The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Voi. XXXVII. Part B6b. Beijing 2008 
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cmM= 
min <J(s+x, t + y) - b(x, y) \(s + x),(l+ y)s£) / ; 
D) 
(2.2) 
In Equations (2.1) and (2.2), D f and £) b are the domains 
of f and b , respectively. For digital image processing, 
function f is input image, function b is structuring element, 
itself a subimage function. At each position of the structuring 
element the values of dilation and erosion at that point are the 
maximum value of (f + b) and minimum value of (f - b ) in 
the interval spanned by b . 
Gray-scale dilation and erosion are duals with respect to 
function complementation and reflection. The general effect of 
performing dilation on a gray-scale image is twofold: 
(1) if all the values of the structuring element are positive, the 
output image tends to be brighter than the input; 
(2) dark details either are deduced or eliminated, depending on 
how their values and shapes relate to the structuring element. 
And for erosion operator, the effect is also dual: 
(1) if all the elements of structuring element are positive, the 
output image tends to be darker than the input image; 
(2) the effect of bright details in the input image that are smaller 
in area than the structuring element is reduced, with the degree 
of reduction being determined by the gray-level values 
surrounding the bright detail by the shape and amplitude values 
of the structuring element itself. 
As the water objects in SAR image represents as some 
consecutive regions consist of pixels with low lightness, we can 
combine the gray-level dilation and erosion to perform gray- 
level closing operator. First perform gray dilation to eliminate 
inconsecutive dark pixels and the water objects were reduced as 
well; and then perform gray erosion to restore the water objects 
without reintroducing the details removed by dilation 
(Easanuruk, 2005; Shih, 1998). 
As the inherent strong speckle noise in SAR imagery, we also 
introduced the order-statistics filters to improve the method 
(Pitas, 1996). Order-statistics filters are nonlinear spatial filters 
whose response is based on ordering (ranking) the pixels 
contained in the image area encompassed by the filter, and then 
replacing the value of the center pixel with the value 
determined by the ranking result. Median filter, as the most 
used order-statistics filter, replaces the value of a pixel by the 
median of the gray levels in the neighbourhood of that pixel 
(the original value of the pixel is included in the computation of 
the median). For certain types of random noise and particularly 
the pulse noise, they provide excellent noise-reduction 
capabilities, with considerably less blurring than linear 
smoothing filters. The speckle in SAR imagery is multiplicative 
noise, and can be reduced by median filter. The max filter and 
min filter are also order-statistics filters. The max filter using 
the 100th percentile results and is useful for finding the 
brightest points in an image. The min filter is the 0th percentile 
and is useful to find the darkest points in an image. They are 
also applicable for water object extraction in SAR imagery. 
In this paper, we combine the gray-level morphology and 
nonlinear order-statistics filter to make the object extraction 
processing more effectively. We define a specific structuring 
element, and transform the gray-level morphology operator to 
nonlinear filter processing. After this, we can employ the 
sequential nonlinear filter to extract water objects in SAR 
imagery. Based on equations (2.1) and (2.2), define D b as 
the N x N neighborhood, and function b as zero function, that 
is its values in domain always are zero. So the equations 
(2.1) and (2.2) can transform to equations (2.3) and (2.4) 
respectively. 
(/e *)(«,/) = 
max{ /0 -x,t-y)\(s- x),(t - y) e £) f , 
(x,y) g J) b } 
(2.3) 
(.f®b)(s,l) = 
min{/(s + x,? + ;)0|(s + x), (t + y)e £) f ; 
(x,y)e £) b ] 
(2.4) 
So we can transform the gray-level dilation processing to max 
filter operator, and gray-level erosion to min filter. In this paper, 
we combine the nonlinear filters to build up a sequential 
nonlinear filter model. First we use max filter to eliminate 
inconsecutive dark pixels in SAR image, and the water object 
with consecutive distribution also be reduced as well. Second, 
we employed the median filter to reduce the speckle noise. 
Finally we use the min filter to restore the water objects which 
were reduced in the first step. In this paper, the size of 
neighbourhood is 3x3. We can also perform the max filter 
several times in series, and perform min filter the same times as 
well. After these steps, we can get water objects in SAR 
imagery and remove almost all the non-water objects. 
Employed this sequential nonlinear filter algorithm, we can 
extract low lightness pixels region effectively, and most of 
these region are water objects. But it also contains some non 
water objects, such as airport, roads, etc. So we need the 
advanced processing to select the water objects from the filter 
results automatically. 
3. WATER REGION MODEL AND WATER OBJECT 
AUTOMATIC SELECTION 
After the processing of sequential nonlinear filter, we can get 
the low lightness targets in SAR imagery. It is necessary to 
mark the targets regions and select the water objects from the