Based on above analysis, a novel multi-scale Level Set method 
is proposed for automatic extraction of water bodies. Compared 
with single-resolution approaches, employing multi-scale model 
for SAR image segmentation offers several advantages. Firstly, 
multi-scale segmentation is a method considering both global 
information and local information of the image, thus, 
segmentation accuracy is increased. The overall structural 
information of the image can be maintained at coarse scales and 
detailed information can be kept at fine scales. Therefore, 
coarser scale segmentation results can be used as a prior guide 
for the finer scale segmentation, so that not only are the 
statistical properties of the signal-resolution image considered, 
but also statistical variations of multiple resolutions are 
exploited. Secondly, computational complexity is reduced since 
much of the work can be accomplished at coarse resolutions, 
where there are significantly fewer pixels to process. Moreover, 
OTSU algorithm (1979) is introduced to initialize the level let 
functional; this simple technique brings significant 
improvements in speed and accuracy. Finally, post-processing is 
applied to segmentation result for removing some confused 
objects. 
2. PROPOSED METHOD 
In this section, the basic principle of the proposed method is 
outlined in Figure. 1. We acquire multi-scale images at several 
scales by decomposing the SAR image using the block 
averaging algorithm. 
The principal steps of our algorithm are as follows: 
1) Decompose the image into L scales by the block 
averaging algorithm. Let K=L. 
2) Use the OTSU algorithm to initialize the level set 
function of scale L. Go to Step 3). 
3) Obtain the scale-K segmentation result using the level 
set method with the Gamma model. 
4) K-K-l. 
5) IfK--0, return to Step 2). 
Blam t 
p 
Scale I. 
Seat 6 
    
  
Sfc vest 
Figure.1 Basic framework of proposed method 
2.1 Level set method based on gamma model 
Chan and Vese proposed a model that implements the 
Mumford-Shah functional via the level set function for the 
purpose of bimodal segmentation. The segmentation is 
performed by an active contour model without boundaries. Let 
© be a bounded open subset of R?, with dQ being its 
boundary. Let up (x, y) : © — R be a given image, and C be 
a curve in the image domain (2 . Segmentation is achieved by 
the evolution of curve C , which is the basic idea of the active 
contour model. In the level set method, C C is represented 
by the zero level set of a Lipschitz function $: (2 — R ; we 
    
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 
    
replace the unknown variable C by unknown variable @ , 
following Zhao et al. (1996). 
Using the Heaviside function H , and the one-dimensional 
Dirac function dy : defined, respectively, by 
pei fI on EER €* 
zz z)=—H(z t 
pug vt e s 
segmentation is performed by evolving $ such that it 
minimizes the energy functional below: 
F(ci.cs.9) 7 u |, 9G. DIV BO dd 
+ jf, H (g(x, y)dxdy 
&A [ eG) - a HGGs yay 
+ À [ luo Gc y) - € P (1 — H(d(x, y)))dxdy 
(1) 
where ug is the given image, constants C, , C? are the 
averages of ug(x, y) inside C and outside C , respectively, 
and s. v. A x À, are non-negative weighted parameters. 
Function @(x,y) represents class ©, for ÿ>0 , and 
OQ» ford «0. 
For SAR images, the probability density function (PDF) of the 
pixel intensity is often given by a Gamma distribution. In this 
work, considering the speckle noise, we model the image in 
each region R; by a Gamma distribution of mean intensity 1; 
and number of looks L : 
Lug (x) 
L 
L (^ G2 14 or Q) 
uj(L) uj 
  
  
Puy (x) = 
For scale images decomposed by bilinear interpolation, the PDF 
of the pixel intensity is also given by a Gamma distribution. 
This follows from Theorem 1. 
Theorem l: For two given images ug(x) and u(X) , u(X) is 
the decomposed image generated by bilinear interpolation. If 
u(x) is modeled by a Gamma distribution, so is u(x) . Proof 
of Theorem 1 is given in Section 2.2. 
Therefore, the level set functional for SAR images can be 
improved according to Equation (6) as follows: 
F(o.P1.P2)= | VH(@dsdy +v| H(p)dsdy 
=n [| H(p)log Pedy G) 
- A5 [ (1- H(p)) log p,dxdy 
The evolution of $ is governed by the following motion partial 
differential equation: 
ô V 
2s, 9) TE v log p,(y|0,) + 4; logp; (3102) 4) 
where J, (¢) is a regularized version of the Dirac function.