belonging probability inverse image approach for forest fire detection

Belonging probability inverse image approach for forestfire detection

Souleyman Benkraouda, Benabdellah Yagoubi*, Mustapha Rebhi and AhmedBouzianeLaboratoire Electromagn�etisme et Optique guid�ee., Laboratoire Signaux et Syst�emes., D�epartement G�enie Electrique., Facult�e des sciences et sciencesde l’ing�enieur., Universit�e de Abd El Hamid Ibn Badis, Mostaganem, 27000, Algeria

Abstract

We present a method for early forest fire detection from a

satellite image using the belonging probability matrix

image. We have considered each satellite image matrix line

as a realization of a nonstationary random process in the

thermal infra-red (TIR) spectral band and then divided each

line into very small stationary and ergodic intervals to

obtain an adequate mathematical model. Furthermore, the

pixels of the satellite image are considered to be statistically

independent; thus, any small interval of each line behaves,

naturally, as a Gaussian stationary noise. In this work, we

have, therefore, selected the latter as a mathematical model

formodelling these intervals of a satellite imagewithout fire,

and then, we have determined the parameters of this

Gaussian realization. So, when a fire occurs in this forest

zone, we can use these parameters to calculate its belonging

probability to the original image without fire. This proba-

bility should be very small because the fire, in any forest, can

be considered as a rare event. As a consequence, we have

presented a matrix image of the probability inverse of each

interval for a better fire detection observation.

Key words: belonging probability matrix image, forest fire,

satellite image, thermal infra-red spectral band

R�esum�e

Nous pr�esentons une m�ethode de d�etection pr�ecoce des

feux de forets par image satellite en utilisant l’image

matricielle de la probabilit�e d’appartenance. Nous avons

consid�er�e chaque ligne matricielle de l’image satellite

comme une r�ealisation d’un processus al�eatoire non

stationnaire dans la bande spectrale TIR (Thermal Infra-

Rouge), puis divis�e chaque ligne en tr�es petits intervalles

stationnaires et ergodiques, afin d’obtenir un mod�ele

math�ematique ad�equat. Ensuite, les pixels de l’image

satellite sont consid�er�es comme statistiquement ind�epen-

dants, et donc chaque petit intervalle de chaque ligne se

comporte, naturellement, comme un bruit gaussien sta-

tionnaire. Dans ce travail, nous avons donc s�electionn�e ce

dernier comme mod�ele math�ematique pour mod�eliser ces

intervalles d’une image satellite sans feu et nous avons

d�etermin�e les param�etres de cette r�ealisation gaussienne.

Ainsi, lorsqu’un feu survient dans cette zone de foret, nous

pouvons utiliser ces param�etres pour calculer sa probab-

ilit�e d’appartenance �a l’image originale sans feu. Cette

probabilit�e doit etre tr�es faible puisque le feu, dans toute

foret, peut etre consid�er�e comme un �ev�enement rare. Par

cons�equent, nous pr�esentons une image matricielle de

l’inverse de la probabilit�e de chaque intervalle pour une

meilleure observation de d�etection des feux.

Introduction

Forest fire is one of the most important factors that affect the

earth ecosystem and contribute to the global warming. Its

early detection is, therefore, very important to limit any

further damage. Early detection is usually performed by

surveillance either by human observers located at different

places in the forest or by video systems. These kinds of

surveillances are, however, not always efficient. Alternative

surveillances which can be performed by satellite were,

therefore, proposed. In this case, many different methods,

mostly based on radiometric analysis of the satellite image

in the thermal infra-red (TIR) spectral domain (Den Breejen

et al., 1998, pp. 517–532), have been suggested to improve

its early detection. Analysing directly the visual TIR satellite

image does not, however, provide always good results. This*Correspondence: E-mail: [email protected]

© 2013 John Wiley & Sons Ltd, Afr. J. Ecol., 52, 363–369 363

is due to the fact that the image observation accuracy may

be degraded by the clouds and humidity in many damp

regions of the world, whereas in dry regions, such as in the

north of Africa, the accuracy should be less degraded.

To detect forest fires, many algorithms based on statis-

tical methodology and random fields have been suggested.

Among them, worthy of mention are those suggested by

Lafarge et al. (2007a,b).

Despite the interesting results provided by such algo-

rithms, difficulties in their implementation and processing

hampering the performance may be found in each of them.

