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Railway station surveillance system design:
a real application of an optimal coverage approach
Francesca De Cillisa, Stefano De Murob, Franco Fiumarab, Roberto
Setolaa, Antonio Sforzab and Claudio Sterleb
a UCBM b DIETI
c Ferrovie dello Stato Italiano
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Control devices location
How to optimize a video-surveillance system ?
Covering Models
Minimizing the number of
CCTVs/devices
Maximization of the coverage
area with a given number of
CCTVs/devices
Set Covering Problem (SCP)
Weighted Demand Covering Problem
(WCDP)
Maximal Covering Problem
(MCP)
Back-Up Covering Problem
(BCP)
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Visibility analysis and coverage matrix
Geometric Visibility Visibility and CCTV features
Coverage Matrix
Visibility and coverage analysis consists in determining which are the points of that can be controlled by a device positioned in a potential location with a certain orientation
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Area of interest and obstacles
• coverage angle (ɵ): angle (expressed in degrees, 0° ÷ 360°) within which the
device is active
• coverage ray (r): maximum distance (expressed in metres) to which the
device is still effective
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Physical visibility parameters
CCTV 1 – 90° R θ
θ R
R: 300
Θ: 90°
R: 650
Θ: 30° 4 non overlapping possible orientations
8 overlapping possible orientations
θ, coverage angle r, coverage ray
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Coverage Matrix
1 2 3 4 5 6 7 8 9 10
11 12 13 14 15 16 17 18 19 20 21 22
23 24 25 26 27 28 29 30 31 32 33 34
35 36 37 38 39 40 41 42 43 44 45 46
47 48 49 50 51 52 53 54 55 56
57 58 59 60 61 62 63 … … … … …
A
C D
B
E F
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 5
6
A 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
B 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
Coverage matrix
(any row corresponds to a feasible location/orientation)
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Sets and parameters: I set of points to be controlled
J set of potential device (CCTVs, sensors, etc.) locations
H set of the installation costs hj of the devices j Ni coverage matrix: set of devices j able to cover a point i, since the distance cij is
lower than or equal to the covering ray R of the device (j : cij ≤ R )
Variables: yj binary variable associated to a device location
The number of these variables is given by the product between
the possible locations and the used orientations for a device
1 a device is installed at the potential location j 0 otherwise
SCP model parameters and variables
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SCP model
Min z = ∑jJ yj
∑j Ni yj ≥ 1 i I
yj = (0,1) j J
Minimizing the number of devices to be installed
At least a device able to cover a point i has to be located
Integrality Constraints
Ni = { j : cij ≤ R } set of devices j able to cover a point i, such that the distance cij between a point i and a camera j is lower than or equal to the covering ray R
Min z = ∑jJ hj yj Minimizing the installation costs
or
Subject to
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MCP model parameters and variables
Sets and parameters: I set of points to be controlled
J set of potential device (CCTVs, sensors, etc.) locations
C coverage matrix: set of devices j able to cover a point i, since the distance cij is
lower than or equal to the covering ray R of the device (j : cij ≤ R ) p is the maximum number of devices to be installed
Variables: yj binary variable associated to a device location
xi binary variable associated to a point to be controlled i
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MCP model
Max z = ∑iI di xi
Subject to
∑j Ni yj ≥ xi i I
∑jJ yj = p j J
xi = (0,1) i I
yj = (0,1) j J
Coverage maximization
Impose that a point i is controlled just in case at least a device among the ones able to control it, Ni, is installed
Maximum number of devices to be installed
Binary constraints
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Case study – Fiumicino airport railway station
78 x 26,5 [m]
(grid 1 x 1 + border points)
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Points to be
covered
(1281)
Cameras possible
locations
(151 x 8 = 1208)
R = 17,5 or 25
m
= 90o
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Optimization results
R=25 ; Cameras: 8; Coverage: 98.17%
R=17,5 ; Cameras :8; Coverage: 75.70%
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Virtual blocks
276 x 26.5 [m]
3 platforms
(584 x 8 = 4627) x 2184
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Optimization results
R=50 ; Cameras: 21; Coverage: 98.37%
R=50 ; Cameras: 21; Coverage: 83,59%
