we denote the corresponding optical flow

byU , V, wherew [1, W],h [1, H] and t [ 1 , T 1 ].The position vectorx , y

of the particle at grid point (w, h) at time t is estimated by solving the followingdifferential equations:

dx

dt U

V

(3.11)

Here used Eulers method to solve them, similarly to [38].By performing advection

for the particles at all grid points with respect to each frame of the clip, to obtain the clips

particle trajectory set, denoted by{x , y |w [1, W], h [1, H], t [ 1 , T ]}.

The spatial locations of the particle trajectories x , y to model the turbulence

motion in the scene. The locations visited by a particle moving due to the fluctuations of

the turbulence have a unimodal and symmetric distribution which approaches a Gaussian

.This is dissimilar from the linear motion of the particles driven by moving objects.

Therefore, we associate each particle with a Gaussian with mean and covariance:

x~N, . (3.12)

By augmenting the intensity model with the motion model the total confidence of

corresponding to the turbulence versus the moving objects for a particle at location x is

expressed as a linear opinion pooling of the motion and the intensity cues:

Cx PIx|, 1Px|, (3.13)

The parameters of the model {, , , , }can be learned by optimization

using training sequences or set toconstant values selected empirically. In the context of

our three-term decomposition, the obtained confidence provides a rough prior knowledge

of the moving objects locations, which canbe incorporated into the matrix optimization

Interestingly, this prior employs motion information; therefore, it is complementary to the

intensity-based rank optimization and can significantly improve the result. At frame t, we

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evaluate all the particles locations against their corresponding turbulence models and

obtain the turbulence confidence mapCR. While C corresponds to the confidence

of a particle belonging to turbulence, the desired corresponds to the confidence of

belonging to the moving objects; therefore, we define the object confidence map as thecomplement of the stacked turbulence confidence maps:

1 [ v e c{C} vec{C}] (3.14)

3.1.3 Restoring Force

The particles carrying the objects motion typically drift far from their original

locations, leaving several gaps in the sequence. In the presence of turbulence, the drifting

also occurs as a result of the turbulent motion. Therefore, the particles need to be

reinitialized every certain number of frames, which, however, creates discontinuities.

This is a typical hurdle in the Lagrangian framework of fluid dynamics which constitutes

a major impediment for the application of particle flow to turbulence videos. In order to

handle the drifting and the discontinuity problems associated with the particle flow, so

use a new force component in the advection equation:

dx

dt U Gx,x

V

Gy,y (3.15)

The new force as Restoring Forcea reference to a local restoration force acting in the

direction of the original location of each particle. We use a simple linear function to

represent the restoring force

Gx, x

(3.16)

where s is a scaling factor which trades off the detection sensitivity and the speed of

recovery for the particles. In other words, if s is set to a high value, the effect of the

restoring force will be negligible and therefore the particles will require a relatively longer

time to return to their original positions. In this case, the sensitivity of moving object

detection will be higher, but more prone to false positives. If s is low, the particles will

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be more attached to their original location, thus less affected by turbulence, but will have

lower detection sensitivity. In our experiments, we set s to 0.5xW =125, which found to

be adequate for all sequences. Using the restoring force allows continuous processing of

the sequence without the need to reinitialize the particles. For instance, if an object movesto one side of the frame then comes back, we can still capture its motion when it returns.

Additionally, the restoring force maintains the particles motion within a certain range

and provides robustness against random noise, thus reducing the number of false object

detections.

3.2 TWO-DIMENSIONAL WAVELET TRANSFORM

Image processing method based on wavelet transform is to transform the image

signal in space or time domain to the wavelet domain and calculate multi-level wavelet

coefficients. According to the features of the wavelet base and the demand of processing,

the characteristics of each level of wavelet coefficients are analyzed and disposed by

regular image processing methods or new methods which are more suited to wavelet

analysis. Finally, the processed wavelet coefficients need to be transformed inversely to

get the desired image.

