INTRODUCTION
Satellite observations at resolutions of about 10 m provide images of land use. The spectral information at the terrain allows a classification of objects of land. Classification is a process aiming at the identification of the regions which constitute the image. The raw satellite image is characterized by its large amount of rich and diverse digital form.
The purpose of the satellite images analysis is to extract the maximum of information interesting for users. In our approach, we use the Random Markov Fields for a supervised satellite images classification.
Remote sensing images: The satellites provide images of the land with
different space and spectral resolutions. The raw satellite images are unusable
in practice. They must undergo treatments to make them exploitable (Bonn
et al., 2002; Kato et al., 1993; Dubes
et al., 1990).
Classification is a stage of this treatment, which aims at exploiting the maximum
of information contained in these images in order to represent them in a comprehensible
and interpretable form (Iftene and Mahi, 1996).
In this study, we used the satellite image of Landsat5 TM dated March 15, 1993 and representing the region of Oran in western Algeria. Data of this study area have been provided by the Spatial Researches Center Arzew-Algeria. The area concerned by our studies is marked in red in Fig. 1.
This area represents an occupation of various regions, which can be interesting due to confusions between the localization of certain classes during the use of the algorithms of traditional classification.
|
| Fig. 1: |
Satellite image of Landsat5 TM representing the region of
Oran in the west of Algeria |
Classification: Generally, in a classification the data to be analysed relate to objects or individuals. The objects are characterized by a set of attributes, which constitute multidimensional observations. One associates each one of them vectors XεRN/X=[ x1, x2......., xn] where them: x1, x2......, xn is N attributes used to characterize the objects to be classified among I classes, noted Ci/i = 1, 2, 3..., n.
In remote sensing the purpose of the classification of the satellite images
is to assign each pixel to a particular class or topic such as sea, forest,
urban, sand, scrub, cultivation of cereals, fallow land, surf, burnt land, maraichage
and sebkha, based on the radiometric values of the pixels according to channels
TM1, TM3 and TM4 of LANDSAT. We applied a supervised classification, because
the number of classes and their characteristics are fixed at the beginning (Achab
et al., 2007; Polverni and Gautret, 2001).
The training must include the following stages:
| • |
Choice of the classes of objects in the image |
| • |
Division of the zones of drive in group: |
| • |
For learning to describe classes in terms of value |
| • |
For verification or tests used for classification |
| • |
To characterize the spectral signatures i.e., to locate them
in spectral space and to evaluate their separability |
| • |
To launch classification |
| • |
To carry out tests of classification of the pixels occupying
the zones reserved for the training |
| • |
To carry out tests of classification of the pixels occupying
the zones reserved for the checking |
Our attention is related to the random fields of Markov like a classification tool, because these last years the MRF became increasingly popular, especially in the image processing.
In this study we used the algorithm of recuit simulated on the image modelled by the random fields of Markov with the model of energy of Potts.
Markovian model: Classification within the framework of the image processing consists in assigning, according to a criterion, the pixels of the image to the class to which they belong.
Among these probabilistic methods, the random fields of Markov (Markov Random
Field-MRF), were increasingly popular, in the last few years, in the image processing
(Smits and Dellepiane, 1996; Bouman
and Shapiro, 1994).
Several reasons made adopt the fields of Markov like mode of research. One
of them it is the increasing attention related to the role of the space context
in the classification of the images, in which label with pixels or groups of
pixels are assigned (Kato et al., 1992; Lorette
et al., 1998).
Definition of a neighborhood and a click:
| • |
S = {s1,s2,s3,.......,sN
} a set of points. Gs: the neighbors oh the point s |
| • |
G = {Gs/s∈S} is a neighborhood system of S
if : s ∉ Gs |
| • |
C ⊆ S is called a clique if any pair of sites in C are
neighbors |
| • |
We denote by D the set of cliques, deg (D) =Max C∈D
|C| |
Gibbs distribution and MRF: X = {Xs/s∈S} is a family of random variables such that: ∀ s∈S: Xs∈Λ avec Λ = {0, 1, 2, ...., L-1} represents the state space any.
Ω = {w = (ws1, ws2, ws3, ........., wsN): wsi ∈Λ ; 1≤ i ≤ N} the set of all possible configurations.
The distribution of Gibbs relating to the system of vicinity is the measurement of probability π in Ω such as:
where, Z is a constant of standardization or a function of partition:
Where,
| T |
: |
Constant called temperature |
| U |
: |
Function of energy of the form: |
Where:
| V C |
: |
Function called potential, it is defined in  and
it depends only of  |
The relation between the distribution of Gibbs and the MRF' S is summarized in the theorem of Hammersley-clifford which is announced as follows:
X is random fields of markov respecting the system of vicinity G if and only if π (w) = P(X = w) is a distribution of Gibbs.
