**3. Methodology**

Our methodology is divided into two parts: the first part concerns the improvement of the computational time required for the evaluation of textural parameters. The second part deals with an approach of SAR images classification.

#### **3.1. Formulation of high order of statistical textural parameters**

Basically, statistical textural parameters are function of the occurrence frequency matrix (OFM), which is used to define the occurrence frequency of n-ordered gray levels in the image.

#### *3.1.1. The occurrence frequency matrix (OFM)*

In an image with *Ng+1* levels of quantification, the OFM of order *n >1* is a *(Ng+1)n* size matrix. In this matrix, each element ܲభమڮ expresses the occurrence frequency of the *n-*ordered pixels *(i0,i1, …,in-1)* following the connection rule *Rn(d1,d2,…dn-1,θ1,θ2,…θn-1)*. This connection rule defines the spatial constraint that must be verified by the various pixels of the *n-*ordered pixels *(i0,i1,…,in-1)* used in the occurrence frequency matrix evaluation. This rule means that the pixel *ik+1 (0<k<n)* is separated to the pixel *ik* by *dk–1* pixels in the *θk* direction. For the sake of simplicity, *Rn(d1,d2,…dn-1,θ1,θ2,…θn-1)* will be noted by *Rn* in the following.

#### *3.1.2. The textural parameters*

A parameter of texture ܲܽݎܽ in any order ݊ is a real function defined in general manner by the equation given after:

$$Para\_n = F \times \{R\_n\} \to \mathfrak{R} \tag{1}$$

Contribution of SAR Radar Images for the Cartography: Case of Mangrove and Post Eruptive Regions 205

*P*

*P*

01 1

*n*

*n*

,

0

1 *<sup>n</sup> <sup>u</sup> <sup>N</sup> pq D <sup>u</sup> <sup>i</sup>*

*pq D <sup>N</sup> i*

0

<sup>3</sup> <sup>1</sup>

1 2

 

*<sup>u</sup> <sup>x</sup> <sup>u</sup> n*

 

, 0

1 1 *<sup>n</sup> pq D*

1 1

1 *n n p q*

<sup>0</sup> ,

<sup>0</sup> ,

 

*<sup>x</sup> N pq D i*

 <sup>1</sup> <sup>2</sup> , 0

*<sup>u</sup> <sup>u</sup>*

*i*

0 1

 

*u vu*

*u v*

*i i*

2

 *x* 

1

1 *<sup>n</sup>*

*N*

*<sup>N</sup> i*

2

11 1 2

*<sup>N</sup> <sup>x</sup> ii i ii i i* 

<sup>3</sup> 11 1 1

11 1 1 2

<sup>1</sup> <sup>2</sup> 00 0

1 *<sup>n</sup>*

*n*

*ii i i*

*n*

... 00 0 <sup>1</sup> ... <sup>0</sup> *<sup>n</sup>*

... 00 0 0

... 0 0 <sup>0</sup> <sup>0</sup>

*<sup>k</sup> <sup>N</sup> ii i i i*

*<sup>N</sup> ii i ii i i*

*<sup>k</sup> <sup>x</sup> <sup>k</sup> n*

*k*

*Pii i*

*k*

0

2 1 <sup>2</sup> 00 0

*n n*

*k lk*

*i P*

*n*

*k*

11 1 ...

*<sup>N</sup> ii i i i*

<sup>0</sup> ... 00 0

11 1 2 0

This method consists in reducing the number of operations necessary for the calculation of the co-occurrence matrix. From each pixel of the image, all others pixels involved in the computation of the co-occurrence matrix are reached and operations are directly made on these pixels. This process allows avoiding the evaluation and the stocking of the cooccurrence matrix in the main memory of the computer. In the tree approach, the route of the image pixels is not made any more line after line and pixel after pixel, but rather by following a generic tree. From a pixel and according to its position, one reaches directly, by

*n*

*<sup>N</sup> ii i ii i*

1

*i P i*

01 1

01 1

*ii i*

*P*

*n*

0 1

*n*

*Pii i i* 

 

*k l*

*n*

2 1 <sup>2</sup> ,

*N*

1 *N pq D i* 

1

6- Standard Deviation

0 0

7- Cluster Shade

0 0 <sup>1</sup> <sup>2</sup> *L L*

0 0

1 1

 

