diffusion. This attenuation increases along time and
is more significant for higher frequencies.
Therefore, by controlling ∆t we can obtain infor-
mation at different bands of spatial frequencies. Con-
sider the simplest case, a lowpass filter. We can spec-
ify a maximum attenuation for the passband α
P
, with
a cut-off spatial frequency of |k
P
|. At the same time,
for the stopband, a minimum attenuation α
S
is re-
quired starting at frequency |k
S
|. Then, the period of
time after which the linear diffusion must be stopped
in order to carry out the so defined filtering is between
these two bonds:
|ln(1− α
S
)|
8π
2
D|k
S
|
2
≤ ∆t ≤
|ln(1− α
P
)|
8π
2
D|k
P
|
2
(6)
Then, providing the means for storing and com-
bining two consecutive samples of the diffused im-
age, taken after ∆t
1
and ∆t
2
from the starting point of
the diffusion, we can compute a bandpass, a highpass
or a bandreject filter. Keep in mind, however, that the
highest frequency feature that can be consideredis de-
termined by the size of the pixel, and therefore a real
highpass filter is actually a bandpass filter.
A crucial property of the structure just defined is
that the diffusion operation is really a simple charge
redistribution which does not consume energy, i. e. it
is realized by a passive network. That is to say, the
signal processing within the structure just described
is massively parallel and ultra power-efficient.
4 AN APPLICATION TO SMOKE
DETECTION
As an application of the approach previously ex-
plained, we present a vision algorithm suitable for a
forest fire detection system based on a wireless vision
sensor network. The vision sensors will be placed on
top of poles in order to focus the canopy of small veg-
etation areas. Each sensor of the network will run
on-site a vision algorithm in order to detect smoke
arising among the vegetation. When a sensor detects
smoke, a warning message is sent to a control center
by multihopping. This structure of the system, based
on a careful placing of the sensors, reduces signifi-
cantly the sources of false alarms with respect to its
counterparts based on lookout towers with automatic
surveillance. On the contrary, because of the neces-
sary dense deployment of vision sensors, energy effi-
ciency is a key point impacting the system cost.
The smoke detection algorithm is based on the
analysis of the sequence of images captured by each
sensor. We define the time interval between two con-
secutively captured images as T
C
. These images are
comparedto a reference image, the background, in or-
der to detect changes generated by smoke dynamics.
This method of motion detection, called background
subtraction (Hu et al., 2004), is suitable for scenes
with a relatively static background. In the case of the
proposed system, the visual field is basically com-
posed of vegetation, and therefore the background
will hardly suffer significant sudden changes. It will
experience, however, gradual illumination changes
throughout the day. Taking this fact into account, the
reference image will be updated every time interval
T
R
.
Regarding the binning process, note that the ap-
pearance of smoke in any scene means the equaliza-
tion of the R, G and B components in the pixels af-
fected by smoke (Chen et al., 2006). Therefore, it
could be a criterion to detect candidate bins. How-
ever, we propose a more data-efficient option based
only on the detection of sudden increases in the B
component with respect to the background. The use
of the B component is owing to its greater sensitiv-
ity in natural scenarios with vegetation to the changes
generated by smoke when compared to the R and G
components and combined luminance. This will also
discard changes introduced by sources different than
smoke, like the motion of tree leaves.
Consider Fig. 3. We have highlighted different
zones in three scenes where the background is mainly
constituted by vegetation. These frames correspond
to different parts of the associated sequences, before
and after a trace of smoke has appeared in the field of
view. Table 1 shows the normalized average increase,
referred to the image without smoke, undergone by
each RGB component and the combined luminance
of the pixels within the marked zones in presence of
smoke. It can be seen that, in all cases, the appearance
of smoke amongvegetation conveysa greater increase
in the B component than that observed in the R and G
components and the combined luminance.
Therefore, each bin will be represented by the av-
erage value of the B component of its pixels. In terms
of spatial frequencies, it is equivalent to say that we
are interested in the information contained at k = 0.
The value of S
B
will depend on the average variation
in the number of smoke pixels during their appear-
ance in the scene: the less the average variation, the
smaller the necessary size of the bins to track the dy-
namics. Consider a sequence of k consecutive images
containing smoke captured by a sensor. The average
variation in the number of smoke pixels will be:
¯
V =
∑
k
i=1
| U
T
[i] −U
T
[i− 1] |
k
(7)
where U
T
[i] is the total number of smoke pixels of the
VISAPP 2009 - International Conference on Computer Vision Theory and Applications
310