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Optimal Placement of Multiple Visual Sensors

using Simulation of Pedestrian Movement

Yunyoung Nam and Sangjin Hong

Xeron Healthcare Corp.

Daerung Post Tower III, 410 182-4 Guro-dong, Guro-gu, Seoul, Korea

Email: [email protected] of Electrical and Computer Engineering,

Stony Brook University-SUNY, Stony Brook, NY, USA

Email: [email protected]

AbstractThis paper present an optimal camera placementmethod that analyzes a spatial-temporal model and calculatespriorities of spaces using simulation of pedestrian movement. Inorder to cover the space efficiently, we accomplished an agent-based simulation based on classification of space and patternanalysis of moving people. We have developed an agent-based

camera placement method considering camera performance andspace utility extracted from a path finding algorithm. We demon-strate that the method not only determines the optimal numberof cameras, but also coordinates the position and orientation ofthe cameras with considering the installation costs. To validatethe method, we show simulation results in a specific space.

I. INTRODUCTION

Traditional video surveillance systems using multiple cam-

eras are used to gather data and to identify clues after an

incident has taken into placed to detect an event requiring

attention. However, to install these cameras for monitoring a

large-scale coverage area, it requires hundreds of cameras and

sensors which can bring the cost of a surveillance system up tomillions of dollars. Most of the surveillance systems require

the layout of cameras to assure a minimum level of image

quality or image resolution and to have as much coverage as

possible within a pre-defined region, with an acceptable level

of quality-of-service and with minimum setup cost.

Therefore, the camera placement is one of the most im-

portant issue to develop the effective surveillance system that

maximizes the observability of the motions taking place. This

paper proposes a new camera placement method to optimize

the views for providing the highest resolution images of ob-

jects under the circumstances of a limited number of mounting

cameras. To efficiently calculate the camera placement with

certain task-specific constraints and minimal camera setupcost, assumptions can be defined as the capabilities of real-

world cameras. In this paper, variants employ several assump-

tions about the capabilities that make these algorithms suitable

for most real-world computer vision applications: limited field

of view, finite depth of field, angle of cameras.

This research is supported by the International Collaborative R&D Pro-gram of the Ministry of Knowledge Economy (MKE), the Korean government,as a result of Development of Security Threat Control System with Multi-Sensor Integration and Image Analysis Project, 2010-TD-300802-002.

The proposed method focuses on optimizing the aggregate

path observability as a whole, based on a probabilistic frame-

work, and calculates the coverage and cost constraints. This

framework tries to optimize coverage area and to minimize

overlapping views. The method used in this paper assumes

that the surveillance systems operate on a set of fixed camerasto monitor moving subjects.

The remainder of this paper is organized as follows. Section

II addresses problems and describes related work. Section

III represents models for a space and an agent. Section IV

presents the automatic camera placement method to determine

appropriate camera positions and an appropriate number of

cameras. Section V shows the details of simulation results.

Finally, Section VI concludes this paper.

I I . PROBLEM DESCRIPTION AND RELATED WOR K

Most of the video surveillance camera placement ap-

proaches that appear in the literature focus on space coverage

and sensor deployment. The sensor deployment problem isclosely related to the Art Gallery Problem (AGP) that deter-

mines the minimum number of guards required to cover the

interior of an art gallery [1] and maximizes camera coverage

of an area, where the camera fields of view do not overlap.

The AGP has been solved optimally in two dimensions and

shown to be NP-hard in the three-dimensional case. Several

variants of AGP have been studied in the literature, including

mobile guards, exterior visibility, and polygons with holes.

Yao and Allen [2] formulated the problem of sensor place-

ment to satisfy feature detectability constraints as an un-

constrained optimization problem, and applied tree-annealing

to compute optimal camera viewpoints in the presence of

noise. Erdem and Sclaroff [3] proposed a camera placementalgorithm based on a binary optimization technique. Only

polygonal spaces are considered, which are presented as

occupancy grids. They converted such a continuous domain

into discrete domain and developed a 0-1 integer programming

for solving the optimal locations of cameras such that all

discrete grid points in the specific areas/lanes are monitored.