1 *L L*

*N i j*

1

*i j <sup>N</sup>*

1 *L L*

*N*

 1 1 <sup>2</sup>

*P*

 1 1 <sup>3</sup>

*P*

8- Importance of Great Numbers

9- Importance of Small Numbers

10- Inverse Differential Moment

2

*P*

*<sup>x</sup> ij i j*

1 1 <sup>2</sup> <sup>2</sup>

*ij N i j i j P*

<sup>2</sup> <sup>2</sup> 0 0 1 *L L ij*

1 1

0 1

11- Mean 1 1

*i j*

1 *L L*

*N*

*N*

0 0 <sup>1</sup> . *L L*

12- Variance

0 0

*i j*

1 *L L ij N i ji i j P* 

*ij*

 1 1 <sup>2</sup>

*i P*

*x ij*

*iP*

*i j*

 01 1 01 1

<sup>1</sup> ...

 01 1 0 1 1

*N*

1

01 1

1

<sup>1</sup> ...

*LL L*

01 1

*n*

*LL L n*

*n*

01 1

01 1

11 1

01 1

*LL L*

**Table 1.** Classical and new formulations of textural parameters of order ݊ʹ.

 01 1 01 1

**3.2. Aborescent method of textural parameters evaluation** 

<sup>1</sup> ...

00 0

*n*

*<sup>N</sup> <sup>x</sup> ii i*

*LL L*

*LL L*

*n*

11 1

*LL L*

*LL L n*

*<sup>x</sup> ij i j i*

where � is an image or window of image on which one is evaluated texture parameter and �� is a rule of connection associated.

Let's consider an image window F of size NLxNC, where NL is the number of lines and NC is the number of columns. The classical expression of textural parameters is given by the following expression:

$$Para\_n = \Sigma\_{l\_0=0}^{N\_g} \Sigma\_{l\_1=0}^{N\_g} \cdots \Sigma\_{l\_{n-1}}^{N\_g} \{ \phi(l\_0, l\_1, \cdots, l\_{n-1}) \times P\_{l\_0 l\_1 \cdots l\_{n-1}} \} \tag{2}$$

where ������⋯����� is the OFM and � is a real function defined in ��.

The synthesis of the generalisation of texture parameters is conciliated on the Table 1 given below.

following expression:

below.

**Parameter** 

1- Contrast

�� is a rule of connection associated.

 

 

  *ij*

01 1

01 1

01 1

01 1

*LL L*

<sup>1</sup> ...

 01 1 01 1

<sup>1</sup> ...

00 0

*n*

11 1 1

*LL L n n*

*n*

<sup>1</sup> ...

01 1

*n*

11 1 <sup>0</sup>

 

*LL L k k n k*

*n*

11 1 1

*LL L n*

<sup>1</sup> ... *<sup>k</sup>*

*LL L n n*

<sup>1</sup> ...

1 11 <sup>2</sup> <sup>2</sup>

*n ijP <sup>N</sup>*

0 00 <sup>1</sup> . *L LL*

1 1

1 1

4- Inverse Difference

1 *L L ij N i j i j P*

*ij i j i j <sup>N</sup> <sup>P</sup>* 

*i j <sup>N</sup>* 

*L L x y ij i j x y i j <sup>N</sup> P* 

 

*x y ij i j*

*<sup>P</sup>*

 

*n ij*

2- Correlation

0 0 <sup>1</sup> .

3- Covariance

0 0 <sup>1</sup> . *L L*

1 1

0 0 <sup>1</sup> .

0 0 <sup>1</sup> . *L L*

5- Dissymmetry 1 1

 

����� =�� ���� → ℜ (1)

���� (2)

01 1

01 1

01 1

*n*

*N*

1

2 1 ,

*N*

*k l*

*k*

*i*

*<sup>n</sup> <sup>k</sup> <sup>n</sup>*

2 1

*ii i*

*P*

 

*n n*

*k lk*

*n*

*k l*

*n*

0 1

*k l*

 

*i i P*

 

*i*

*i i P*

*P*

*P*

*n*

*in order n* 

2 1 <sup>2</sup> <sup>2</sup>

, 0 1

*u v pq D u lv <sup>n</sup> <sup>N</sup> i i* 

1

0 <sup>1</sup> ,

*<sup>u</sup> <sup>u</sup>*

*i*

1 *<sup>u</sup>*

 

*n*

*<sup>n</sup> pq D*

, 0

1 1

1 *n n pq D*

1

*u v N pq D u vk*

, 0 1

1 *n n*

0

0 1

 

 

 

