| SAR Imagel | | SAR Image2 | .. "1 SAR ImageN-1 11 SAR ImageN | 
y 
D NLmeans Spatio-Temporal Filtering | 
  
  
  
   
  
    
Reference Image 
calculation 
  
     
  
  
  
  
  
  
  
  
  
      
  
  
  
  
  
  
  
  
[Filtred Image! | | Filtred Image? | *** [ Filtred ImageN-1 | [_ Filtred ImageN | 
| Reference 
Image 
RDR Dual change e 
detection I 
KLR Dual change 
detection 
| Change Mapl | E | Change MapN | | Change Mapl | ses | Change MapN zl 
v v 
  
| DSMT change detection fusion | 
Y 
w Temporal Classification Map | 
v 
Change monitoring 
Figure 1. SAR Change detection and monitoring bloc diagram. 
  
  
2. NL MEANS SPATIO-TEMPORAL FILTERING 
As SAR images are inherently affected by the speckle which 
can be described as a multiplicative noise, the first step 
concerns a spatial and temporal adaptive filter which aims to 
reduce the speckle noise and to maximize the discrimination 
capability between the unchanged and the changed classes. The 
considered filter is based on the same scheme as the Non-local 
means filter [1] by substituting the Euclidean distance with a 
similarity criterion adapted to speckle noise which is the 
Rayleigh Distribution Ratio (RDR). 
The weights [2], depending on the RDR indicator, are based on 
the similarity between a noisy patch that surrounds the central 
pixel and the ones that surround a given neighbouring pixel in 
the spatial and the temporal domain. The filtered reflectivity is 
the given by this expression [10]: 
N a 
y ut.) Au 
: t : 
Rr= (1) 
3 wit, te) 
t 
where w(t, t.’) defines the similarity between patches from ¢ to 
t,’ images, A, is the SAR amplitude and N is the number of 
images in the temporal sequence series. 
This non-local patch-based filter leads to define a filtered image 
for each SAR image of the time series. The filtered and non 
filtered images are then compared to the reference image 
according to suitable change detectors combination in a next 
step. 
3. REFERENCE IMAGE CALCULATION 
The second step of the proposed approach concerns the 
reference image calculation. The reference image corresponds 
to the most stable state of the spatio-temporal patches for a 
given pixel through the Non-local means filter applied in the 
first step. That’s why it is considered as an intermediate image 
throughout the time sequence series and the temporal changes 
will be considered according to this stable state. 
  
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 
   
For the time series SAR images, we calculate this intermediate 
image by extracting , for each pixel, the maximum number of 
the most similar spatio-temporal patches using the NL means 
weights already calculated in the first step. 
The reference image is then calculated starting from the 
original SAR images. However, since the change detector is 
applied on filtered SAR images, the reference image is also 
spatially filtered using the spatial NL means filter. 
4. CHANGE DETECTION MEASURES 
In this paper, we take into account the radar signal features. 
SAR images are inherently affected by the speckle which can 
be described as a multiplicative noise. Indeed, if the intensity / 
follows an exponential law with parameter R, we can write / as: 
F=Rs (2) 
where s defines a random variable following an exponential 
distribution with parameter 1. The same explanation can be 
done with the SAR amplitude by considering a multiplicative 
factor R. Thus, despeckling a radar image comes back to 
suppress the factor s in the equation 2, which is equivalent to 
estimate the reflectivity R in each pixel of the image. Therefore, 
filering radar image intensity will be obtained directly by 
estimating the parameter R, and despeckling radar image 
amplitude will be obtained by considering +/R . 
4.1 Rayleigh Kullback-Leibler measure 
Since the adaptive spatio-temporal NL means filtering (section 
2) reduces considerably the speckle noise without resolution 
loss, the estimated reflectivity R f should describe as close as 
possible the Rayleigh distribution of noisy data. Thus, a 
Rayleigh Kullback-Leibler [3] (RKL) based measure is applied 
in order to detect changes between the generated filtered 
reference image and each filtered SAR image. 
The RKL measure belongs to the local statistics change 
detection family operators and assumes a Rayleigh distribution. 
This symmetric Kullback-Leibler divergence measure is given 
by: 
Im E fig, [ 
Ry Ry, 
Kino RAE G 
where X and Y designate, for a given pixel, the filtered 
reference image and the taken filtered SAR image. 
4.0 RDR measure 
Besides, since the SAR amplitude follows a Rayleigh 
distribution and by using the logarithm of noisy amplitudes 
ratio which can transform the multiplicative speckle noise into 
additive, we apply the Rayleigh Distribution Ratio (RDR) used 
for filtering process as a change detection measure [3]. This 
indicator is given by: 
ALL To pgs Ly ES 
RDRip.p) — 7 > logí 
(khe 
Ay, (5,0). (4) 
Ay, (D) Ay D 
where V defines a neighbourhood for the pixel p or p’ which is 
a window of size w. The RDR operator is then applied on non 
filtered amplitude SAR images.