The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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This approach combines geostatistical filtering for suppression 
of image background with local indicators of spatial 
autocorrelation (LISA), which are used routinely in health 
sciences for the detection of clusters and outliers in cancer 
mortality rates. 
2.1 Data Pre-Processing 
Taking some urgent applications into account, we have to 
traverse some considerably large images and extract interesting 
objects with a time limitation. Our way to resolve this problem 
is to resample the original image to a much lower spatial 
resolution with a kind of quad tree-like resampling method to 
reduce the number of pixels involved in the calculation. In this 
step, we need some priori knowledge about how many pixels a 
ship usually take in the image or width and height of the 
smallest block on the original image that includes one ship. 
Then the resample scale (the resample block size) can be 
confirmed. In the resampling processing, new gray value of 
each block will be calculated only using pixels in four 
directions (the two diagonals, horizontal midline and vertical 
midline), also for the purpose of saving computing time. In the 
output images, no more than 15 pixels can cover one ship which 
usually needs more than 1500 pixels in the original image, and 
the spectral characteristics of the original image was well 
preserved. As the result of this step, the ships to be detected in 
the image have been indicated by the cluster of pixels which 
has a remarkable spectral contrast with the background. 
2.2 Anomaly Detection 
The anomalies extraction is based on the geostatistical noise 
filtering and local indicator of spatial autocorrelation (LISA 
value) analysis. 
2.2.1 Geostatistical filtering 
This step involves removing from each spectral band of the 
original image the low-frequency component or regional 
variability. For the k th band, the low-frequency component, 
denoted m k , is estimated at each location u as a linear 
combination of the n surrounding pixel values: 
mk(u) = Aik x zk(ui) 
(1) 
7 = 1 
Where Aik is quantified using the semivariogram, which is 
estimated as 
1 N(h) 2 
MW = 2N ^ Z [ Zk ( Ua + h ) ~ zk ( Ua )\ ( 2 ) 
Then the following system of linear equations is solved to 
compute the weights: 
y Ajk/k(ui -Uj) + fik(u) = 0(7 =; 1,...,«) 
j=} 
(3) 
2.2.2 Detection of anomalies using the local Moran’s I 
Depending on the different size of the anomalies, a detection 
kernel, whose size corresponds to the expected size of the 
anomalies, is defined and the pixels around the kernel consist of 
the kernel neighbour. The detection of local cluster is based on 
local Moran’s I, which is the most commonly used LISA statics. 
Moran’s I is calculated for each pixel u in each band z k : 
LISAk(u) = n(u) 
4z 
(4) 
Where rk(u)=z k {u)-m{u) ? n(u) ij} the average value of the 
residuals,over the detection kernel centred on pixel u, and J is 
the number of pixels in the LISA neighbourhood^.g. = 12 for a 
2X2 kernel and J= 16 for a 3 X 3 kernel).Cluster of low or high 
values, which respond to the presence of positive local 
autocorrelation, will lead to positive values of the LISA statistic. 
In addition to the sign of the LISA statistic, its magnitude 
informs on the extent to which kernel and neighbourhood 
values differ. To test whether this difference is significant or 
not, a Monte Carlo simulation is conducted, which consists of 
sampling randomly and without replacement from the whole 
image area and computing the corresponding simulated 
neighbourhood averages. 
Sim _ LISAk(u)n = 
(5) 
This operation repeats many times and these simulated values 
are multiplied by the detection kennel average to produce a set 
of values of the LISA statistic at the current pixel. This set 
represents a numerical approximation of the probability 
distribution of the LISA statistic, under the assumption of 
spatial independence. Lager probability value indicate large 
negative LISA statistic, corresponding to small values 
surrounded by high values or the reverse. Conversely, small 
probability value corresponds to large positive LISA statistics, 
which indicate cluster of high or low values. 
Then we combine the probability values of the set of every 
band, an S statistics are conducted to summarize for each node 
the information provided by the three bands and to detect target 
pixels. 
s = —r Z *(«; k )^ = Z z ( w; < 6) 
K k=i k=i