*u vu*

*u*

1

*n <sup>u</sup> <sup>N</sup> pq D <sup>u</sup> <sup>i</sup> i*

*u*

*u*

*u v*

*i i*

*i i*

*i*

*i*

1 *n n*

where � is an image or window of image on which one is evaluated texture parameter and

Let's consider an image window F of size NLxNC, where NL is the number of lines and NC is the number of columns. The classical expression of textural parameters is given by the

> ����� <sup>=</sup> ∑ ∑ <sup>⋯</sup> <sup>∑</sup> ������ ���⋯������ �������⋯����� �� ����

The synthesis of the generalisation of texture parameters is conciliated on the Table 1 given

*Order 2 Classical formulation of order n Arborescent formulation* 

11 1 2 1 <sup>2</sup> <sup>2</sup> ... 00 0 0 1

*k lk n <sup>N</sup> ii i ii i*

1

*n*

<sup>1</sup> ... 00 0 0

... 00 0 <sup>0</sup>

11 1 ...

*<sup>N</sup> ii i i i*

1

... 00 0 0 1

*k lk <sup>N</sup> ii i ii i*

*k <sup>k</sup> <sup>N</sup> ii i <sup>i</sup> ii i i* 

*i*

*<sup>N</sup> ii i ii i*

�� ����

where ������⋯����� is the OFM and � is a real function defined in ��.

��

**Table 1.** Classical and new formulations of textural parameters of order ݊ʹ.

#### **3.2. Aborescent method of textural parameters evaluation**

This method consists in reducing the number of operations necessary for the calculation of the co-occurrence matrix. From each pixel of the image, all others pixels involved in the computation of the co-occurrence matrix are reached and operations are directly made on these pixels. This process allows avoiding the evaluation and the stocking of the cooccurrence matrix in the main memory of the computer. In the tree approach, the route of the image pixels is not made any more line after line and pixel after pixel, but rather by following a generic tree. From a pixel and according to its position, one reaches directly, by

$$\begin{cases} \quad \boldsymbol{i} = (a, b) \\ \quad \boldsymbol{j} = f\_0(\boldsymbol{i}, d\_1, \theta\_1) \\ \quad \boldsymbol{k} = f\_{00}(\boldsymbol{j}, d\_2, \theta\_2) \\ \quad \boldsymbol{l} = f\_{01}(\boldsymbol{j}, d\_2, \theta\_2 + 180^\circ) \\ \quad \boldsymbol{m} = f\_1(\boldsymbol{i}, d\_1, \theta\_1 + 180^\circ) \\ \quad \boldsymbol{n} = f\_{10}(\boldsymbol{m}, d\_2, \theta\_2) \\ \quad \boldsymbol{o} = f\_{11}(\boldsymbol{n}, d\_2, \theta\_2 + 180^\circ) \end{cases} \tag{3}$$


$$Asym2 = \sum\_{i=0}^{N\_g} \sum\_{j=0}^{N\_g} |i-j| \times p(i,f) \tag{4}$$

$$Asym2 = \sum\_{l=0}^{N\_g} \left( \sum\_{j=0}^{N\_g} \underbrace{|i-j| + |i-j| + \dots + |i-j|}\_{p(l,j)\text{ times}} \right) \tag{5}$$

$$\text{Asym2} = \sum\_{l=0}^{N\_g} \text{ASS}[l] \tag{6}$$

$$\text{LSS}[i] = \Sigma\_{j=0}^{N\_{\mathcal{S}}} \left( \underbrace{|i - j| + |i - j| + \dots + |i - j|}\_{p(l, j) \text{ times}} \right); \tag{7}$$


$$\text{ASS}[i] = |i - NG(a, b)| + \left| l - NG\left[ f\_0(a, b, d\_1, \theta\_1) \right] \right| + \left| l - NG\left[ f\_1(a, b, d\_1, \theta\_1 + 180^\circ) \right] \right| \tag{8}$$

$$Asym2 = \sum\_{l=0}^{N\_g} ASS[j].\tag{9}$$


	-

$$\begin{cases} \begin{array}{c} \text{ASS[0]} = |0-4| + |0-2| = 6 \\ \text{ASS[1]} = |1-4| = 3 \end{array} \\ \begin{array}{c} \text{ASS[2]} = |2-4| + |2-3| + |2-4| + |2-3| + |2-3| + |2-0| = 9 \\ \text{ASS[3]} = |3-2| + |3-2| + |3-2| = 3 \end{array} \\ \begin{array}{c} \text{ASS[4]} = |4-4| + |4-2| + |4-0| + |4-2| + |4-1| = 11 \end{array} \end{array} \end{cases}$$

