OPTIMIZATION OF THE LOCATION OF CAMERA IN TWO DIMENSIONAL

FLOOR LAYOUT

SITI MUSLIHA BINTI NOR-AL-DIN

A thesis submitted in partial fulfilment of the requirements for the award of degree of

Master of Science (Mathematics)

Faculty of Science

Universiti Teknologi Malaysia

JANUARY 2013

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To my beloved husband, Mohd Khairul Faizal bin Ramli,

father, Nor-al-din bin Md. Lela, mother, Salihah Jusoh, sisters, brothers

and all of my dear friends

for their advices, love and support.

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ACKNOWLEDGEMENT

I wish to express my deepest appreciation and thankful to my great supervisor,

Dr. Yeak Su Hoe, for encouragement, support, supervision and companionship

throughout the duration of this study. I am also would like to thank Dr. Yeak Su Hoe for

helping me especially in providing much valuable research reference resources and

willingness to allocate his precious time in supervising me when I am facing problems in

completing this report.

Moreover, I would like to be grateful to all of my fellow friends and course

mates for their support and help in solving some of the problems. Their views and

opinions are most appreciated and useful indeed. Unfortunately, it is not doable to list all

of them in this limited space. I am also grateful to all my family members.

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ABSTRACT

Installation of the security cameras is increasing rapidly in our society that

required a secure environment. It motivates us to discover an optimum camera

placement in order to improve the coverage of a camera network. It is a significant

design problem in order to have a proper camera placement in a distributed smart

camera network by considering the number of cameras required. Thus, a method was

proposed in order to determine the camera placement by using C and FORTRAN

language. Besides that, it is advantageous to maximize the coverage area by using a

minimum number of cameras. Hence, in order to reduce the number of cameras used, we

divide the area of polygon into grid points. Then, we calculate the camera locations

which can cover the grid points as much as possible. We formulate the above problem as

a set of maximizing coverage problem.

Moreover, the optimal camera problem was solved by developing a general

visibility model for visual camera networks through Binary Integer Programming (BIP).

Extensive performance analysis is exhibited using FORTRAN programming. Based on

the results of this study, we found that by using a minimum number of cameras, it is

sufficient to cover the entire area. Finally, the current results and future

recommendations are presented in the report.

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ABSTRAK

Pada masa kini, pemasangan kamera keselamatan semakin meningkat dikalangan

masyarakat kita yang memerlukan jaminan keselamatan yang efisien. Ini mendorong

kita untuk membentangkan penempatan kamera yang optimum untuk meningkatkan

liputan rangkaian kamera. Ianya merupakan reka bentuk masalah yang penting untuk

menempatkan kamera yang berada dalam rangkaian kamera pintar yang teragih dengan

mengambil kira bilangan kamera yang diperlukan. Oleh itu, satu kaedah telah

dibentangkan bagi menentukan penempatan kamera dengan menggunakan

pengaturcaraan C dan FORTRAN. Selain itu, ianya juga wajar untuk memaksimumkan

keluasan yang dilitupi oleh bilangan kamera yang minimum. Oleh yang demikian, untuk

mengurangkan penggunaan bilangan kamera, kami membahagikan keluasan poligon

kepada titik grid. Kemudian, kami mengira lokasi kamera yang mampu melitupi titik

grid sebanyak mungkin. Kami memformulasikan masalah di atas sebagai satu set

masalah dalam memaksimumkan pelitupan.

Tambahan pula, masalah penggunaan kamera yang optimum telah diselesaikan

dengan cara menghasilkan model penglihatan umum untuk rangkaian kamera visual

melalui Pengaturcaraan Integer Perduaan (BIP). Analisa pengaturcaraan yang lebih

meluas dipamerkan menggunakan pengaturcaraan FORTRAN. Berdasarkan keputusan

kajian ini, kami mendapati dengan menggunakan bilangan kamera yang minimum, ianya

mencukupi untuk melitupi seluruh kawasan. Dan akhirnya, keputusan kajian semasa dan

cadangan masa depan juga dibentangkan dalam laporan ini.

