2042 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 8, AUGUST 2010
Camera Scheduling and Energy Allocation
for Lifetime Maximization in User-Centric
Visual Sensor Networks
Chao Yu, Student Member, IEEE, and Gaurav Sharma, Senior Member, IEEE
Abstract—We explore camera scheduling and energy allocation
strategies for lifetime optimization in image sensor networks. For
the application scenarios that we consider, visual coverage over a
monitored region is obtained by deploying wireless, battery-pow-
ered image sensors. Each sensor camera provides coverage over
a part of the monitored region and a central processor coordi-
nates the sensors in order to gather required visual data. For the
purpose of maximizing the network operational lifetime, we con-
sider two problems in this setting: a)
camera scheduling, i.e., the
selection, among available possibilities, of a set of cameras pro-
viding the desired coverage at each time instance, and b) energy al-
location, i.e., the distribution of total available energy between the
camera sensor nodes. We model the network lifetime as a stochastic
random variable that depends upon the coverage geometry for the
sensors and the distribution of data requests over the monitored
region, two key characteristics that distinguish our problem from
other wireless sensor network applications. By suitably abstracting
this model of network lifetime and utilizing asymptotic analysis, we
propose lifetime-maximizing camera scheduling and energy allo-
cation strategies. The effectiveness of the proposed camera sched-
uling and energy allocation strategies is validated by simulations.
Index Terms—Camera scheduling, energy allocation, image
sensor networks, network lifetime, visual coverage.
I. INTRODUCTION
W
IRELESS visual/image sensor networks (VSN) have
recently evoked intense research interest due to the in-
creasing demand for applications such as security surveillance,
smart home care, and environment monitoring [3]–[6]. These
sensor networks provide visual coverage over a monitored
region by deploying portable wireless sensors with imaging,
signal processing, and communication capabilities. Because
the sensors are usually battery powered, power consumption
Manuscript received March 20, 2009; revised March 09, 2010. First pub-
lished March 29, 2010; current version published July 16, 2010. This work
was supported in part by the National Science Foundation under grant number
ECS-0428157. Parts of this work have been presented at Visual Communica-
tions and Image Processing (VCIP), January 2009, San Jose CA, and at the
IEEE International Conference on Image Processing (ICIP), November 2009,
Cairo, Egypt. The associate editor coordinating the review of this manuscript
and approving it for publication was Dr. Amy R. Reibman.
C. Yu is with the Department of Electrical and Computer Engineering, Uni-
versity of Rochester, Rochester, NY 14627 USA (e-mail: chyu@ece.rochester.
edu; devincyu@gmail.com).
G. Sharma is with the Electrical and Computer Engineering Department
and the Department of Biostatistics and Computational Biology, University of
Rochester, Rochester, NY 14627 USA (e-mail: gaurav.sharma@rochester.edu;
g.sharma@ieee.org).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIP.2010.2046794
imposes a critical constraint on the network lifetime of a VSN,
which is defined as the duration of effective visual coverage
over the monitored region. In this paper, we consider
user-cen-
tric application scenarios where only part of the visual data,
defined as the user’s “desired view,” is of interest at a given time
instant, though the desired view varies with time and thereby
involves the entire VSN. An example of such an application
scenario is a visual surveillance network [7], [8] deployed
for tracking and recording imagery of moving objects in a
monitored region [9], [10]. In this scenario, the series of image
requests arising from the object tracking can be modeled as a
series of virtual “user” requests. Another sample application
is a VSN deployed for tele-presence applications, where the
desired view corresponds directly to the users’ requested view
[11]. In these user-centric VSNs, the visual data of interest at
a given time instant overlaps the fields of view (FoVs) of a
number of cameras (sensors) and one may select among the
cameras providing the requested coverage. We refer to this
selection as the camera scheduling problem and investigate
camera scheduling strategies with a view to maximizing the
lifetime of the network. In some scenarios, the deployment
of the cameras is constrained, and the allocation of available
energy among these cameras can have a significant impact
on the network lifetime. We therefore also investigate energy
allocation to distribute the total available energy among the
sensor nodes. Our abstraction of the user-centric VSN setting
in terms of a time varying “desired view” allows us to focus on
the camera scheduling and energy allocation problems without
bringing in other application specific aspects of these VSNs,
which have a limited impact on these specific problems.
