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.