$$\begin{aligned} Asym2 &= \left( |0 - 1| \times P\_{01} \right) + \left( |0 - 2| \times P\_{02} \right) + \left( |0 - 3| \times P\_{03} \right) + \left( |0 - 4| \times P\_{04} \right) \\ &+ \left( |1 - 0| \times P\_{10} \right) + \left( |1 - 2| \times P\_{12} \right) + \left( |1 - 3| \times P\_{13} \right) + \left( |1 - 4| \times P\_{14} \right) \\ &+ \left( |2 - 0| \times P\_{20} \right) + \left( |2 - 1| \times P\_{21} \right) + \left( |2 - 3| \times P\_{23} \right) + \left( |2 - 4| \times P\_{24} \right) \\ &+ \left( |3 - 0| \times P\_{30} \right) + \left( |3 - 1| \times P\_{31} \right) + \left( |3 - 2| \times P\_{32} \right) + \left( |3 - 4| \times P\_{34} \right) \\ &+ \left( |4 - 0| \times P\_{40} \right) + \left( |4 - 1| \times P\_{41} \right) + \left( |4 - 2| \times P\_{42} \right) + \left( |4 - 3| \times P\_{43} \right) \\ &= \left[ \left( 1 \times 0 \right) + \left( 2 \times 1 \right) + \left( 3 \times 0 \right) + \left( 4 \times 1 \right) \right] \end{aligned}$$

$$+[(1\times0)+(1\times0)+(2\times0)+(3\times1)]$$

$$+[(2\times1)+(1\times0)+(1\times0)+(2\times2)]$$

$$+[(3\times0)+(2\times0)+(1\times3)+(1\times0)]$$

$$+[(4\times1)+(3\times1)+(2\times2)+(1\times0)]$$

Experimentally, one parameter has been selected. The mean parameter in order 3 after several tests on our studies site has been selected. The method of choice of the index and order of textural parameters is largely presented in (Fotsing et al., 2008).

Contribution of SAR Radar Images for the Cartography: Case of Mangrove and Post Eruptive Regions 213

(12) ܽݔଵܽڮ ଵିݔଵିܽ ݔܽൌݕ

form m-modal histograms in general, we approached a curve of type polynomial regression.

The continuous function ݂ (the continuous line passing through the vertices of each peak of the histogram) adjusted using the least squares method, allows to set the degree of the

The choice of the number of cluster centers in a radar image is difficult. In his thesis, (Lorette, 1999) uses the entropy criterion for determining the number ݊ of cluster centers for

As part of this project, we used a map of ancient plant formation of the study site. For this, we proposed to re-issue the said card with latest radar image from the perspective of studying the direction of evolution of different forest communities. In general, we decided to use the same number of class with maps of land of the study sites in our possession.

Detection modes and valleys take place on the transformed histogram, based on the concept of change in concavity of the curve of a function. Indeed, a curve changes concavity through a local minimum (valley) or by a local maximum (mode). The points where the curve changes concavity points are very sensitive and rich in information. The detection of these on the histogram of the transformed SAR image is used to inform the analyzer on the existence of thematic classes. Thematic classes are groups of pixels with similar characteristics (or almost) with respect to their brightness values in the different thematic data. The analyst has the role to determine the usefulness of different thematic

As part of this work, identification of thresholds is conducted by analyzing the histogram of

Our detection of these thresholds used Fisher's method which uses the criterion of minimizing the sum of the inertia of each class. The calculation algorithm is the dynamic type and evaluating an optimal sequence of partitions according to the scheme described in

We used to detect patterns by Bhattacharya method (Bhattacharya, 1967) that models the histogram by a weighted sum of Gaussian and identifies each mode by its mean and

These polynomials have formulated by the equation 12:

where ݊ is the degree of polynomial.

number of classes centers.

*4.3.2. Determination of degree n* 

the analysis of urban areas on satellite images.

**4.3.2.1. Search valleys "inter-modal thresholds"** 

gray levels and looking for local minima.

(Cocquerez et al., 2001).

**4.3.2.2. Search modes** 

*4.3.3. Principle of threshold detection* 

classes.

