The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
A first rough estimate for the height h of the bridge (knowing 
the altitude of the sun cp) is achieved by simply measuring the 
length of the shadow 5 in the image (Equation 2). 
h = tan(#?) • 5 (2) 
3.2 Displacement of elevated objects in SAR imagery 
In SAR imagery, the ortho-rectification process leads to similar 
effects as in optical imagery. Elevated objects stay distorted in 
the image if they are not included in the DEM the image is 
rectified with. However, the lasting distortion is more severe 
because SAR sensors acquire imagery with high off-nadir 
angles. Additionally, the SAR technique consists of measuring 
distances and hence the bridge body is imaged closer to the 
sensor than the bottom end of its pillars (layover effect). 
Therefore, three-dimensional objects that are not accounted for 
during the ortho-rectification process show more distortion than 
in corresponding optical data. This effect can be exploited in 
order to obtain height values of elevated objects both from a 
single SAR image and from combined optical and SAR imagery. 
Figure 6: SAR image of the railroad bridge near Zellingen 
acquired with the airborne MEMPHIS sensor in ka-Band 
(illumination direction from top to bottom), (top) SAR image 
ortho-rectified with DEM, (centre) bridge distortion becomes 
obvious compared to the parallel red lines, (bottom) the blow 
up of the centre image shows that the bridge distortion follows 
the terrain undulation 
In Figure 6, a high resolution SAR image of the Zellingen 
bridge scene, already shown in optical imagery in Figure 4 and 
Figure 5, is displayed. It was acquired in Ka-Band by the 
airborne sensor MEMPHIS, like the images shown in Figure 2. 
The bridge appears particularly bright in the image because it is 
a railroad bridge. Strong backscattering and multiple bounce 
effects occur at the steely railroad tracks and at the 
superstructure of the bridge. Occluded areas due to the bridge 
body and the pillars can nicely be seen. This shadowing effect 
can be exploited for several purposes. First, the shadow 
distinguishes a three-dimensional object from a two- 
dimensional object. Hence, a shadow is helpful for a 
classification and detection process in order to distinguish 
between roads (2D) and bridges (3D). Second, the shadow can 
be used in order to derive bridge height estimates directly from 
a single SAR image as it will be explained in detail in the 
following paragraph. 
3.3 Bridge height estimation from a single SAR image 
Assuming a flat wave front as well as locally flat terrain, the 
height of an object imaged by a SAR sensor can be directly 
derived from the image. Figure 7 displays the basic SAR 
imaging principle. Let object P with elevation h be the railroad 
bridge from Figure 6. Its true horizontal position on the ground 
is P\ The SAR sensor (SAR) acquires the scene with incidence 
angle cq. Due to the distance measuring radar technique, object 
P is imaged to point PS in the SAR image. Since the bridge top 
P is closer to the sensor than P’, it comes to a layover effect, i.e., 
P is imaged closer to the sensor (to point PS) than P\ Hence, 
the distance between P’ and PS is due to layover. 
SAR 
Figure 7: Height estimation of an elevated object from a single 
SAR image 
Elevated Object P not only leads to layover but also to 
occlusion. It occludes the entire area between P’ and POC 
leading to a shadowing effect. This occluded area between P’ 
and POC corresponds to the shadow of one of the bridge pillars 
in Figure 6. In case the true bridge position P’ is known, a 
simple Pythagoras formula (3) can be applied in order to obtain 
an estimate for the height h of the bridge. 
h = jPQCP'-P'PS (3) 
However, the true bridge position P’ may not always be known 
and the bridge height has to be determined directly from the 
distance between POC and PS (D). Knowing the depression 
angle di (= 90° - off nadir angle 0i) of the SAR sensor, the 
bridge height can then be obtained with trigonometric formulas 
(7). 
POC P' = h/tan a x (4) 
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