The scale function and wavelet function of wavelet transform can be expressed as

x,yandx,y,where n is the number of decomposition, and j is the scale factor, so

any picture can be decomposed as the formula below:

fx, y cj, j,x, y w,j= ,x,y (3.17)

In the formula, the first item represents the sub-image of low frequency and the

last item represents the sub-image of high frequency. Mallat algorithm gives the discrete

wavelet transform tower multi-resolution decomposition and reconstruction method. The

wavelet transform of two dimensional image signal f(x, y) can be decomposed into two

one-dimensional wavelet transforms along x and y directions. Firstly, the image is

decomposed along x direction with scale function and wavelet function, then decomposed

the image along y direction similarly. So four sub-images are get: low frequency sub-

image A, high frequency sub-image H along x direction, high frequency image sub-V

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along y direction and high frequency sub-image D along diagonal. Increasing the scale

factor j, the low frequency can be decomposed into four sub-images again. By

decomposing the low frequency sub-image in multi-level, the multi-resolution analysis

of two-dimensional image can be realized. The schematic diagram of decomposition isshown below:

Image fusion is an information processing to achieve a better description of the

scene by compositing different images of the same scene getting from different sensors.

Fusion can be conducted at different levels. This image fusion can make the image more

clearly.

Figure 3.2 Schematic diagram of two-dimensional wavelet decomposition

According to the information abstraction, the fusion level can be divided into four

categories: signal level, pixel level, feature level, symbolic level. Pixel level image fusion

directly based on the pixels information of imaging sensor, and fusion result is an image

which is usually more suitable for human and machine perception, or more suitable for

subsequent processing tasks such as segmentation, feature extraction and target

recognition. At present, most of the fusion algorithm are concentrated at this level. The

traditional image fusion methods is mainly to obtain multiple images of the same scene

by several sensors. Because of the multi-resolution multi-scale feature of wavelet

transform, the original image can be decomposed into a series of sub-images with

different spatial resolution and frequency domain characteristics which fully reflect the

local variation of the original image. Fusing the sub-images on multi-level and multi-band

can enhance target and restrain noise.

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3.3 SUMMARY

In this chapter, it is discussed about the existing method of Three-way

decomposition. The infrared sequences significantly distorted by atmospheric turbulence

and also containing a moving man is decomposed into static background, object andturbulence error. In this the object decomposed, there outlier is not clear and still facing

of full decomposition failure. The frames still contain noise. So in order to increase the

clarity of the outlier of the object, here proposed a method using the principles and

advantages of wavelet transform and image fusion. Then check the performance of the

output image with the existing methods. The next chapter will discuss about the proposed

approach and then apply it in application.

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CHAPTER 4

OBJECT DETECTION USING WAVELET TRANSFORM METHOD FOR

THREE-WAY DECOMPOSED IMAGES

In the proposed method, target detection algorithm based on wavelet transform and

image fusion is used in this paper. Firstly, wavelet transform is used in dealing with a

single frame image which is obtained by fusing the object and background of three-way

decomposed images and the fused image is decomposed into a low frequency part and

some high frequency parts in different scales, then every high frequency part is

reconstructed to get a number of sub images. Secondly, every sub image is fused based

on the data fusion method to restrain background and strengthen target. Thirdly, the grey

image after fusion is segmented to a threshold image. Fourthly, target recognitionalgorithm is used to specify and recognize the bright spots in the threshold image to

distinguishing the target and the interference noise. Lastly, the centroid of the target is

marked in the original image.

The flow chart is as given in fig 2. In this paper, bd3 wavelet is selected. It is

compactly supported with external phase and highest number of vanishing moments for

a given support width. Associated scaling filters are minimum-phase filters. Not only with

a fast calculation, but also without truncation error, it can reconstruct the signal precisely.

Assuming that the scale of the target is T and scale of the selected wavelet kernel isT.