### **4.3. Principle of detection modes and valleys of the histogram**

#### *4.3.1. Histogram modeling*

The histogram of an image is a graphic representation having abscissa values of gray levels, and the ordinate the number of pixels associated with each gray level value. The mode is a local maximum and valley a local minimum of the histogram. The maximum and minimum (no zero) of a histogram indicate a group of pixels and is used to detect cluster centers. Kourgly et al. (Kourgly et al., 2003) exploit observed nesting on the experimental variogram textures for segmentation urban image.

How to extract the classes contained in a SAR image? A good method for extracting classes is that will arrive at a correct interpretation. To achieve this goal, we used thresholding techniques. We go with the principle that, the thresholding has aim to segment an image in to several classes using only histogram. This assumes that the information associated with the image alone allows the segmentation, which is to say that a class is characterized by its gray level distribution. At each peak of the histogram has an associated class.

There are numerous methods of thresholding a histogram (Diday et al., 1982; Otsu, 1979). Most of these methods are applied correctly if the histogram actually contains separate peaks. Moreover, these methods have often been developed to treat the particular case of segmentation in two classes (that is to say moving to a binary image) and generality face multi-class case is rarely warranty. In this work, we assume that each class corresponds to a different range of gray level. The histogram is then m-modal. The position of minima and maxima of the histogram ܪ can set the thresholds ሺ݉െͳሻ to separate the ݉ classes.

In mathematical terms, the thresholds ܵ are obtained by equations given below:

$$H(\mathbb{S}\_l) = \dim[H(k)] \text{ with } k \in [m\_l, m\_{l+1}] \tag{10}$$

$$H'(\mathbb{S}\_l) = \max[H(k)] \text{ with } k \in \lfloor m\_l, m\_{l+1} \rfloor \tag{11}$$

Equations (10) and (11) indicate the thresholds for valleys and modes of the histogram, respectively. Similarly, in these expressions ݉ and ݉ାଵ are the mean values (modes or valleys) of the light intensity in the classes ܥ and ܥାଵ. The range ሿ݉ǡ ݉ାଵሾ is obtained on the basis of average values of the valleys, these when the threshold is calculated by the equation (10) and by (11) otherwise.

The histogram gives comprehensive information on the distribution of gray levels in the image. If we note ݔ the value of gray level, another way to represent the histogram can be to search for a mathematical expression ݕൌ݂ሺݔሻ with ݕ the number of pixels whose gray level ݔ. The form of the function ݂ determines the signature of the analyzed image. Based on the form m-modal histograms in general, we approached a curve of type polynomial regression. These polynomials have formulated by the equation 12:

$$y = a\_n \mathfrak{x}^n + a\_{n-1} \mathfrak{x}^{n-1} + \dots + a\_1 \mathfrak{x} + a\_0 \tag{12}$$

where ݊ is the degree of polynomial.

212 Cartography – A Tool for Spatial Analysis

*4.3.1. Histogram modeling* 

associated class.

textures for segmentation urban image.

Experimentally, one parameter has been selected. The mean parameter in order 3 after several tests on our studies site has been selected. The method of choice of the index and

The histogram of an image is a graphic representation having abscissa values of gray levels, and the ordinate the number of pixels associated with each gray level value. The mode is a local maximum and valley a local minimum of the histogram. The maximum and minimum (no zero) of a histogram indicate a group of pixels and is used to detect cluster centers. Kourgly et al. (Kourgly et al., 2003) exploit observed nesting on the experimental variogram

How to extract the classes contained in a SAR image? A good method for extracting classes is that will arrive at a correct interpretation. To achieve this goal, we used thresholding techniques. We go with the principle that, the thresholding has aim to segment an image in to several classes using only histogram. This assumes that the information associated with the image alone allows the segmentation, which is to say that a class is characterized by its gray level distribution. At each peak of the histogram has an

There are numerous methods of thresholding a histogram (Diday et al., 1982; Otsu, 1979). Most of these methods are applied correctly if the histogram actually contains separate peaks. Moreover, these methods have often been developed to treat the particular case of segmentation in two classes (that is to say moving to a binary image) and generality face multi-class case is rarely warranty. In this work, we assume that each class corresponds to a different range of gray level. The histogram is then m-modal. The position of minima and

Equations (10) and (11) indicate the thresholds for valleys and modes of the histogram, respectively. Similarly, in these expressions ݉ and ݉ାଵ are the mean values (modes or valleys) of the light intensity in the classes ܥ and ܥାଵ. The range ሿ݉ǡ ݉ାଵሾ is obtained on the basis of average values of the valleys, these when the threshold is calculated by the

