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