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TABLE OF CONTENTS

CHAPTER TITLE PAGE

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT iv

ABSTRACT v

ABSTRAK vi

TABLE OF CONTENTS vii

LIST OF TABLES x

LIST OF FIGURES xi

LIST OF SYMBOLS /ABBREVIATIONS xii

LIST OF APPENDICES xiii

1 INTRODUCTION 1

1.1 Background of the Problem 1

1.2 Problem Statement 3

1.3 Objective of the Study 4

1.4 Scope of the Study 4

1.5 Significance of the Study 5

1.6 Outline of the Study 6

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2 LITERATURE REVIEW 7

2.1 Introduction 7

2.2 Surveillance Cameras 7

2.3 Visibility Algorithm 9

2.4 Field of View (FoV) of the cameras 11

2.5 Camera Placement Algorithm 12

2.6 Binary Integer Programming (BIP) 13

2.7 Modification of Branch and Bound with

Boolean technique 16

2.7.1 Problems and Modifications 18

2.7.2 Branching and Accelerating Test 20

2.7.3 Modified Algorithm 22

3 METHODOLOGY;

CAMERA PLACEMENT ALGORITHM 23

3.1 Introduction 23

3.2 File Input and Output 24

3.2.1 File Open (fopen) 24

3.2.2 File Close (fclose) 25

3.3 Looping 26

3.3.1 Looping with for 27

3.3.2 Looping with while 27

3.3.3 Looping with do … while 28

3.3.4 The nested loop 28

3.4 The Sample Work of Camera Placement Problem 29

3.4.1 Boundary and Internal Nodes 30

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3.4.2 Slope of Two Nodes 36

3.4.3 Intersection of Two Short Lines 39

3.4.4 Intersection Point 40

3.4.5 Camera View 41

3.4.6 Grid 43

3.5 Branch and Bound & Boolean Method;

Research Methodology Chart 44

3.6 Overall flowchart 46

4 RESULT AND DISCUSSION 47

4.1 Introduction 47

4.2 Visibility 48

4.3 Grid 53

4.4 Integer Binary Programming 56

4.5 The Optimization Placement of Camera 58

5 CONCLUSION AND SUGGESTIONS 62

1.1 Introduction 62

1.2 Conclusion 62

1.3 Suggestions 63

REFERENCES 65

APPENDIX A 66

x

LIST OF TABLES

TABLES TITLE PAGE

3.3 The global index and local index of 26 boundary nodes 3

3.4 Possible of the location of two lines 39

3.5 Possible of the intersection point 40

4.4 The number internal node and percentage 55

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LIST OF FIGURES

FIGURES TITLE PAGE

1.1 Sample of the two-dimensional floor plan layout 2

2.1 A visibility polygon example. 9

2.2 The example of a polygon represents as occupancy grid 11

The field of view (FoV) of a camera

2.3 A sample of simple region divided into four grid cells 15

2.4 The different position of cameras C1, C2 and C3 15

3.1 Two-dimensional floor plan (5×5 nodes) with local nodes representation 29

3.2 Two-dimensional floor plan (5×5 nodes) with global nodes representation 29

3.6 Slope of two nodes 36

3.7 Possible of the location of two lines 39

3.8 Possible of the intersection point 40

4.1 Two-dimensional floor plan (5x5 nodes) with global nodes representation 48

4.2 The coverage area from different boundary node 51

4.3 Sample of finer grid (9×9 nodes) from the original floor plan 53

4.5 The internal view from several boundary nodes 60

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LIST OF SYMBOLS/ABBREVIATIONS