Therefore, we suggest in this work a method based on the

belonging probability of a rare event to a Gaussian

realization based on simple matrix line segmentation

instead of a Gaussian field realization. As it is well known,

in any problem of modelling, the choice of the model is a

very important task. So it is important for the images to be

characterized by a mathematical model to carry out any

kind of processing. The image can be modelled by a classic

monodimensional model, and consequently, we can use all

the tools and the mathematical analysis techniques of the

monodimensional signals which are well developed in the

literature. This mode of representation has been applied for

the line-by-line processing of the images, in particular for

the coding, the filtering and the storage (Zhong & Sclaro,

2003, pp. 44–50). In the first place, we selected a type of

model with reasonable results that can be applied to a

possible large number of images. After many tests on

several types of models, we have decided to choose the

Gaussian model, mainly because of its simple computing

and the good results obtained. This is basically a conse-

quence of the central limit theorem, which is one of the

most important concepts in statistics and probability. In its

simplest form, this theorem applied to a natural image,

indicating that the pixels’ intensity becomes normally

distributed as more and more pixels are observed. In the

following, we start our discussion by a highlight on

random processes and how they are used for the image

analysis and then apply them to a satellite image, and to

show, particularly, how to detect fires from the image of

the inverse of the belonging probability. In our case, we

apply a Gaussian stationary noise, which is a stationary

random process with noncorrelated samples.

Material and methods

The image shown in Fig. 1 with fire occurred in Californian

forest zone in July 2006 is provided by the Landsat7 polar

orbiting satellite in the TIR spectral band range 10.4–

12.5 lm and is being used for assessing the applicability of

our suggested method to forest fire detection. This image

was acquired at night with a resolution of 60 9 60 m and

showing the wildfires in the short wavelength infra-red

(SWIR) bands, whereas the terrain is visible only in the TIR

band. The software used to perform the image processing is

the image toolbox of Scilab5.3.3, INRIA, Scalay (Paris,

France) which is free software.

The proposed method for forest fire detection is described

as follows:

1 Determine the mean value M of the entire image matrix

of the forest region of interest without fire.

2 Segment each line of this matrix into small stationary

patches and compute their variances using thewholematrix

mean value M to model each interval as a Gaussian model.

3 Consider any pixel with intensity below 70% of the

maximum intensity to be equal 99%M to avoid false alarm.

4 When a fire takes place in this zone, use these previously

estimated Gaussian parameters for the image without a fire

to calculate the inverse of the belonging probability of each

interval to belong to this region of interest with a fire.

5 Arrange the inverses of these probabilities in a matrix

form as their corresponding intervals to observe them as

an image for a quick detection.

Results and discussion

We first survey the segmentation of a random process,

which motivated the use of a Gaussian stationary noise

Fig 1 Thermal infra-red satellite image of forest with fires

(California, U.S.A.). Available at http://landsat.usgs.gov/gal-

lery_view.php?category=nocategory&thesort=pictureId

© 2013 John Wiley & Sons Ltd, Afr. J. Ecol., 52, 363–369

364 S. Benkraouda et al.

model to represent any small interval of each satellite

image matrix line. This Gaussian stationary noise is

deemed a particular case of a random process, which is

reviewed in the following section.

Random process

By repeating a same experiment infinitely in time, we

obtain an infinite number of random curves representing

this experiment. These curves represent a random process

evolution in time. The auto-correlation is, usually, used to

compare two states of the same process; its value indicates

how much two states at different instants of a process are

correlated. For the random process, the auto-correlation is

calculated by the inner product in Hilbert space using the

mathematical expectation (Scharf, 1991; Krabs, 1995;

Hwang & Brown, 1997; Kay, 1998; Yagoubi, 2011) as

follows:

/Xði; jÞ ¼ E½Xi � Xj� (1)

where Xi and Xj are two vectors of the process at two

different instants i and j. If the elements of any parallel

diagonal to the principle of the auto-correlation matrix are

different, then the process is nonstationary. An example of

a nonstationary process may be represented by the curves

(o,., *, and +) of Fig. 2. We can see that the process in the

intervals [0, 25] and [25, 50] do not look the same; hence,

the auto-correlation is not constant for the intervals with

the same length. However, if we focus on a small space or

on a small interval such as [20, 25] and [45, 50] of the

same process, then the curves may not vary too much and

thus the auto-correlation could be considered as approx-

imately constant for the same small intervals. It is possible,

therefore, to divide the process into many small stationary

intervals. Furthermore, the smaller these intervals, the

more stationary and ergodic they will be, because their

mean value calculated vertically can be the same as that

obtained horizontally on any curve in these intervals. This

mean value that can be calculated by the mathematical

expectation is, therefore, almost constant E[Xi] = cte = mx.

