OPTIMIZATION OF THE LOCATION OF CAMERA...
Transcript of OPTIMIZATION OF THE LOCATION OF CAMERA...
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
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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
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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
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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
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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
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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.