running at 3.07 GHz with 2.99GB of RAM and a Windows- 
based operating system. 
In our proposed method, there are three main parameters we 
need to consider; these take values that depend on image type 
and scale. Parameter « is the coefficient of regularization term, 
which controls the boundary smoothness of the segmented 
image. After some experiments, we found that for large size 
images (over 1000x1000 pixels), segmentation based on the 
level set method with SDF converged poorly, sometimes with 
no solution being reached even after several thousand iterations. 
Thus, the variable parameter method is introduced for large 
images. The specific strategy is to increase & by small amount 
every certain iteration. According to Theorem 1, it can be seen 
that the scale image is also modeled by a gamma distribution 
with four times larger image looks. So we suppose that the 
parameters in the coarser image are four times smaller than 
those in the finer image. The parameter v is set to zero always, 
that is, we don't restrict the area of each region. Specific 
parameter values are given in Table 1. All values were chosen 
empirically. 
3.1 Experiment on SAR imagery 
Figure 2 shows a real SAR image and its extraction results. 
Figure 2 (a) shows a famous image acquired from the website 
http://www.sandia.gov/radar/images/dc_big.jpg is a part of a 
Ku-band SAR image. The size of the . image 
is 2000 x 810 pixels, with 1-m spatial resolution in the area of 
Washington, D.C., USA. There are three types of land cover: 
water, road, building and bare land. In general, the actual 
positions of boundaries within a SAR scene are unknown. So, 
the segmentation quality measures are modified to allow 
comparison of the automatic segmentation approaches with 
manual segmentation, as illustrated in Figure 2(b). Figure 2(c)- 
(e) shows the extraction result generated by ALGI, ALG2, 
ALG3, respectively. In Figure 2(f), we show the extraction 
result obtained by proposed method, and figure 1(g) shows the 
result after post-processing. It can be clearly seen that our 
method performance a better result. Detailed comparisons of 
accuracy and efficiency are given in Table I. 
  
(b) 
    
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012 
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia 
    
  
Figure.2 Water extraction result 
3.2 Quantitative evaluation 
In order to calculate the accuracy, assuming that the size of an 
original SAR image is M x N , we denote the label image 
obtained by segmentation as X , whose size is also M xN. 
Correspondingly, A represents the label image from manual 
segmentation (it also indicates an ideal segmentation) for the 
same original SAR image. The error image is therefore defined 
as E- X — R. In order to compare the performance of the 
above methods, a measurement that evaluates the accuracy of 
segmentation, called the percent of error pixels ( pep ), 1s 
defined by Gao et al. (2008) as: 
/ 
z — —— x1009^6 (7) 
pep MxN