Markovian model of classification of image: X is a MRF relating to the system of vicinity G with a function of potential energy U2 and one VC
Such as:
And
To find classification optimal, one uses the rule of Bayes the classification
which maximizes the distribution with posterior P(X=w/F) (Rignot
and Chellappa, 1993):
P(X=w/F) =P (F/X=w) P(X=w) / P (F)
As P (F) is independent of W, then P (F) is constant, the MAP estimator is to give by:
To find a solution optimal of the Eq. 6, we used the algorithm of simulated recruit.
Algorithm ICM (iterated conditional mode): Proposed by Besag this algorithm converges quickly with a MAP optimal estimator. It is given by:
| • |
To choose the initial configuration W0 k = 0 and
E> the 0 threshold |
| • |
 |
k
= k+1 and to go to 2) until|U (w
K)-U (w
k-1)|<E
Within the framework of this study, we used approach ICM. This last uses the model multi-scale.
Markov model multi-scale: Supposing that S = {s1 s 2...., s NR} a grid (W*H), such as:
S≡Γ = {(i, j) 1<=I<=W and 1<=J<=H}
where, W = wN and H = hm
That is to say G a system of vicinity on these sites and X a MRF on G with
the function of energy U and the potential energies {VC}C
εD (Kato et al., 1993; Kato,
1994; Bouman and Liu, 1991; Derin
and Elliott, 1987). The following process generates a model multi-scale:
| • |
 |
| • |
For all 1< = I < = M (M = Inf(n, m)); S is divided into
blocks of size (W1 * HI). These blocks form a scale
B1 = {b1I, b2I, b3I.....,
bNorI} with: NI = N/(w*h)I |
The classes assigned with the sites of a block are the same ones; the classes
common to the block BK1 are noted by 
the
forced generates a space of configuration Ω1 which is a subset
of original space .
For each 0≤i≤M: Ωi ⊆ ⊆i-1 ⊆......⊆0≡one
consider the system of vicinity on a scale I It is clear that bK1
and bL1 are close if and only if, there are two neighbors
and
Then
there are the same ones click that in D.
Click Them are defined in the following way: that is to say d = Deg (D), for 1≤J≤D: the whole of the blocks CJ1 container J sites on the scale, I is one clicks of order J if there is one clicks CεD ( is with being said one clicks on the finest scale) such as:
The whole of click on scale I is noted by D1 (D0
D). The whole of all click them which satisfy a and b for C1J given is noted by:
One shares the original unit D in several following disjoined sets:
For each 1≤J≤D; that is to say AIJ the whole of click CεD for which:
There is one click CIJ which satisfies a and b by considering the definition of D and AIJ one obtains:
By using this decomposition, the function of energy U can be written like continuation:
where, 
the
potential ones of one click CIJ of order J on scale I,
we obtain on the scale B1 the potential following ones:
To simplify the model, one associates a unique site to every block. These sites have the common label of the corresponding block and they form a coarse S1 that is isomorphs to the ladder corresponding Bi (Fig. 2).
The space of configurations 
on
the coarse scales is isomorphous with Ω1. Isomorphism Φ1
of S1 to B1 is only one projection of the field on the
coarse labels on the grid the finest 
|
| Fig. 2: |
Isomorphism Φi between Bi and Si |
where, Φ1 keeps the same system of vicinity on S1 as out of B1 Click on S1 inherit the potentials click defined on B1. These grids form a pyramid, where level I contains the grid S1 The energy of level I (i = 0..., M) is given by:
I = 0, ...., M
Where:
The algorithm multi-scales will solve the problem of minimization by using a strategy of descent in the pyramid. Each lower level is initialized by the result obtained in the preceding layer. The algorithm is given by:
| • |
Either  and
let us divide S in blocks of the size W1xH1 (1≤
I≤M). To assign a single site with each block. These sites form a coarse
grate. |
| • |
Calculate the potentials on the coarse grids by using the
Eq. 6. |
| • |
Either i = M. Find the global minimum  of
U1 in Eq. 7 |
| • |
Initialize the layer (i-1) by the projection of  |
| • |
If i = 1 then stop, otherwise return to Step 4. With I = i-1 |
The advantages of this algorithm are clear. Each gives
an estimator to least good of the final result and the higher levels are simpler
to solve because the space of configuration has less elements.
Application of the model multi-scale: It is supposed that the size of
a block is n X n, i.e., w=h=n. Thus we obtain:
Where:
And
The values of pi, q1 depend on the size of the blocks and the system of vicinity. p1 is the number of click pertaining to the same block on the scale Bi.
q1 is the number of clicks which are between two neighbour blocks on the scale Bi.
In considering the blocks of size n x n and a system of vicinity of order 1, we obtain:
p1 = 2n1 (ni-1)
q1 = ni
| • |
β: is the hyper parameter which controls the homogeneity
of the areas |
Algorithm of the model multi-scales: One needs two entries: the image
observed and the parameters 
(average)
and 
(Standard
deviation) of each class. This amounts to:
| • |
To establish the pyramids and to calculate the parameters
μi and σi on the coarse grids |
| • |
To calculate the energies |
| • |
To minimize the energies in the pyramid with a downward strategy |
| • |
To take the final etiquette on the finest level as being final
result of classification |
Application of the MRF to the satellite image: By considering the zone
of study, the result of the applications based on the Markovian approaches always
depend on the samples of the departure and the value of the Beta parameter (Rabahi
and Ismail, 2003; Kaddar and Fizazi, 2009). Consider
the following example (Fig. 3).