It is can be estimated that the max number of the transform levels for small targets

detection islogT/T). Based on the need for the data fusion, scale of the target and

calculation time, the image can be decomposed of three levels.

After wavelet decomposition of the original image, the background mainly

concentrates in low frequency area, while the target and the noise mainly concentrate in

high frequency area. What is more, correlation of the target energy is big in each

frequency range, while distribution of the noise is relatively independently. So, the low

frequency background is cleared directly in the experiment and the high frequency part is

fused twice according to different resolutions and different directions. As the high

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frequency images after decomposing contain much noise, weighted average method is

used to restrain the noise in the first fusion level.

After wavelet transform and data fusion, image contrast becomes high,

background gray scale becomes relatively uniform and occupies most of the pixels andtarget gray scale becomes much higher than the background. After segmentation mark the

centroid of the targeted image.

Figure 4.1 Flow chart of the proposed algorithm

Marking Centroid

Ob ect Detectin

Threshold Segmentation

Input frames

Three-way Decomposition

Turbulence

Data/ Pixel Fusion

Wavelet Transform

Object Background

Image Fusion

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4.1 SUMMARY

In this chapter, it is discussed about the proposed method that is, object detection

using wavelet transform method for three-way decomposed images. An algorithm is

developed for the purpose, and using the advantages of wavelet transform and imagefusion it can increase the outlier of the object clearly. Since the target in the imaging

plane is a bright spot with only one or a few pixels that is the moving objects are sparse

in the sequence. This means that the number of pixels occupied by the moving object is

small (or can be considered as outliers) compared to the total number of pixels in the

frames. Using this method in which wavelet decomposition of image and fusing the large

frequency components and segmentation will provide the output object outlier clearly.

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CHAPTER 5

RESULTS AND DISCUSSION

The proposed method experimented extensively using four infrared sequencessignificantly distorted by the atmospheric turbulence and also containing a moving

human. Each frame is 250 x 180 with 450 frames per sequences. The algorithm in this

paper can detect target in the complex background precisely. First the input image which

is decomposed into background, object and error. Then the object and background images

are fused. Further process such as wavelet transform and fusion are done, the amount of

noise is reduced using the filter, and the target is obtained and signed as shown in final

image. The algorithm described in section 4 was written in matlab file and was simulated

using MATLAB 2012b software which is installed in the computer environment of

specifications with 64 bit Intel core i3 processor with 2.40GHz and 4GB RAM and

obtained simulation outputs as follows.

5.1 SIMULATION RESULTS FOR THREE-WAY DECOMPOSITION

First consider the frames of sequence1, 2, 3 and 4. In which some frames are taken

for the experimental simulation. For example two frames are taken for the

experimentation. Then three-way decomposition is applied. Three-term decomposition

results for two example frames from each testing sequences. Column F shows the original

sequence (after preprocessing) that is the noise caused by turbulence often has several

random and spurious components which are difficult to model. So temporal averaging is

used to mitigate such components. The preprocessed image was decomposed into

background (column A), turbulence (column E) and moving object (column O).

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F A E O

(a)

(b)

Figure 5.1 Three-term decomposition results for two example frames from testing

sequence 1. Column F shows the original sequence (after preprocessing) which was

decomposed into background (column A), turbulence (column E) and moving object

(column O).

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F A E O

(a)

(b)


sequence 2

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F A E O

(a)

(b)


sequence 3

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F A E O

(a)

(b)


sequence 4

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5.2 SIMULATION RESULTS FOR PROPOSED METHOD

While examine the decomposed images the process is not much efficient for fully

decomposing the images. Also the outlier of the object decomposed is not clear. It is

still facing noise problem. So here, utilizing the principle and advantages of the target

detection using wavelet transform and image fusion.

