Achieving Full View Coverage with RandomlyDeployed Heterogeneous Camera Sensors
Yibo Wu, Xinbing Wang
Department of Electronic Engineering
Shanghai Jiao Tong University, China
1
Outline
Introduction
Definition & Model
Necessary Condition of Full View Coverage
Sufficient Condition of Full View Coverage
Evaluation & Conclusion
2
Introduction
Design issues of coverage problems:
 Sensor Model
 disk or cone
 boolean or attenuated
 static or mobile
 homogeneous or heterogeneous
 Coverage Type
 area or barrier coverage
 1- or k- coverage
 Deployment Method
 deterministic or random
 Target Area
 2D, 3D or others
 Network Connectivity
 1- or k- connectivity
3
Introduction
 [1] originated the analysis
framework of asymptotic
coverage, which supposed the
sensor number goes to infinity
(suitable for large-scale
networks).
 Coverage of a square region is
transferred to coverage of all the
grid points in it.
[1]S. Kumar, T. H. Lai and J. Balogh, “On k-coverage in a mostly sleeping sensor
networks,” in Proc. of ACM MobiCom 04, Philadelphia, Pennsylvania, USA, Sept. 26-Oct.
1, 2004.
4
Introduction
 [2] found out the critical conditions for strong barrier coverage
by applying bond percolation to the process of constructing
barriers.
 A square is covered if it has
a sensor.
 It's diagonal is thus called
"open".
 Consecutive open edges
form a barrier.
[2]B. Liu, O. Dousse, J. Wang and A. Saipulla, “Strong barrier coverage of wireless
sensor networks,” in Proc. of ACM MobiHoc 08, Hong Kong SAR, China, May 26-30,
2008.
5
Introduction
 For camera sensors, [3] proposed a new coverage type
named "full-view coverage", aiming to guarantee the capture
of the face image, and thus to raise the recognition probability.
 1-coverage
 k-coverage: fault tolerance
and image fusion
 full-view coverage: balanced
distribution of cameras
enables the capture of the
stickman's face
[3]Y. Wang and G. Cao, "On full-view coverage in camera sensor
networks",
in Proc. of IEEE INFOCOM 2011, Shanghai, China, April 10-15, 2011
6
Introduction
Motivation of this work:
 As network construction is quite consuming, it's essential for
operaters to know under what conditions (sensing parameters
and sensor number) could the target area be full view covered
ahead of actual deployment.
 The only result concerning the above question is in [3], but it's
in a complicated form and therefore provides limited insights.
 Our objective is to find a "concise" critical condition for full view
coverage. Namely, how sensing parameters and sensor
number should be to achieve full view coverage in an area.
7
Outline
Introduction
Definition & Model
Necessary Condition of Full View Coverage
Sufficient Condition of Full View Coverage
Evaluation & Conclusion
8
Defination & Model
 Sensor Model: Cameras in this
work are static boolean cones
with heterogeneous parameters.
 Important directions for sensor S
and object P.
 sensor's orientation:
where the lens are towards
 object's facing direction:
where the object looks at
 object's viewed direction:
which side of the object is
captured by the camera
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Defination & Model
 Description of heterogeneity
 Total n sensors are partitioned into u groups.
 Group y has cyn sensors, whose radius is ry and field of
view is φy.
 Sensing area:
 Weighted summation of sy:
 Critical sensing area is defined to help evaluate the
network. The overall requirements of heterogeneous
sensors are thus generalised to one single parameter.
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Defination & Model
 Target Area: The target area is a unit square.
 Deployment Method: Sensors are randomly and uniformly
dropped in the target area.
 Coverage type: Full view coverage is formally defined
below. Such coverage sets an upper bound for the angle
between an object's facing direction and viewed direction.
11
Introduction
Definition & Model
Necessary Condition of Full View Coverage
Sufficient Condition of Full View Coverage
Evaluation & Conclusion
12
Necessary Condition of Full View Coverage
 Thinking that critical condition is hard to find directly, we begin
with necessary condition, and obtain
 The proof can be decomposed into four steps A, B, C, D.
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Necessary Condition of Full View Coverage
 Step A: coverage of whole region
coverage of grid points
We need the grid to be
dense enough (m >= n log n)
to make the transfer valid.
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Necessary Condition of Full View Coverage
 Step B: find probability of covering one grid point P
 Construct a series of sectors
as the left figure shows.
 To achieve full view coverage,
each sector needs at least
one sensor covering P.
 The impact of Tα is proved to
be the same as the red sector
showed in the figure.
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Necessary Condition of Full View Coverage
 Step B: find the probability of covering one grid point P

: point P fails to meet the necessary condition.
 After some calculation we have
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Necessary Condition of Full View Coverage
 Step C: bound the probability of covering all grid points


: one point doesn't meet the necessary condition
: not all grid points meet the necessary condition
Area of the red circle
Area of the shaded region
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Necessary Condition of Full View Coverage
 Step C: bound the probability of covering all grid points
 Then we have
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Necessary Condition of Full View Coverage
 Step D: prove that
For
is the CSA for event
where ξ>0 ,
we prove
For
where q>1,
we prove
 The result will follow according to Definition 2.
19
Introduction
Definition & Model
Necessary Condition of Full View Coverage
Sufficient Condition of Full View Coverage
Evaluation & Conclusion
20
Sufficient Condition of Full View Coverage
 Similar as the situation in necessary condition, we have
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Sufficient Condition of Full View Coverage
 Only difference: probability of covering one grid point
 The central angle of the sectors is θ, instead of 2θ in the
necessary condition.
22
Introduction
Definition & Model
Necessary Condition of Full View Coverage
Sufficient Condition of Full View Coverage
Evaluation & Conclusion
23
Evaluation & Conclusion
 Decisive role of sensing area
 Requirements for network coverage lie on "sensing area"
sc(n), rather than sensing radius or field of view.
 It's an inherent feature of random and uniform deployment,
that coverage probability is propotional to the covering area
of a sensor.
 Sensors with different sensing radius or field of view will
behave similarly, if they own the same sensing area.
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Evaluation & Conclusion
 Gap between necessary and sufficient conditions
 In necessary condition full view coverage is not guaranteed
(orange direction is unsafe because β>θ).
 In sufficient condition there may be redundant sensors
(orange sensor S can be removed since β<2θ).
 Is there an exact critical condition?
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Evaluation & Conclusion
 Impact of θ and n

when n is fixed. This
result matches our intuition
since cameras are distributed in
a balanced form.
 When θ = 60o, we need 500
cameras whose sensing area is
more than 1/10 of the target
area to achieve full view
coverage.
 It's so demanding that turning
to deterministic deployment or
barrier coverage is a desired
step to make full view coverage
practical and economical.
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Thank you!
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