# 3D Monitoring of Buildings Using TerraSAR-X InSAR, DInSAR and PolSAR Capacities
## 5 Polarimetric Analysis
### Benefit of Polarimetry for Building Monitoring  
#### 5.2.1 Main Investigation: Orientations and Materials  
Most polarimetric classification methods rely on the study of second-order parameters, estimated from several statistical samples.  
Generally, a spatial estimation is made by choosing the samples either in an immediate neighbourhood or in other areas of the image. Recently, it has been demonstrated that for metric resolution images, a polarimetric spatial estimation, even if carried out carefully, leads to a very high entropy, whereas temporal estimation makes it possible to find low entropies on bright point-like scatterers [21]. This means that for these pixels, only a temporal estimation is able to characterize the scattering process on a deterministic point of view. Since we are interested in parameters for industrial structures, or building elements, we restrain the analysis of these deterministic processes.  
Two properties are of interest in the analysis of structures and their possible deformation:  
* The orientation of buildings. Indeed, our measurements of local deformations on buildings presuppose that this deformation is mainly in the vertical direction. However, if a scattering structure element has a different orientation, the axis of deformation will also be different. It is interesting firstly to be able to identify these cases and in a second step to use this information to project the measured deformation in the structure direction.
* Building materials. Again, this is crucial for a potential deformation measure: the effects of thermal expansion which seems to be predominant deformation effect measured with DInSAR data, depend on the material.  
Several studies are concerned with the contribution of polarimetry to the evaluation of these characteristics. In particular, the potential of polarimetry to extract orientation and dielectric properties of individual coherent scatterers has been investigated in [30]. However, up to now, due to the lack of real polarimetric data at high resolution, they mainly concern simulation [31]. Generic behaviours were deduced, in particular the backscattering seems to be sensitive to the dielectric permittivity of the buildings [32].  
Several deterministic approaches are possible, for example but not exhaustive, Huynen parameters, [PERSON]'s classification, or research efforts in optical ellipsometry, for example polar decompositions. The later are interesting because they do not consider the metallic hypothesis: they are adapted equally well to dielectric structures, which is not the case for the first two which more specifically address the geometry of the PEC targets and do not take into consideration the effects on materials. Note that ellipsometry has been more applied to surface scattering, but has already been used frequently to determine the effects of orientations, such as those present in biological tissue fibers [33].  
Therefore, in order to investigate the potential of polarimetry in the characterization of deformations, our approach is as follows:  
* First, the both polarimetric acquisitions have been co-registered together at a sub-pixel precision, using [34].
* For each pixel, we applied to the Sinclair matrix the polar decomposition described in [35], to be able to describe diattenuation and retardance properties. Diattenuation concerns only the change in the amplitudes of the components of the electric field vector, whereas the retarder changes only the phases of components of the electric-field vector.  
* We extract the two main parameters, retardance and diattenuation, as well as the orientation of the axes of the two main Stokes vectors (maximum retardance axis and maximum diattenuation axis).  
The resulting parameters are analyzed for the four available polarimetric images.