International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
  
M represents the total number of pixels in a 
neighborhood window of specified size centered 
around the pixel, and 
N(b) is the number of pixels of gray value b in the 
window where 0x b x L-1. 
Now the following measures have been extracted by using 
first order probability distribution (Pratt, 2001). 
Mean: 
uu Ld 
$, =b= X 6P(6) (2) 
b=0 
Standard deviation: 
LA y 
S, =0, = pal -p) P6) G) 
Skew-ness: 
Li = 
S, - —- Y (b - b) P(5) (4) 
GC, b-0 
Kurtosis: 
L-l = 
= © 
O, b=0 
Energy: 
L-l 
s, - ZPO «e 
h=0 
Entropy: 
s,=-EPlojog. {Po} © 
The first two features are the mean and standard deviation of 
pixel intensities within the image window. 
[In order to get information on the shape of the distribution of 
intensity values within window, the skewness and kurtosis 
are determined. The skewness, characterizes the degree of 
asymmetry of the intensity distribution around the mean 
intensity. If skewness is negative, the data spread out more to 
the left of the mean than to the right. If skewness is positive, 
the data are spread out more to the right. 
The kurtosis measures the relative peakness or flatness of the 
intensity distribution relative to the normal distribution. The 
kurtosis of the normal distribution is 3. Distributions that are 
more outlier-prone than the normal distribution have kurtosis 
greater than 3. Lower outlier-prone distributions have 
kurtosis less than 3. 
The energy and entropy are also determined. The energy is 
useful to examine the power content (repeated transitions) in 
a certain frequency band. Entropy is a common concept in 
many fields, mainly in signal processing (Coifman, 1992). 
2.2 Texture features 
Many land cover/land use classes in urban areas can be 
distinguished from each other via their shape or structure 
characteristics. Therefore, it is important to extract features 
that are able to describe relevant "texture" properties of 
classes. In other researches, different kinds of texture feature 
such as multi channel filtering feature, fractal based feature 
and cooccurrence features (Ohanian, 1992) have been 
proposed. In the proposed algorithm for classification, the 
cooccurrence features are selected as the basic texture feature 
118 
detectors due to their good performance in many pattem 
recognition applications including remote sensing 
It should be noted that when computing cooccurrence 
features using all or relatively high number of possible pixel 
intensity values, the derived texture information will be easily 
blurred by noise in the image (Ohanian, 1992). Hence, it is 
preferable to transform the original intensity values into a 
small number of possible levels either via a scalar or vector 
quantization method. For the cooccurrence feature extraction 
in this study, the original image pixel intensities which have 
been in 256 different discrete values were transformed into 
the set {0,1,...,31} by histogram transformation (Gonzales, 
1993). 
A gray level cooccurrence matrix is defined as a sample of 
the joint probability density of the gray levels of two pixels 
separated by a given displacement. In Cartesian coordinates 
the displacement of the cooccurrence can be chosen as a 
vector (Ax, Ay). The gray level cooccurrence matrix N is 
defined as 
N(ij)={#pair (ij)|image(x,y)=i and image(x+Ax, y+Ay)=j} 
where i,j are gray levels. 
The cooccurrence matrices extracted: from each band have 
been combined to avoid data redundancy. This generalized 
matrix calculates average of the gray level cooccurrence 
matrices. We used Ax=0, Ay=2 to generate the generalized 
cooccurrence matrix in this research. 
Second-order histogram features are based on the gray level 
cooccurrence matrix. This histogram estimate of the second- 
order distribution is 
  
P(a, b)= NC b) (8) 
where M is the total number of pixels in the measurement 
window and N(a,b) is obtained from cooccurrence matrix 
(Ohta, 1980). If the pixel pairs within an image are highly 
correlated, the entries in P(a,b) will be clustered along the 
diagonal of the array. The measures listed below have been 
proposed as measures that specifies the energy spread about 
the diagonal of P(a, b). 
Autocorrelation: 
L-1 L-1 
$,- V Y abP(a,b) (0) 
a=0 b=0 
Covariance: 
14 4 d 
5. -S${a-2}6-F}ptas) 0o 
a=0h=0 
where 
Ld d 
a= aP(a,b) (11) 
a=0b=0 
icd d el 
b- bP(a,b) (12) 
a=0b=0 
Inertia: 
1L 2 
S; z VY (a-b) P(a,b) (13) 
az0bz0 
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