Camera scheduling and energy allocation in user-centric
VSNs are challenging because of two reasons. On the one
hand, meaningful definitions of lifetime for a VSN must take
into account the visual coverage provided by the network. On
the other hand, the stochastic nature of data requests needs to
be suitably addressed. The main contribution of this paper is a
stochastic formulation for the expected value for the network
lifetime addressing both of these aspects. Visual coverage
information of the network is incorporated into the formulation
of network lifetime, wherein the data requests are addition-
ally modeled as a random variable (r.v.) with a distribution
that is either known a priori or estimated from the record
of prior requests. Using an abstraction for this formulation,
we obtain expressions for the expected network lifetime and
develop computationally efficient approximations and suitable
lifetime-maximizing sensor scheduling strategies. Using the
1057-7149/$26.00 © 2010 IEEE
YU AND SHARMA: CAMERA SCHEDULING AND ENERGY ALLOCATION FOR LIFETIME MAXIMIZATION IN USER-CENTRIC VISUAL SENSOR NETWORKS 2043
Fig. 1. Target plane
R
is monitored by a VSN consists of cameras
fC g
.
C
covers a subregion
V
of the target plane. A central processor (CP) keeps record
of the energy distribution, coverage geometry of the network, and receives the
user requests. For each user’s desired view
U
, the CP selects a subset of cameras
to provide data and synthesizes the desired view
~
U
. No direct communication
is feasible between the cameras. The intensity of subregions indicates coverage
information: regions covered by more cameras appear darker.
same analysis, the energy allocation problem is formulated as
a max-min optimization problem that aims to maximize the
duration of coverage for the most critical part of the monitored
region for which the available energy is the least. By trans-
forming the min-max optimization into an equivalent linear
programming (LP) problem, we present a computationally
efficient solution for the energy allocation problem.
Strategies for optimizing network lifetime in generic wireless
sensor networks (WSNs) have been previously considered in the
literature [12]–[15]. The coverage model for VSNs, however, is
drastically different from the common WSN model of circular
coverage centered at the sensor. For instance, physically adja-
cent cameras in a VSN may have completely nonoverlapping
FoVs. Second, in typical uses of VSNs, only a subset of the data
is of interest, e.g., in a surveillance network, coverage may only
be desired for the moving objects. The analysis of lifetime in
user centric VSNs must therefore consider stochastic data re-
quests, which are typically absent in conventional WSNs. In the
context of a VSN, [16] addresses the problem of optimal assign-
ment of cameras to monitor subregions of a monitored area in
order to maximize the lifetime of the camera network. However,
user interactions are not considered. To account for user inter-
actions, [17] proposes a heuristic approach for camera sched-
uling by defining a cost function associated with each camera
depending upon the remaining energy of the camera and the cov-
erage geometry. In this paper, we extend and complement this
prior work by developing a mathematical model that leads to
analysis and simulation results which provide additional insight.
Though our formulation is valid for several classes of VSNs,
for concrete discussion, here we consider an application sce-
nario illustrated in Fig. 1, where image sensors are deployed to
provide visual coverage over a monitored region. The network
allows users to navigate around the monitored region by spec-
TABLE I
L
IST OF SYMBOLS
ifying a desired viewpoint (position and direction) that varies
over time. The user’s viewpoint determines the part of the scene
that should be captured and transmitted to the user. The desired
view at the viewpoint is synthesized at a central processor (CP)
by combining parts of the image sent from selected cameras.