In our case, we have not only applied the algorithm Multi-scale to the satellite image, but we made a variation of parameters. To do this, we chose two steps:
|
| Fig. 3: |
Classified images of each level |
| • |
To fix the samples and to vary the parameter Beta |
| • |
To fix the parameter Beta and to vary the samples |
First step: Initially, we based ourselves on the variation of the parameter β, which is used to control the homogeneity of the areas. With each scale, we have a new value of the energy, which depends on to the parameter β. In our experiment, we varied parameter β from 0.001 to 3.0.
RESULTS
During our experiments, we noticed that the parameter β has an influence on the classification. In order to better analysis and to interpret the results, we gathered all the results obtained, for each class and various values of the parameter β.
For instance we consider β = 0.001 and classifies it Sea, one has that 12.11 % of the Sea topic in the totality of the classified image. We have expressed as a percentage to gather the preceding results by curves indicating the variations each topic according to β (Fig. 4).
According to the results obtained, we notice that there are apparent confusions on the level of following areas: Sea and surf, Sebkhat and scrub, Sebkhat and fallow land. That is noted by the means of the curves so above and classified images obtained below.
It is noticed that starting from the value β = 0.50, the Sea and the Surf are stabilized. This stability is due to the homogeneity of the sea zones and surf. In other words, the pixels of each class are gathered in the same mass.
One also notes a very great confusion between the topics: fallow land, Sebkhat and Scrub. This is due to an overlapping between the classes. For stage this degradation, one increases β until reaching value 3.0.
This is highlighted starting from the preceding graph where it is noted that there are no more confusions between the topics.
To illustrate the confusions obtained in our results and to show the influence
of the parameter β on confusions, we schematised them by the Fig.
5-7.
This approach allows us to say that the parameter β can solve the problem of confusion between the various classes and that it can be regarded as parameter of improvement of classification since the images obtained correspond to the field reality.
Second step: It consists to fix β and vary the samples in order
to make a classification. For that, we based ourselves on the values of the
parameter β of the preceding experiments having given an image close to
the reality, in other words, in which the areas are distinct. A better illustration
of this step, is shown in Fig. 8 and 9 which
present the results of the classification, as well as the rate of classification
Tc for two choices of samples.
|
| Fig. 4: |
Curve of variation expressed as a percentage of each topic
according to parameter β |
|
| Fig. 5: |
Results of classification according to parameter  for
area fallow land |
|
| Fig. 6: |
Results of classification according to parameter β for
area scrub |
|
| Fig. 7: |
Results of classification according to parameter β for
area surf |
|
| Fig. 8: |
Result of classification for the first sample Tc = 90.26% |
|
| Fig. 9: |
Result of classification for the second sample Tc = 95.45% |
DISCUSSION
To validate the results obtained in this article, we have compared them with
those obtained in (Achab et al., 2007). The researchers
of this study used the MRF model single-grid to classify the same regions shown
in Fig. 1. The results show that the classification rate in
the case of MRF-multi-scale Tc = 95.45 is significantly higher than the MRF
model single-grid Tc = 58.68 where they are a lot of confusions between classes.
There is even a total lack of the burnt class, while in the MRF-multi-scale
all classes are present and the result of the classification matches the reality.
We compared our results with those obtained using K-means (Iarkani
and Amel, 2008). The parameter to be determined in the K-means is the value
of k that represents the number of classes (in our case k is equal to 12). The
best recognition rate obtained in their work is Tc = 83.01%, but with a persisting
confusions between classes sebkhat and urban, sand and land.
Our approach has improved the classification rates and the results obtained correspond to the reality.
CONCLUSIONS
For the selected method Models Multi-scales and for the steps considered, we noticed that the results obtained depend highly on the choice of training samples.
In our first step, which consists in fixing the sample and varying the parameter,
we noted that confusion persists on the Sebkhat level, scrub and fallow land.
That is highlighted by Fig. 5.
For stage this degradation, one can add other data such as the slope, altitude,
etc As regards the second step, which consists to fix Beta and vary the sample,
the results obtained show a clear improvement of classification compared to
the first step. That is well to illustrate by Fig. 6 and 7.
The results obtained starting from the experiments showed, that by making a good choice of the sample and β parameter we can minimize confusions and improve classification of the satellite images by the random fields of Markov, approaches Multi-scales.
The development of fast and robust algorithms for processing and analysis of
this type of data is therefore of great importance. It has been demonstrated
recently that a Markov-random-field (MRF) model, based on the statistical properties
of imaging, provides an ideal framework processing remote sensing data The proposed
approach improves classification accuracy when applied to the segmentation of
multispectral remotely sensed images with ground truth data.
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