ING IMAGES 
an, China 
Defense of CPLA! 
1e analysis and modelling 
bject classes while Getis 
letermined by the range 
; (FCM) algorithm which 
hat spatial autocorrelation 
measure of local spatial 
ve in distinguishing “hot 
| be used, for example, to 
s that represent a spectral 
re (Myint et al., 2007). 
tial autocorrelation is 
cal function and can be 
s of typical object classes 
information of spatial 
variogram can be used as 
nogeneity (Franklin et al., 
:ctly related to the size of 
Balaguer et al, 2010). 
> the proper window size 
lation analysis. 
ind modelling of spatial 
the segmentation quality 
semivariograms are used 
bject classes, while Getis 
1 spatial autocorrelation 
by semivariograms. Two 
Fuzzy C-Means (FCM) 
e conducted. The results 
eatures can effectively 
high resolution satellite 
D DATA 
Quickbird images of two 
vith the resolution of 
pectral band 2.44 m. The 
els X 642 pixels and 349 
  
  
pixels X 220 pixels, respectively. In this paper, multi-spectral 
bands (band 4, band 3 and band 2) are used for experiments. 
The color images by fusing 4, 3, 2 bands are showed in Figure 1, 
and by field survey, the object classes of site 1 mainly include 
vegetation, waters, roads and ships, and in site 2, its typical 
object classes include buildings, shadows, vegetation and bare 
lands. Most of these object classes are spectrally heterogeneous 
in the images. 
  
(b) site 2 
Figure 1. Quickbird color images of the study area 
3. METHODOLOGY 
31 Semivariogram 
The semivariogram is a geostatistical function which describes 
the spatial variability of the values of a variable. The 
experimental semivariogram is defined as 
ae Nat a) 
2ZN(h) 
where z (x;) is a regionalized variable, representing the value of 
the variable at the location x; . The lag À is the vector from pixel 
x; to pixel x; + h, and N (h) is the number of pixel pairs x; and x; 
m. 
  
  
  
— 
4 
  
Figure 2. Semivariogram and its parameters 
Semivariogram has three basic parameters (Figure 2): nugget, 
sill and range. The nugget is an estimate of variance at distance 
(or lag) zero, which may be interpreted as a measure of 
variability inside the pixel cell. The semivariance is a function 
of lag h, and the sill is the maximum semivariance level reached. 
The lag at which the sill reached is the range, which can be used 
as a measure of spatial dependency or homogeneity (Franklin et 
al., 1996) and it has been proved to be directly related to the 
size of objects or patterns in an image (Balaguer et al., 2010). In 
this paper, it is used to guide the selection of proper window 
sizes for local spatial autocorrelation analysis. 
3.2  Getis statistic 
Getis statistic is a local indicator describing spatial 
autocorrelation, which provides a measure of spatial 
dependence for each pixel. The standardized Getis statistic 
G;*(d) is defined as (Wulder & Boots, 1998) 
. T w,(d)x, - W, x 
Cero Q) 
CTS Q-W)m-DI^ 
  
where (wj (d)) is a symmetric one/zero spatial weight matrix, 
with ones assigned to all locations within distance d of 
observation i, including i itself (i.e. w;=1), and zero otherwise; 
w= wd): x=) x/n and s? => x, In-x 
are the mean and variance of values of all pixels, respectively. 
Getis statistic describes the autocorrelation of a variable in a 
local region, and in particular, it is effective in identifying 
clusters of high values called “hot spots” or clusters of low 
values called “cold spots” in an image. In this paper, it is used to 
calculate the degree of local spatial autocorrelation. 
3.3 Window determination by semivariogram and spatial 
autocorrelation analysis by Getis statistic 
Since Getis statistic is a function of distance d, it has the 
characteristics of scale. Therefore, one problem we have to deal 
with is how to select proper parameter d for local spatial 
autocorrelation analysis, which is also a problem determining 
proper window size (defined as (2d+1)*(2d+1)) for each pixel. 
We may take many different d values for repeated experiments, 
but it is time-consuming. Fortunately, the range of the 
semivariogram provides information about the length of spatial 
correlation in the images; pixels (or objects) separated by a 
distance less than the range are spatially correlated, whereas 
pixels at separations longer than the range are not (Meer, 2012). 
To make full use of local spatial autocorrelation information, we 
limit window width (2d+1) not exceeding the maximum range 
of all the semivariograms characterizing all selected object 
classes, which could greatly reduce repeated experiments but 
also include autocorrelation information as much as possible 
within the window. In detail, we first select typical objects or 
their samples in the image and then modelled them by 
semivariograms. From semivariograms, the range of spatial 
variability of each object can be determined approximately by 
visual inspection (As window parameter d is a positive integer, 
approximate range values are enough for window 
determination). Then spatial autocorrelation degree is easily 
calculated using Getis statistic by equation (2) within 
neighborhood window (2d+1)*(2d+1). For each spectral band, 
spatial autocorrelation feature band can be obtained by 
assigning the value of spatial autocorrelation degree of each 
pixel to this pixel.