Pe - Polygon

Pi - Simple polygon

Pk - Simple polygon holes

- Boundary operator

Pv - Visibility polygon

- A set of candidate camera

FoV - Field of view

BIP - Binary Integer Programming

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LIST OF APPENDICES

APPENDIX TITLE PAGE

A. Optimal Placement of Security Cameras in In-door Spaces 65

1

CHAPTER 1

INTRODUCTION

1.1 Introduction

Enlarging the vision of the surveillance camera has become a very hot

research topic in recent years. The social demand for the security system is highly

required to perform variety tasks such as general surveillance in various type of

industry. Mathematics in Industry Study Group (MISG) is a well-known

collaborative problem-solving workshop which involving the expert applied

mathematicians. MISG will give the best solution for the real life problems shared by

local companies, and also provide an opportunity for the mathematicians to be

exposed in industrial problems. Having a link between industry and university will

encourage the greater use of mathematical modeling and analysis in industry. One of

the problems in MISG workshop is the camera replacement problem which was

proposed by MIMOS Berhad.

There are various areas of research related to security monitoring, especially

efficient equipment placement. The placement of surveillance sensor on a surface,

like telecommunication relay towers, fire and watch towers, prison watch towers, has

been undertaken for Art Gallery guard placement. The Art Gallery problem is one of

the problems which have been widely discussed in the computational geometry

2

literature. The aim of the findings is to minimize the number of guards for a polygon

such that every point in the polygon is visible by at least one guard. The problem was

developed in addressing restricted guard visibility, but generally unrealistic guard

capabilities are assumed (Erdem & Sclaroff, 2004).

If we desire to provide an efficient security vision to the floor layout (Figure

1.1), the system required to perform variety tasks such as general surveillance

(detection of loitering behavior, detection of unusual or suspicious behaviors,

detection of abandoned objects, monitoring of crowd movements, etc.), subject

tracking, activity classification, gesture recognition, etc. Each of these tasks may

have different requirements and features of interest. As a result, optimal camera

placement may vary from task to task. In addition, task location will vary throughout

the area since people are free to move throughout the area of interest in any direction

they like (Bodor & Schrater, 2005).

Figure 1.1: Sample of the two-dimensional floor plan layout

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1.2 Problem Statement

It is reported that security at numerous public places such as hotel, bank,

hospital need to be further enhanced. Most of the criminal acts were happened while

they were there because the traffic at these locations helps the criminals to act upon

their illegal activities such as robberies, grazing, stealing, etc. Public places that

demand a very tight security system such as banks, hotel lobby, exhibition centre,

mosque, etc. were using the camera surveillance in order to observe and monitor the

places. But, in a practical scenario, the cameras are randomly scattered in a wide area

and each camera may adjust its orientation but cannot move in any direction. Thus,

the surveillance cameras are failed to fully utilize because of the blind area.

Blind area is the area where the cameras are not able to provide a security

vision because of the presence of obstacles that obstructed the camera views. As

applied in cellular telephone networks, the aim of the application is to have as much

coverage as possible within a predefined region, with an acceptable level of quality-

of-service. In this paper, we pose the problem of optimal camera placement for a

given region and vision task. We focus on the camera placement problem where the

goal is to determine the optimal positioning and minimize the number of camera used

for a region to be observed, given a set of task-specific constraints and a set of

possible cameras to use in the layout. Maximizing the field of coverage tends to

tighten the security system, and also contribute to minimize the cost spent in security

vision.

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1.3 Objective of the Study

Installation the surveillance cameras with the effective vision system is the

most significant optimization task in the operation of the security systems. Solving

the problems related to surveillance cameras is computationally expensive.

Meanwhile, the complexity of this problem grows exponentially in order to make

sure that it is satisfying the demand and reserve requirements. Several solution

strategies have been proposed to provide quality solutions to the problem and

increase the potential approach among researchers. The objectives of the study are as

follows:

To tighten the security system of public places by using the minimum

cost.

To minimize the total number of surveillance cameras used.

To place the cameras at the best location where give the maximum

viewing coverage area.

To introduce the region of interest and apply it in solving the problem.

To develop and introduce C and FORTRAN program that will be the

effective solution which satisfying the demand and reserve requirements.

