Contribution of SAR Radar Images for the Cartography: Case of Mangrove and Post Eruptive Regions - Cartography: A Tool for Spatial Analysis - page 205

6- Standard Deviation

   

LL  11 LL   11 L 1



2



2

1 1 1

 

2

 



   

i



i   ...

i P

P

 

0 0

x

x x

ii i

...

N

ij

N N

 

  i i i

01 n  1

i  00 j  00  0 pq ,  D

0 1 n  1

7- Cluster Shade

3

3

LL  11

1

LL    11 L 1



n 1

  

1

n  1

 

3

1



ij  2 

  

P

i





...   n 

P

i



  n 

x

 

N

ij

 

k

ii i

...

N i

u

x

N

x

i  00 j

 

i i

01 n  1

 

 00   0 0 k

u  0

0 1 n  1

8- Importance of Great Numbers
11

 

LL  LL  11 L  1



n  1

 

n  1



1 1 1



2





2



2

2



  



j

i



P

... 

i



i

 

P

 

 

   

ij

ii i

...

N N i

k

N

u

 

 

i

 

 

 



01 n  1



i  00 j  00

i

 0 k  0 pq ,  D u  0

0 1

n  1

9- Importance of Small Numbers

   

P
j

   

LL  11

1

P ii i

ij LL  11 L  1



1 1 1





  

  



01 n  1

N

 



2

2

   

N

n  1

N

n  1

i 00 j



i



2



2

 

ii i

 

 

 00  0 pq ,  D

       

i i

 

0 1 n  1

   

k u

    k  0 u  0

10- Inverse Differential Moment

 

 

 

 

1 1

P P

 



LL  11 LL  11 L  1

1

1

ii i

ij



...
21



  

 



nn  21

01 n  1

N

 

 

2

 



pq , 

N

 

2 nn 

 1  i  i 

N

 

1 ij

 

2

 

i 0 j i 1

i

 00

i i

 0



uv

 1  i  i 

 

0 1 n  1

 

kl uvu  0 1

 

kl  0 k 1

11- Mean
11

LL  LL  11 L  1

1 1

1

 





 

i

i

. iP 



P



ij

ii i N

0

N i 

0 ...



N

 

01 n  1

i  00 j  00

i i

 0 pq ,  D

0 1 n  1

12- Variance

LL  11 L  1

   

LL  11

1 

2

 1

2

1

2





 

   

i i

...  

i   P

P

 

ii i

x ij 0

N i

0 

N

N

x x

 

 

01 n  1

 00

i i

 0 pq ,  D

i  00 j

0 1 n  1

Table 1. Classical and new formulations of textural parameters of order ≥2 .

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 co-
occurrence 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