This paper is organized as follows. Section II presents a
stochastic formulation for the expected network lifetime in a
user-centric VSN and formulates the optimal camera sched-
uling strategy to maximize network lifetime. In Section III, we
provide an abstraction of the problem, and present exact, ap-
proximate, and asymptotic analysis for estimating the network
lifetime. A lifetime-maximizing camera selection strategy is
developed in Section IV. We next propose our energy alloca-
tion strategy in Section V for maximizing the approximated
lifetime. Detailed implementation of the application scenario
is described in Section VI. Finally, we describe simulation
setup and results in Section VII and conclude the paper in
Section VIII. For readers’ convenience, a list of symbols is
included as Table I.
II. P
ROBLEM
FORMULATION
We consider the network as illustrated in Fig. 1. For sim-
plicity, the monitored region is assumed to be a planar surface,
a situation that may occur for aerial surveillance where the
scene can be well approximated by a 2-D plane when viewed
at a large distance. The target plane
is monitored by cam-
eras
. Each camera has a battery with energy and
covers a subregion of
denoted by . We uniformly divide
into blocks, represented by where rep-
resents the set
. We represent the coverage
geometry of these cameras in terms of this discretized represen-
tation, and define a coverage matrix
as
(1)
where subscripts
respectively denotes the row and column
index of the matrix and
indicates region(set) lies
within region(set)
, we also use to represent the indicator
function
if is true
otherwise.
2044 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 8, AUGUST 2010
Fig. 2. Discretization of the target plane
R
and desired view
U
. Camera views
fV g
are similarly discretized. The texture image on
R
is used in our
simulations.
The subset of cameras that cover block is represented by
(2)
The user specifies a desired viewpoint and accordingly a de-
sired view
on the target plane . This desired view is
also uniformly divided into
blocks, represented by
. The discretization of and is illustrated in Fig. 2. The
coverage geometry of
is similarly defined as (1) by a coverage
matrix
, where
(3)
and the subset of cameras that cover the block
is denoted by
(4)
The discretization of
, yields suboptimality, finer dis-
cretization results in better performance at the expense of
higher computational load. Also note that we consider uniform
discretization for ease of description. Alternatively,
, can be
divided according to different levels of intersections between
,
and . We assume the coverage geometry represented
by
is known.
1
The network provides the user-desired view in a block-by-
block manner. For each block
in the desired view,
the CP selects a camera
satisfying the coverage requirement,
i.e., having
, to transmit relevant data to the CP where
an synthesized view
is generated. We assume the energy re-
quired in order to transmit each block
to the CP is equal for
all
.
We assume each block
, on the monitored plane
is requested by the user independently throughout the operation
of the network and the probability that the block
is requested
is given by
, where . Let denote the energy
of camera
at time . The remaining lifetime of the network,
denoted by
, at time is a r.v. with a probability mass function
(p.m.f) determined by
(note we consider as a
discrete r.v. in this paper), where
1
Section VI describes a practical approach to determine
B
;
B
in the VSN
we consider.
represents the probability distribution (p.m.f.) of users’ requests
and
denotes the energy distribution, i.e., is the energy at the th
camera node at time
. We denote by the expec-
tation of
, where denotes the expectation operator. At time
, if camera is selected to record and transmit data, is up-
dated to
. The optimal camera selection strategy at time
is defined as the strategy that maximizes the expected remaining
lifetime of the network with respect to the updated energy, i.e.,
.
We next map the energies of the cameras onto the monitored
region and define the coverage energy of a block
as the sum
of the energies of all the cameras that cover
. To this end, we
define
(5)
thus,
and the th entry represents the cov-
erage energy of
at time . Specifically, the coverage
energy of
becomes zero when for all cameras
. We refer to the coverage energy of a block as
the energy of the block for brevity.