1.4 Scope of research

This study will focus on how to appreciate the use of C language in solving

the optimization of the camera placement in two-dimensional layout. Most of the

problems in two-dimensional that has been effectively solved through C endows with

a new avenue for solving other challenging problems that is the problem in three-

dimensional. Furthermore, mathematical approach will be beneficial to use in solving

complex and intractable problems by availability of the fast and inexpensive

5

computer. However, in this research, we will only restrict our scope of the camera

placement problems in two-dimensional layout.

1.5 Significance of the Study

The result of this study will help engineers in positioning the cameras at the

best location. It will automatically assist the engineers in reducing the use of time in

finding the solution. It is not manageable for engineers to spend too much time in

doing the research to get the best camera placement, but still need to take into

account the technical aspects. Therefore, it must be recognized that the use of C and

FORTRAN language are very helpful in various aspects such as in security system,

financing, economics, etc. Advancement in computer technology also enables us to

formulate and solve complex system as well as the visualization of solutions quickly

and accurately.

Minimizing the cost is one of the main objectives of this study. The

installations of the surveillance cameras are among the inexpensive approach in order

to tighten the security system. However, this study will able to minimize the cost of

installation because the numbers of cameras used are also in optimum level.

The increasing crime rates shows that the security system should be tighten in

order to ensure the safety of all. This study also significant in fulfilling the increasing

practical need and social demand for the security system in industry. We choose the

most inexpensive approach, which the use of C programming could be an effective

way to reduce the criminal acts in our society.

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1.6 Outline of the report

This report consists of three chapters. Chapter 1 is the introduction of camera

placement, describing background of the problem, statement of the problem,

objectives of the study, significance and outline of the report.

Chapter 2 states about the literature review done for this project. It explains

generally about the surveillance camera, explanation of methods used in binary

integer programming in order to minimize the number of cameras while increasing

the coverage. It focuses more on the combination of the Branch-and-Bound

technique and also the Boolean method.

Chapter 3 provides more exposure and further discussion on the research

methodology which consists of the visibility algorithm, camera placement algorithm,

layout configuration, and the optimization model and research framework. This

report ends with the expected outcomes and also the conclusion of the project.

Chapter 4 discusses about the results that obtained from C and FORTRAN.

The first draft of polygon was draw out by using Microsoft Excel. We can solve the

problems from the ratio view of internal nodes to the total number of internal nodes

using C programming.

Finally, chapter 5 concludes the study and some related and useful

recommendations are suggested for further research.

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REFERENCES

1. J. Ferreira, A. Vale, R. Ventura. Optimizing range finder sensor network

coverge. 7th

Symposium on Intelligent Autonomous Vehicles. September 2010.

University of Salento, Lecce, Italy, 1-6.

2. A.Hendricks, Yi-Chun Xu. Camera Network Coverage Improving by Particle

Swarm Optimization. November 2010. University of Technology, The

Netherlands, Volume 2011.

3. M. Erdem , S. Sclaroff. Automated camera layout to satisfy task-specific and

floor plan-specific coverage requirements. December 2004. Boston University.

4. A. Iancu. New Local Search Algorithm for Binary Optimization. April 2012.

Stanford University, pp 1-14.

5. R. Bodor, P. Schrater. Multi-Camera Positioning to Optimize Task Observability.

2005, University of Minnesota

6. T. Murray , A. Kim, W. Davis. Coverage optimization to support security

monitoring. January 2006. The Ohio State University.

7. F. Rutherford. Integer Programming. November 2011. ETH Zurich.

8. Chian Fen. Optimization of Location of Camera in 2D Layout. July 2012.

Universiti Teknologi Malaysia.

9. Hammer, P. L. and Rudeanu, S., Boolean Methods in Operations Research and

Related Areas, 1968, Springer Verlag, New York.

10. Utusan Melayu (Malaysia) Berhad, September 2012. Malaysia.