The effort [4] is made to tackle the problem of task-

specific camera placement, in which the authors optimize

camera placement to maximize observability of the set of

Workshop on Computing, Networking and Communications

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actions performed in a defined area. Yao et al. [5] presented a

camera placement algorithm to optimally preserve overlapped

FOVs and minimize the installation cost with respect to a

maximization of the quality of the recorded data.

In the previous work [6], we presented a camera placement

approach to minimize occlusion for effective object detection

and tracking. In [7], they addressed grid coverage problems

and sensor deployment with sensors sensing events that occur

within the sensing range of the sensor. In the approache, space

was presented as a regular grid. In [8], they developed and

presented a framework that had a novel approach for deter-

mining the optimal number of sensors, along with locating

and setting their orientational sensor-specific parameters on

a synthetically generated 3-D terrain with multiple objectives.

Their solution approach relies on the rational tradeoff between

three conflicting objectives that maximize the coverage area

while maintaining the maximum stealth, and minimize the

total acquisition cost of deploying the sensors.

In this paper, we explain several models in agent-based

pedestrian simulations based on a space model as a two-

dimensional grid map. To determine appropriate camera posi-tions and an appropriate number of cameras to be installed in

view of installation cost, the automatic camera placement is

accomplished by four steps. These steps are space modeling

including a priority space extraction, agent modeling, trajecto-

ries generating with estimating priority areas, and a placement

location selection.

III. SIMULATION MODEL

A. Space Model

Space design is constrained by the performance and applied

algorithms of a camera in constructing a conventional video

surveillance system. The space modeling module models a

specified space as a 2D grid map. The space priority extractionmodule expresses the space priority of each cell of the grid

map in a numerical value based on an amount of movement of

an agent in a first area of the grid map and a probability that

the agent will move from the first area to a second area. The

space model unit consists three layers that are a structure layer,

an area layer, a priority layer. The structure layer contains

accessible areas and inaccessible areas in a space in which

vision sensors are to be placed. This information is applied to

a path-finding algorithm.

The area layer contains information about the amount of

movement of a person in a specified area of a 2D grid

map and information about a probability that the person will

move from a starting point to a destination. The area layercontains area attribute needed to extract a priority area. The

area attribute includes location (x, y), range r, the amount

of movement of a person, and probability that the person

will move from a starting point to a destination. A movement

probability refers to a probability that a person arriving at a

second area (a destination) from a first area (a starting point)

on a 2D grid map. The probability is calculated based on

(n 1) destinations excluding a current destination, at whichthe person has arrived, among a total number n of destinations.

The priority layer presents space priorities that are de-

termined based on a path-finding of the agent. The space

priorities are updated based on the movement pattern of the

agent and used to determine locations at which cameras are

to be placed.

B. Agent Model

Agent trajectories are simulated based on the assumptionthat the agents are people. The artificial intelligence-based

path-finding algorithm considers neither a local field of view

by assuming that the agent has learned regional geographical

information nor the cost of the direction change.

In order to minimize the difference between paths actually

traveled by people and selected by an agent, the path-finding

algorithm should be improved by estimating available routes

around a route that is found using a path-finding algorithm.

First of all, an agent examines all accessible areas to move to

all destinations and performs an inference-based path-finding

simulation. In this paper, eight different directions in a 2D

grid map are considered to apply the A* algorithm [9] to the

improved path-finding algorithm using a heuristic evaluationfunction as follows:

F = G + H, (1)

where G is the total cost of movement from a start node to

a current node and H is the total cost of movement from the

current node to a goal node, which ignores obstacles between

the two nodes.

Therefore, F is a final criterion used in the A* algorithm

to determine a priority in path-finding. The cost of movement

is set to 1 for up, down, right, and left directions and is set to2 for a diagonal direction. In addition, the cost of movement

between the start node and the current node is calculated using

the Manhattan method [10].