In order to obtain a useful and tractable formulation of our
problem, we approximate the remaining lifetime as a function
of
. Note that in this process, we have collapsed the
dependency of
on the two parameters i.e., the updated camera
energies
at time and the coverage matrix into the
single parameter
. In this process, we are neglecting the
fact that the change in the energy of the selected camera
will
in fact change the energy distribution not only over the block
being requested, which we shall account for, but also over the
other blocks for which
provides coverage. Since the param-
eters
are updated afresh at each time step by utilizing
(5), scheduling based upon this approximation does not cause a
serious compromise in optimality. Now if block
is requested
at time
, the optimal camera selection strategy is to select a
camera from
so that the network has maximum expected
lifetime with the updated energy allocation. Mathematically, the
optimal camera index is given by
(6)
In order to obtain a solution for (6), we proceed by analyzing
the expected network lifetime in(6).
III. E
XPECTED NETWORK LIFETIME
Fig. 3 illustrates an abstraction of the sensor scheduling
problem: Consider
boxes respectively
containing
balls. At each (discrete) time
instant, a ball is requested from one of these boxes where the
probability of the request from
is for some
and . We are concerned with the number of
requests
after which one of these boxes first becomes empty.
This abstraction models our scheduling problem of (6) where
corresponds to the number of blocks in the monitored
region,
represents the updated
YU AND SHARMA: CAMERA SCHEDULING AND ENERGY ALLOCATION FOR LIFETIME MAXIMIZATION IN USER-CENTRIC VISUAL SENSOR NETWORKS 2045
Fig. 3. Abstracted representation of the network lifetime.
M
boxes
B
(
i
2
[
M
])
contains
m
balls respectively. At each request, a ball is taken from
B
with probability
p
. After
L
requests, one of these boxes first become empty.
[
L
]
corresponds to the expected network lifetime.
block-wise coverage energy when camera is selected,
represent the probabilities with
which the blocks are requested (as before) and
denotes the
remaining lifetime. For the camera scheduling problem,
may
also be dynamically estimated during the network operation.
For notational simplicity, we drop the superscript
in our
discussion, and write the expectation
as .
For a simplistic scenario where
, the distribution for
and the expectation are obtained analytically in Propo-
sition 1. In the general case that
, we present a recursive
approach to exactly evaluate
in Proposition 2. The com-
putational load of this recursive approach is prohibitive as
increases, motivating us to investigate efficient approximations
of
in Proposition 3 and its asymptotic behavior in Proposi-
tion 4. Based upon the asymptotic analysis of
, we develop
our camera scheduling and energy allocation strategies which
maximizes the expected network lifetime. The proofs for Propo-
sitions 1–4 can be found in Appendices I–IV, respectively.
Let
denote the p.m.f of a negative binomial distri-
bution [18] which characterizes the number of failed Bernoulli
trails prior to
successful trails. Specifically, repre-
sents the probability that in
Bernoulli trials, are failures
and the other
, including the last trial, are successful, where the
probability of each trial being successful is
. Using this nota-
tion, we obtain the following proposition.
Proposition 1: For
, the p.m.f of can be written as
(7), shown at the bottom of the page, where
and denote
the probabilities
and , respectively. The expectation of
can be obtained as
(8)
where
for (9)
(10)
(11)
where represents the corresponding cumulative dis-
tribution function (c.d.f) of the negative binomial distribution.
Also note
is characterized as a regularized incom-
plete beta function [19], which along with the p.m.f
,
is available in standard scientific software packages. Thus,
can be directly evaluated using (8).
We next consider the case where
and obtain a re-
cursion for the p.m.f of
proceeding as follows. We consider
a sequence of
experiments, where in the th experiment
only the first boxes are utilized in
the experiment, with a ball requested from the
th box with nor-
malized probability
. In the th experiment,
let
denote the number of requests after which one of the
boxes
first becomes empty, then immediately we see
. The following proposition allows us to recursively
calculate the p.m.f of
from the p.m.f of .
Proposition 2: See equation (12) at the bottom of the page.
where
denotes the vector , and
(13)
represents the maximum possible value of
.
