CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation 
152 
combination of wavelets and curvelets. A total variation based 
segmentation algorithm divides the image in structured regions, 
that are subsequently denoised by a curvelet-based method, and 
homogeneous regions, denoised by a wavelet approach. For large 
scenes with different land cover types, this method seems to be 
very promising. As we concentrate on urban applications in this 
paper, we use a purely curvelet-based approach. 
Change detection in SAR images being a very difficult task has 
often been discussed in literature. An overview to principal SAR 
change detection methods, their advantages as well as their dis 
advantages can be found in (Polidori et al., 1995). Some more 
specialized methods are touched in the following. The approach 
of (Balz, 2004) uses a high resolution elevation model (e.g. ac 
quired by airborne laserscanning) to simulate a SAR image which 
is subsequently compared to the real SAR data. The quality of the 
results is naturally highly dependent on the resolution of the digi 
tal elevation model and its co-registration to the SAR image. This 
nontrivial co-registration constraints this approach to small scale 
exemplary applications. Another idea starting with the fusion of 
several SAR images of different incidence angles to a ’’superreso- 
lution” image is presented by (Marcos et al., 2006) and (Romero 
et al., 2006). Man-made objects, i.e. geometrical particularities 
that are not captured by the digital terrain model used for the or 
thorectification of the SAR image, are classified by their diverse 
appearance in the single orthorectified images due to the different 
acquisition geometries. So, seasonal changes in natural surround 
ings can easily be distinguished from changes in built-up areas. 
One disadvantage is the large number of different SAR images 
of the same area needed to generate the ’’superresolution” image. 
(Wright et al., 2005) exploits the coherence (phase information) 
of two SAR images, which implies a relatively short repeat-pass 
time to avoid additional incoherence caused by natural surfaces. 
(Derrode et al., 2003) and (Bouyahia et al., 2008) adopt a hidden 
and a sliding hidden Markov chain model respectively to select 
areas with changes in reflectivity even from images with differ 
ent incidence angles. Although this method allows to process 
very large images and does not need additional parameter tun 
ing, except the window size, according to the authors still a lot of 
research work has to be done to improve the preliminary results. 
3 CURVELET REPRESENTATION 
The curvelet representation consists of three components accord 
ing to (Candes and Donoho, 1999): 
Ridgelets These two dimensional waveforms are the basic ele 
ments of the curvelet representation. In the spatial domain, 
they appear like a ridge or a needle (see Fig. 1); in the 
curvelet domain their contribution to the original image is 
(a) Spatial domain 
(b) Curvelet coefficients 
Figure 2: City center of Munich, imaged by TerraSAR-X, High 
Resolution Spotlight mode, Polarisation VV, Spatially Enhanced 
Multi Look Ground Range Detected product 
measured by a coefficient. The magnitudes of the ridgelets 
extracted from Fig. 2(a) are depicted in Fig. 2(b) by gray- 
values. Bright pixels mark high magnitudes. In contrast 
to wavelets, curvelets are additionally defined by their ori 
entation in the two dimensional space (Ying et al., 2005). 
Hence, this is a method of image analysis suitable for image 
features with discontinuities across straight lines. 
Multiscale ridgelets As the decomposition into ridgelets is de 
pendent on the scale, a pyramid of windowed ridgelets is 
used, renormalized and transported to a wide range of scales 
and locations. For example, a ridgelet on the finest scale 
(N4-neighborhood) can only be horizontally or vertically 
oriented, i.e. two different orientations, while a ridgelet on 
the next coarser scale has already twice as much, i.e. four 
different orientations. Consequently, the resolution in ori 
entation increases with coarser ridgelet scales. The number 
of directions is given by the formula 2 subband . For redun 
dancy reduction a wavelet decomposition is commonly used 
on the finest scale, where only horizontal and vertical direc 
tions are discriminable anyway (Candes et al., 2005). The 
different scales appear in Fig. 2(b) as single rings, whereas 
the outer rings show the finer scales. The gaps between the 
rings are just for visualization.