To reduce the difference between trajectories actually trav-

eled by people and found using the A* algorithm, a path

expansion algorithm is applied to the A* algorithm. The path

expansion algorithm infers areas where people can move in an

accessible space and updates a priority in priority area layer.

IV. CAMERA PLACEMENT

A. Camera Coverage Model

The position of one camera is represented by X and Y

integer coordinates on a 2D grid map, and the camera has

a look direction angle of maximum 360 degrees at a fixed

position. Figure 1 shows the FOV model of a camera that has

a triangular structure which is defined by a viewing distance

d, an angular range a, and a look direction angle of the

camera at a camera position P=(xc, yc). Thus, the F OV isdenoted by

F OV =

x y

, (2)

where xctan(a2 )d x xc+tan(a2 )d and yctan(a2 )d y yc + tan(a2 ) d. After the new camera position istranslated to an origin (0, 0), the new F OV is denoted by

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Fig. 1. FOV model of a camera

F OV =

x y

(3a)

=

x xc y yc

(3b)

After the triangle is rotated counterclockwise degrees by

the coordinate origin, new F OV are follows:

F OV =

x y

(4a)

=

x cos() y sin()y cos() + x sin()

(4b)

Thus,

x d (5)tan( a

2) x y tan( a

2) x (6)

Equation 7 is calculated by using equations 2, 3, 4, 5.

(x xc) cos() (y yc) sin() d (7)Equation 8 is calculated by using equations 2, 3, 4, 6.

tan( a2 ) {(x xc) cos() (y yc) sin()} (y yc) cos() + (x xc) sin()

tan(a

2) {(x xc) cos() (y yc) sin()} (8)

In order to calculate the coverage of a camera considering

the detection ratio of moving objects, the space is divided

into accessible areas and inaccessible areas such as walls and

obstacles in the FOV of the camera. The utility of an area

is measured by the coverage ratio of FOVs. Thus, the utility

of accessible area Uacc is calculated by ratio of FOVs and a

space as follows:

Uacc(P) =Racc(V)

Rzcc(S) , (9)

where P is a camera position, V is a FOV, S is a space, and

Racc is ratio of accessible areas to the overall space.

The utility of paths is calculated by the number of paths

that are passed by agents. Let Rpath be the path ratio of grid

cells of the area to overall grid cells on paths. Thus, the utility

of paths extracted by A* algorithm Upath is calculated by

Upath(P) = Ppath Rpath(V)Rpath(S)

, (10)

where Ppath is the path probability and is determined by the

probability extracted from area layers.

Similarly, the utility of expansion paths Uexp is calculated

by Upath and the number of expansion paths as follows:

Uexp(P) =Upath(P)

N, (11)

where N is the number of expansion paths.

The utility of inaccessible areas Uinacc should be consideredto calculate the coverage of a camera. After determining the

inaccessible areas such as walls and obstacles in the FOV of

the camera, Uinacc is calculated by

Uinacc(P) =Rinacc(V)

Rinacc(S). (12)

Finally, the utility U(P) of each camera position is calcu-lated by four priorities as follows:

U(P) = Uacc(P) + Upath(P) + Uexp(P) Uinacc(P). (13)B. Camera Placement Method

The utility of visibility at each location on the 2D grid mapvaries depending upon space utility values of cells in an FOV

of the camera with the performance as well as the cost of the

camera. The space utility of each cell on the 2D grid map

is expressed in a numerical value based on the amount of

movement of an agent in a specified area of the 2D grid map

and a probabilixty that the agent moves from a starting point

to a destination.

In this paper, a greedy algorithm is used to select locations

at which cameras are to be placed. Using the greedy algorithm,

a priority area is extracted from the space priority contained in

the area attribute of space modeling and path obtained using

an agent path-finding algorithm. Then camera locations are

selected in the extracted priority area. Through the greedystrategy, all coordination of points on a space model are

examined to find a coordination of points that has a highest

utility in the FOV of a camera.