If, in addition, the ergodic process samples are indepen-

dent, as those of the satellite image, then each small

interval of any image matrix line behaves as a stationary

noise and can thus be described by the following auto-

correlation relation in Hilbert space:

/wði; jÞ ¼ r2dij (2)

in which r2 is the constant representing the process

variance or its power spectral density and dij is the unit

sample.

Image modelling method

Toobtain themathematicalmodel (Bracewell, 2003; Zang&

Sommer, 2007) for the original image without fire (Fig. 3),

we have segmented each matrix line into small stationary

intervals. To represent each of these intervals by a Gaussian

stationary noise (Rice, 1945; Hida &Hitsuda, 1993; Chan &

Fig 2 Nonstationary random process. Intervals [20, 25] and [45,

50] are smaller enough to be considered as stationary Fig 3 Real satellite image of forest without fires


Forest fire detection method 365

Zhou, 2010; Chang & Liu, 2010; Nakamori, 2010) as

described above, we have computed the Gaussian param-

eters the mean min and the variance r2in for each resulting

interval using the following expressions, respectively:

min ¼ 1

L

Xl�1

k¼l�L

xinðkÞ (3)

r2in ¼1

L

Xl�1

k¼l�L

ðxinðkÞ � minÞ2 (4)

where xi (l � L),…,xi (l � 1) are the values of the nth

(n = 1,2…N) interval of the ith (i = 1,2…I) image matrix

line, L is the interval length and l = n.L. In our case, the

intensity of the pixels representing the forest is roughly

uniformly distributed in the image without fire, and hence,

any pixel value, sufficiently deviated from the image

matrix mean value, can be considered as a rare event. This

matrix mean value is deemed the intensity threshold away

from which any pixel behaves as a rare event. Two

symmetrical pixels (hot and cold) with respect to this

matrix mean value have, however, the same Gaussian

probability. It is, therefore, important to fix a threshold

70% of the maximum grey level, below which all the pixels

are considered to be equal to 99% of the matrix mean

value to filter (illuminate) the cold zones and to avoid false

alarm. So, instead of computing the average for each

segment using Eq. 3, we calculate the whole matrix mean

value using the following expression of the image mean

value and consider it as the average for every segment.

M ¼ 1

I:J

XIi¼1

XJj¼1

xði; jÞ (5)

where x(i,j) denotes the (i,j) pixel intensity. Substituting (5)

for min in the expression (4) of the estimated variance for

each segment, we obtain

r2in ¼1

L

Xl�1

k¼l�L

ðxinðkÞ �MÞ2 (6)

The choice of the number N of intervals of each matrix line

depends on the quality of the reconstructed image (Fig. 4);

for higher N, we obtain a good representation for the

original image.

An original satellite image without fire is shown in Fig. 3,

and its corresponding reconstructed image using the

Gaussian model in Fig. 5. To show the accuracy of this

model, we have plotted three arbitrary original lines and

their corresponding reconstructed versions in Fig. 4. Once

the adequate Gaussian model of the image without fire has

been obtained, we save its parameters; variances andmeans

for each interval. These parameters, which characterize

Fig 4 Original (solid line) and reconstructed lines 3, 250 and 500, from top to bottom



the image, will be used in the following to calculate the

Gaussian belonging probability of any rare event to,

eventually, belong to this image.

The belonging probability method for the fire detection

The same forest zone (California (U.S.A.) [12]), as that of

the image given in Fig. 3 but with fire, is shown in Fig. 1,

and the image of the inverse of the belonging probability

image of these fires corresponding to the Gaussian reali-

zation is given in Fig. 6. It is shown in the latter that the

isolated spot on the right of the belonging probability

image and corresponding to the smallest fire detected by

our method is about two pixels. Because the landsat7

resolution is 60 9 60 m, the size of the smallest forest fire

that can be detected, using our algorithm, could be

<3600 9 2 = 7200 m2.