By observing that , it can be veri-
fied that (7) is a special case of (12). The expected network life-
time
can be directly calculated
using the p.m.f of
. However, in order to obtain the p.m.f of
(7)
(12)
2046 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 19, NO. 8, AUGUST 2010
, the p.m.f of has to be recursively cal-
culated, therefore, the computational load becomes prohibitive
as
increases, especially when the values in the vector are
large.
In order to obtain an efficient approximation of
for the
general case
, we present an alternative representation
of
in terms of the c.d.f of a multinomial distribution. Let
denotes the c.d.f of a multinomial distribution, and
denotes the p.m.f. of this multinomial distribution
for non-negative integer-valued vector which satisfies
, where represents number of different pos-
sible results of a trail,
is the total number of trails, and
represents probabilities of each pos-
sible result, and
denotes the total number of the th result
out of
trials.
Proposition 3: The expectation of
can be represented as
(14)
where
is defined in (13), denotes an vector, each
of whose entries is unity.
Equation (14) allows direct evaluation of without recur-
sively calculating the p.m.f of
. Furthermore, has
an accurate approximation which can be relatively efficiently
evaluated using the method in [20]. We thus obtain an approx-
imation of
as
(15)
where
denotes approximation of as described in [20].
The accuracy of the approximation based upon (15) is consid-
ered in Table II, where the results indicate that the proposed ap-
proximation of (15) is accurate. The computational advantage
of the approximation can be seen via an example for
,
for all , and uniformly generated
, normalized to have unit sum. In this case, calculating the
approximate network lifetime using (15) takes 1.4 s, while ob-
taining the exact value using the recursion (12) requires 107.7 s.
2
2
Both simulations are implemented in Matlab™, and executed on a work-
station with an Intel Pentium(R) IV 3.0 GHz CPU and 1 GB memory, other
simulations are run on the same platform.
TABLE II
E
XPERIMENTAL
EVALUATION OF THE
APPROXIMATION FOR
(14) USING
[20]. T
HREE BOXES
CONTAIN
(
m; m;
2
m
)
BALLS
RESPECTIVELY. THE
PROBABILITIES THAT A
BALL
BEING REQUESTED
FROM ONE OF
THESE
BOXES ARE
CORRESPONDINGLY
(
0
:
25
;
0
:
25
;
0
:
5)
. E
XACT:
THE EXACT
LIFETIME CALCULATED BY
EXHAUSTIVELY
CALCULATING THE C
.D.F
OF THE
MULTINOMIAL DISTRIBUTION IN
(14). APPROX:A
PPROXIMATE
LIFETIME USING
(15). S
IMULATION: THE
AVERAGE LIFETIME
RESULTING
FROM 200 M
ONTE CARLO
SIMULATIONS
However, (15) still requires considerable computation, and
it is not immediately clear how to develop a camera selection
strategy based upon(15). To this end, we proceed to investigate
the asymptotic behavior of
when is sufficiently large.
Proposition 4: For
and sufficiently large,
(16) holds (see bottom of the page), where
denotes the
probability density function (p.d.f) of a Gaussian distribution,
i.e.,
We experimentally evaluate the accuracy of (16) and illustrate
the results in Fig. 4. The result is measured by the relative error,
which is defined as
where is the (approximate) exact value obtained from (15)
and
is the asymptotic approximation using (16). We ob-
serve from Fig. 4 that (16) achieves high accuracy, the rela-
tive error converges to 0 at an exponential rate as the number
of balls increases. In particular, we observe from Fig. 4(b) that
in the case
, the refined approximation in
(16) achieves high accuracy, however, the simple approxima-
tion
, represented by the curve labeled
by
in Fig. 4(a), also achieves satisfactory accuracy (1%
relative error) for this case where
. This
observation leads us to propose the following approximation for
the general cases where
(17)
Following analysis similar to Appendix IV, it can be seen that
approximation using (17) is close and the relative error
reduces at an exponential rate as increase, provided is
sufficiently large and the difference between the two smallest
values in
is not negligible. We proceed to
propose and experimentally evaluate camera selection strategies
based upon this approximation.
if
if
(16)