The utility of visibility is set to a maximum value that can

be obtained at a specified coordination of point on a grid map

among sums of space utility values of cells within a virtual

FOV of a camera for all directions and angles. That is, the

utility of visibility is calculated based on the maximum space

utility coverage that is obtained at the position of a specified

cell on a grid map.

From all cells on the utility map of visibility, cells in which

a camera is to be placed are selected in order of highest to

lowest utility of visibility of the camera. Then, a predeterminedrange from the position of a selected cell on the utility map of

visibility is reconfigured upon the installation of the camera.

If cameras cover all space priorities updated on the priority

layer of an input space in its FOV, the placement of the

camera is completed. However, the method based on space

utility coverage does not ensure the optimal placement of the

camera. Thus, we considered (1) a placement cost limit and

(2) minimum coverage of the observable space to determine

the optimal number of cameras to be placed. The placement

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Fig. 2. Experimental environments and a simulation application

cost limit is the maximum cost when a maximum number of

cameras is placed which does not exceed the placement cost

limit. The minimum space coverage is ratio of the observable

space to the overall space when a minimum number of cameras

is placed which satisfies the minimum space utility coverage.

The number of cameras to be placed may be calculated based

on resources or the range of an area that can be monitored by

a camera as summarized in Algorithm 1.

Algorithm 1 Camera placement algorithm

1) Create the utility map of visibility based on the greedy

strategy by the cost of a camera and space coverage of

the FOV of a camera in the entire map space.

2) Select a point having a highest utility of visibility value

on the utility map of visibility.

3) Place the camera at the selected point and update a

camera placement list.

4) Terminate camera placement when it is determined that

an optimal number of cameras has been placed.

5) Recalculate the utility of visibility around the positionof the camera on the utility map of visibility.

6) Return to step 2.

V. SIMULATION RESULTS

A. Simulation Setup

In order to compare with simulation results and experimen-

tal results on level terrain (2-D), the experiments have been

conducted with one top-down camera installed in the fourth

floor. We used a layout of the building with base length 63

meter and height 40 meter. To input areas and regions, a

graphical user interface has been developed as shown in Figure

2.The utility of visibility varies depending upon the perfor-

mance as well as cost of the camera. In this paper, three types

of cameras are used to evaluate the camera placement method.

The viewing distance of the camera B is 1.5 times longer than

that of the camera A. The available angle of the camera A is

about 1.33 times greater than that of the camera B. Though

the viewing distance of the camera C is 2 times longer than

that of the camera A, the installation cost of camera C is 2.5

times larger than that of camera A.

(a) Trajectories extracted for 3 hours (b) Trajectories extracted for 6 hours

Fig. 3. Priority layer with trajectories

(a) Cost limit is 500 (b) Cost limit is 1000

(c) Cost limit is 1200 (d) Cost limit is 1500

Fig. 4. Camera positions that meet a camera installation cost limit set

Figure 3(a) and Figure 3(b) shows the priority layers withtrajectories that are extracted from the structure layer and the

area layer of the building for 3 hours and 6 hours, respectively.

As time goes on, it is obvious that the extracted trajectories

are represented by target motion paths taken through an area

of interest as shown in Figure 3.

B. Results

The camera placement algorithm using the greedy algorithm

calculates the utility of visibility as well as the utility of cost of

each type of camera in each cell on a grid map. The utility map

of visibility is continuously updated until an optimal member

of cameras to be placed is finally set.

Figure 4 shows camera placement positions and FOVsdepend on each camera installation cost limit set. In the figure,

it is optimal to install 6 A-type cameras, 5 C-type cameras,

15 A-type cameras, and 18 A-type cameras, when cost limits

are 500, 1000, 1200, 1500, respectively.

Figure 5 shows the space coverage until 20 cameras are

installed. As shown in Figure 5(a), as the number of installed

C-type cameras increases, coverage rate per camera is lower

than the others. The camera C is the most appropriate for

installation, when the number of camera is less than 5 cameras.