Because any starting fire is deemed a rare event in any

forest, its probability is typically smaller than that of the

background of the satellite image of a forest. The matrix X,

with I = 1200 lines and J = N.L = 1200 columns of the

image with fires, may be represented as follows:

X ¼

x1ð0Þx1ð1Þ � � � x1ðL� 1Þ|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}Lsamples

� � � x1ðN:L� 1Þ

x2ð0Þx2ð1Þ � � � x2ðN:L� 1Þ...

xIð0ÞxIð1Þ � � � xIðN:L� 1Þ

2666664

3777775

So, when a fire takes place in the same location of the

image without a fire, we can use the Gaussian parameters

previously estimated from the image without fire to

calculate the belonging probability of the intervals of the

above image matrix X to detect this fire. The Gaussian

probability pin of each stationary and ergodic interval with

statistically independent samples is given by the following

expression, which is, usually, applied to random and

statistically independent Gaussian variables:

pinðxiðl� LÞ; ; � � � ; xiðl� 1Þ; r2in;MÞ

¼ 1

rinffiffiffiffiffiffi2p

p� �L Yl�1

k¼l�L

exp �ðxiðkÞ �MÞ22r2in

!(7)

where r2in and M are, respectively, the variance and the

image matrix mean value already estimated from the

image without fires. So, instead of the probability pin, we

have rather calculated its inverse 1pin

using Eq. 7 of the

belonging probability pin of each interval n and arranged

them in a matrix form as their corresponding intervals of

the image matrix X with fires, as follows:

1

P¼

1p11

1p12

� � � 1p1N

1p21

1p22

� � � 1p2N

..

.

1pI1

1pI2

� � � 1pIN

266664

377775

This procedure, for visualizing early forest fire detection,

allows the smaller values of the probabilities to appear with

Fig 5 Reconstructed satellite image model without fires

Fig 6 Image of the inverse of the belonging probability



higher intensity in the inverse of the belonging probability

matrix 1P image as shown in Fig. 6.

The good quality of the reconstructed image, obtained in

Fig. 5 with N = 300 intervals in each matrix line, after

many tests, indicates that the inverse of the belonging

probability shown in Fig. 6 is more accurate, and thus, it

has, approximately, the same spatial intensity distribution

as the real image in Fig. 1. This accuracy can be, further,

clarified by the mean square error (MSE) results between

the original and the reconstructed lines. The MSE values

are about 0.5 9 10�4, 0.8 9 10�4 and 10�4 for lines 3,

250 and 500, respectively. The plot of these three

reconstructed lines and their corresponding original ones

shown in Fig. 4, indicating that they are almost discon-

certed, which is a fairly firm indication that the Gaussian

parameters are highly well estimated. This belonging

probability procedure allows only the fires to appear in

Fig. 6, and the rest of the background remains dark. In

comparing the real image with fires (Fig. 1) to that of the

belonging probability (Fig. 6), we can say that the

advantage of using the belonging probability for fire

detection is that we can easily identify early fires in the

dark background as indicated by the small spot on the

right of the image (Fig. 6), while it is slightly confusing

and difficult to distinguish them from the background of

the real image (Fig. 1). Both the real satellite image and

the belonging probability image can be, furthermore, used

to reduce the probability of false alarm (Ollero et al., 1999,

pp. 123–131).

Although this study concerns Californian zone due to

the availability of the satellite image, we believe that our

forest fire detection method is well suitable to the North

African environment because it is very much similar to the

Californian environment. To cope with more diverse

vegetation communities, the Gaussian model used for

our forest fire detection method requires parameters

updating as well as adjustments in the thresholds to

accommodate other grasslands which are not, eventually,

similar to the Californian zone studied in this work.

Conclusion

We have estimated the belonging probability inverses of

the Gaussian stationary processes representing the real

satellite image and set them in an image form so that the

rare events, such as the fires, appear with higher intensity.

This procedure, for observing early forest fire detection,

can be, therefore, a good support to the direct observation

of the real satellite image. For forest fire detection, we

usually compare the image of a region of interest without

fire to the same one after a fire takes place. However, a

particular advantage of our method over this one is that

instead of restoring the whole image (1200 9 1200)

without fire, we restore only 301 values, N = 300 and M

(the image mean value), of the Gaussian model for

comparison when a fire takes place. This method can be

used for a real-time detection of a fire and it can be

incorporated into a surveillance system monitoring a zone

of interest in a forest for early fire detection.

Acknowledgements

The authors would like to thank the Algerian Government

for the financial support for this national project.

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(Manuscript accepted 23 September 2013)

doi: 10.1111/aje.12128



belonging probability inverse image approach for forest fire detection

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