The histogram gives comprehensive information on the distribution of gray levels in the image. If we note ݔ the value of gray level, another way to represent the histogram can be to search for a mathematical expression ݕൌ݂ሺݔሻ with ݕ the number of pixels whose gray level ݔ. The form of the function ݂ determines the signature of the analyzed image. Based on the

ܪሺܵሻ ൌ ܯ݅݊ሾܪሺ݇ሻሿݓ݅ݐ݄݇ א ሿ݉ǡ ݉ାଵሾ (10)

ሺܵሻ ൌ ܯܽݔሾܪሺ݇ሻሿݓ݅ݐ݄݇ א ሿ݉ǡ ݉ାଵሾ (11)

maxima of the histogram ܪ can set the thresholds ሺ݉െͳሻ to separate the ݉ classes.

In mathematical terms, the thresholds ܵ are obtained by equations given below:

ᇱܪ

equation (10) and by (11) otherwise.

order of textural parameters is largely presented in (Fotsing et al., 2008).

**4.3. Principle of detection modes and valleys of the histogram** 

The continuous function ݂ (the continuous line passing through the vertices of each peak of the histogram) adjusted using the least squares method, allows to set the degree of the number of classes centers.

#### *4.3.2. Determination of degree n*

The choice of the number of cluster centers in a radar image is difficult. In his thesis, (Lorette, 1999) uses the entropy criterion for determining the number ݊ of cluster centers for the analysis of urban areas on satellite images.

As part of this project, we used a map of ancient plant formation of the study site. For this, we proposed to re-issue the said card with latest radar image from the perspective of studying the direction of evolution of different forest communities. In general, we decided to use the same number of class with maps of land of the study sites in our possession.

#### *4.3.3. Principle of threshold detection*

Detection modes and valleys take place on the transformed histogram, based on the concept of change in concavity of the curve of a function. Indeed, a curve changes concavity through a local minimum (valley) or by a local maximum (mode). The points where the curve changes concavity points are very sensitive and rich in information. The detection of these on the histogram of the transformed SAR image is used to inform the analyzer on the existence of thematic classes. Thematic classes are groups of pixels with similar characteristics (or almost) with respect to their brightness values in the different thematic data. The analyst has the role to determine the usefulness of different thematic classes.

#### **4.3.2.1. Search valleys "inter-modal thresholds"**

As part of this work, identification of thresholds is conducted by analyzing the histogram of gray levels and looking for local minima.

Our detection of these thresholds used Fisher's method which uses the criterion of minimizing the sum of the inertia of each class. The calculation algorithm is the dynamic type and evaluating an optimal sequence of partitions according to the scheme described in (Cocquerez et al., 2001).

#### **4.3.2.2. Search modes**

We used to detect patterns by Bhattacharya method (Bhattacharya, 1967) that models the histogram by a weighted sum of Gaussian and identifies each mode by its mean and variance. The algorithm of the method of deployment is widely presented and discussed (Cocquerez et al., 2001).

Contribution of SAR Radar Images for the Cartography: Case of Mangrove and Post Eruptive Regions 215

used (Figure 5) is a SAR image, acquired by ERS-1 satellite in C band (λ = 5.66cm) with VV polarization and SLC (Single Look Complex) format. Its spatial resolution is about 25m and the side of a pixel is 12.5m. This image of 8000 columns and 8269 lines has been acquired on

Due to the lack of a *priori* knowledge on these test sites, various litho-structural maps, formation plant maps including topographic maps and lithographs at 1: 200 000 of scale

The histogram of original image of the mangrove region (Figure 4) is illustrated on figure 6. The previous histogram is approximated by the regression curve ݂ which is shown on

The previous approach, which has the advantage of being simple and fast, is well suited to

The texture image is obtained from the parameter "Mean" in order 3. The calculation was performed on a window of size 7x7 around each pixel. The choice of this window size is justified by the fact that we get results like the original image with best representation of thematic classes. In addition, we found that the larger of window size was wide, there were

The histogram of the texture image is shown in figure 8 and corresponding signature is shown on the figure 9. The irregularities observed on the histogram of texture images

more smoothing of the resulting image with absence of fine structure in the image.

the 7th November 1998.

allowed us to identify the various themes.

**Figure 5.** Original image of the Mount Cameroun region

**5.2. Histogram and thresholds detection** 

images having forms regularly distributed.

Figure 7.