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The number of cameras

0 5 10 15 20

Spacecoverage

0.0

20.0x10 3

40.0x10 3

60.0x10 3

80.0x10 3

100.0x10 3

120.0x10 3

Camera A

Camera B

Camera C

(a) Space coverage


0 5 10 15 20

Spacecoverageratepercost

0

100

200

300

400

500

600

700

Camera A

Camera B

Camera C

(b) Space coverage rate per cost


0 5 10 15 20

Accumulatedspacecoveragerate(%)

0

20

40

60

80

100

Camera A

Camera B

Camera C

(c) Accumulated space coverage rate

Fig. 5. Space coverage

When the number of camera is more than 6 cameras and

less than 8 cameras, the camera C is the most appropriate

for installation. The camera A is the most appropriate for

installation when the number of camera is more than 9

cameras. As shown in Figure 5(b), the camera A has the

highest coverage rate per cost. Figure 5(c) shows accumulated

space utility coverage rate. When 20 cameras are installed,

coverage rates of the camera A, B, C are 85.74%, 96.69%,

99.87%, respectively. Although the coverage rate is 98.98%

when 14 C-type cameras are installed, the cost of the camera

C is the highest. Because cameras are selected in order of

highest to lowest utility of visibility of the camera, Figure5(c) shows the fastest rate of increase of coverage at first.

However, the rate of increase of coverage rate is continuing to

decline. For example, the coverage rate of the camera C falls

below 0.08% when the number of installed cameras is over

15.

Figure 6 shows the space utility coverage and the cost when

each type of camera is installed with the cost limit or the

minimum space coverage rate. When the cost limit is below

810 or over 1200, the camera A is the most appropriate for

installation as shown in Figure 6(a). The camera C is the most

appropriate for installation, when the cost limit is over 810

and below 1200. As shown in Figure 6(b), the camera C is

the most appropriate when the coverage rate is less than 54%.The camera A is the most appropriate when the coverage rate

is more than 54%.

VI . CONCLUSIONS

We have presented the camera placement with certain

task-specific constraints and the minimal camera setup cost,

assumptions defined as the performance of real-world cameras.

The camera placement method uses an agent which is modeled

and implemented using the A* algorithm to estimate the

Cost

500 600 700 800 900 1000 1100 1200 1300 1400 1500

Coverage

100x10 3

200x10 3

300x10 3

400x10 3

500x10 3

600x10 3

Camera A

Camera B

Camera C

(a) Space utility coverage

Coverage rate

20% 40% 60% 80%

Cost

0

200

400

600

800

1000

1200

1400

1600

Camera A

Camera B

Camera C

(b) Space utility coverage cost

Fig. 6. Space utility coverage and cost

trajectories of moving people. The camera placement method

determines appropriate camera positions and an appropriate

number of cameras to be installed in view of installation cost.

The number of cameras to be placed has been calculated

based on minimum camera placement cost and maximum

space coverage. We considered three types of camera and

sum of installation cost of each camera. It is essential to

deal with a combination of various types of cameras to

determine appropriate camera positions and an appropriatenumber of cameras. In the future, we will improve our method

to calculate overall utility of visibility considering various

types of camera by mixture.

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[3] U. M. Erdem and S. Sclaroff, Optimal placement of cameras infloorplans to satisfy task requirements and cost constraints, in In Proc.of OMNIVIS Workshop, 2004.

[4] R. Bodor, A. Drenner, P. Schrater, and N. Papanikolopoulos, Optimalcamera placement for automated surveillance tasks, Journal of Intelli-gent & Robotic Systems, vol. 50, pp. 257295, 2007.

[5] Y. Yao, C.-H. Chen, B. Abidi, D. Page, A. Koschan, and M. Abidi,Sensor planning for automated and persistent object tracking withmultiple cameras, in Computer Vision and Pattern Recognition, 2008.CVPR 2008. IEEE Conference on, 2008, pp. 1 8.

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[8] H. Topcuoglu, M. Ermis, and M. Sifyan, Positioning and utilizingsensors on a 3-d terrain part i - theory and modeling, Systems, Man,and Cybernetics, Part C: Applications and Reviews, IEEE Transactions

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