(a)

(b)

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(c)

(d)

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(e)

Figure 5.5. Proposed method results for one frame from testing sequence 1.(a) Input

Image (b) wavelet sub-image and data fused image (c) Noise removed Image (d)

Segmented Image (e) Outlined Image

(a)

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(b)

(c)

(d)

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(e)

Figure 5.6. Proposed method results for second frame from testing sequence 1.(a) Input



(a)

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(b)

(c)

(d)

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(e)

Figure 5.7. Proposed method results for one frame from testing sequence 2.(a) Input



(a)

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(b)

(c)

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(d)

(e)

Figure 5.8. Proposed method results for second frame from testing sequence 2.(a) Input



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(a)

(b)

Figure 5.9 Proposed method results for one frame from testing sequence 3. (a) Input

Image (b) Outlined Image

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(a)

(b)

Figure 5.10 Proposed method results for second frame from testing sequence 3. (a) Input


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(a)

(b)

Figure 5.11 Proposed method results for one frame from testing sequence 4. (a) Input


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(a)

(b)

Figure 5.12 Proposed method results for second frame from testing sequence 4. (a) InputImage (b) Outlined Image

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5.3 PERFORMANCE ANALYSIS

To evaluate the performance, we measured the Peak Signal-to-Noise Ratio (PSNR)

between the first frame of the sequence and the rest of the frames, and reported theaverage results for all the frames in Table 5.1.

Given a reference image f and a test image g, both of size 125 x 90 , the PSNR

(Peak Signal to Noise Ratio) between fand g is defined by:

PSNRf, g 10 log255/MSEf,g (5.1)

where MSEf, g

fj gjj== (5.2)

The PSNR value approaches infinity as the Mean Square Error (MSE) approaches

zero; this shows that a higher PSNR value provides a higher image quality. At the other

end of the scale, a small value of the PSNR implies high numerical differences between

images.

Table 5.1 Comparison Based on Performance (in dB)

Original Registration

[9]

3-way Decomposition

[8]

Proposed Method

Sequence 1 26.55 31.86 31.20 27.81

Sequence 2 27.49 34.05 33.01 28.78

Sequence 3 27.91 31.79 31.94 28.02

Sequence 4 27.82 32.72 32.72 29.17

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It is clear that both three-way decomposition and registration can significantly

stabilize the sequences and improve the PSNR. However, the moving object is not

explicitly handled in the registration; therefore, it impedes the process by causing the

control points to incorrectly shift in the direction of the objects motion, resulting inseveral artifacts in the surrounding area. In contrast, three-term decomposition handles

such difficulties by separating the moving object; therefore, it can recover background

without artifacts and with significantly reduced turbulence. But faces of problem of

failing to obtain the clear outlier of the object. But in the proposed method using the

wavelet transform and image fusion technique. So this method can obtain the object

outlier clearly. The falling of PSNR value for the proposed method is due to the output

image with outlined object is with background. The result shows that the method can used

for small target and the background detection and detection of the small target in

combination with the multi-definition ability of the wavelet transform and the

comprehensive analysis ability of the image fusion.

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CHAPTER 6

CONCLUSION

This project analyses the principle advantages of the target detection using wavelettransform and image fusion in Three-way decomposed images. The algorithm which aims

at the characteristics of small target and the background detects the small target in

combination with the multi-definition ability of the wavelet transform and the

comprehensive analysis ability of the image fusion to overcome defects of low signal-to-

noise ratio of the small target images. It is verified that this algorithm which has high

noise-immunity can detect target correctly with clear outlier with background. This

method can also extend for the application of small target detections.

6.1 FUTURE WORK

In future, this work can be extended to video processing in which simultaneously

removing the turbulence and applying the multi-resolution wavelet transform and data

fusion for detecting the small targets using surveillance camera.

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APPENDIX

LIST OF PUBLICATIONS

1. Aju John and Dr.V.R.Vijaykumar, A paper entitled Object Detection UsingWavelet Transform Method for Three-Way Decomposed Images is presented in

the 5th National Conference on Signal Processing, Communication and VLSI

Design (NCSCV2013), Anna University Regional Centre, Coimbatore on May

10th and 11th, 2013.

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