Classification of Fully Polarimetric SAR Data

Abstract - Based on the principles outlined in the previous chapters a couple classification approaches for fully polarimetric SAR data can be derived, of which some are outlined in the following sections. This part is basically taken from my thesis [Hellmann2000]. In this treatment I only try to outline some polarimetric approaches. It's neither meant to be complete nor exhaustive. It's merely to give you an idea how polarimetry can be used for classification purposes. Therefore, I don't go much into details about the use of advanced classification algorithms like artificial neural networks because it's beyond the scope of this tutorial. I will also not talk to much about the validation and accuracy

For the analysis discussed in this treatment we choose the test area of Oberpfaffenhofen, Germany. Keywords: classification, decomposition theorems

The Entropy - $\alpha$ Feature Space

As discussed in the previous chapter, we may derive two features, well suited for classification purposes, from fully polarimetric SAR data sets; the entropy H and the $\alpha$ - angle. As outlined earlier the entropy can be related to the amount of effective scattering mechanisms, while the $\alpha$ - angle can be interpreted as the type of scattering. By combining the two features we can form a two - dimensional feature space. Any feature vector located within this feature space can then be assigned to a physical scattering mechanism, as shown in Fig. 5.1 [Cloude95].

Figure 5.1: H - $\alpha$ - feature space with physical scattering mechanisms [Cloude95]

This is an important property for classification purposes, since it provides physical information about the geometry of the scatterers on ground, without additional a priori information. This property makes polarimetric classification approaches superior to conventional (e.g. texture classifiers) methods, which are dependent on a priori knowledge, like ground truth measurement, in order to train the algorithms.

By relating the physical scattering mechanisms to cartographic objects we can now build a classifier for cartographic purposes, which is unsupervised, independent of a priori knowledge and suitable for automation. Some classification algorithms based on these principles were developed in the frame of this thesis and shall be discussed in the following.

In order to derive a classification for cartographic applications we have to relate the physical scattering mechanisms to cartographic objects. To get this relation we have to consider how the waves interact with cartographic relevant objects or object classes, like forest, buildings, water etc. and how the properties of the wave changes under the scattering process. As discussed in chapter 3 we are only able to separate such classes from another, if the classes have a different behavior with respect to the analyzed features. This means the classes should tend to form clusters in the feature space. This means that different classes should have different scattering properties. Considering these restrictions, with respect to the desired classes, we find, that higher wavelengths like L-band are better suited for the separation of medium vegetation (bushes) and forest. C-band for example is not able to distinguish between bushes and forest, since , due to the limited penetration depth, the scattering process in forest takes place only in the canopy and does not differ significantly from the scattering process in bushes. Therefore C-band may give additional information but is not suited for our task, if applied alone.

Classification Approaches

The classification approaches described in the following have the advantage, that they are (at least in theory ;o) the data set independent. This is due to the fact, that polarimetric classification approaches evaluate the scattering mechanisms the basic classification rules apply to any data set of the same frequency. Only the different resolution of different sensors (e.g. SIR - C 25 x 25 meters, E - SAR 3 x 3 meters) leads to different numbers of classes for different sensors. E.g. small line like structures like roads and rail tracks are not clearly detectable in the space borne (e.g. SIR-C) data.

H - $\alpha$ classification

For the first approach we use a fully polarimetric SIR-C L-band data set. With respect to the given resolution of 25 meters by 25 meters, we can separate four the cartographic relevant classes: settlements, forest, low vegetation and water as follows:

• Zone 1: Low Entropy Surface Scatter (water)
  In this zone occur low entropy scattering processes. These include Geometrical Optics (GO) and Physical Optics (PO) surface scattering, Bragg surface scattering and specular scattering phenomena [Ulaby86] which do not involve $180^o$ phase inversions between $HH$ and $VV$. Physical surfaces such as water at L- and P-bands, sea-ice at L-band, as well as very smooth land surfaces, fall into this category.
• Zone 2: Low Entropy Multiple Scattering Events (buildings and man made structures)
  This zone corresponds to low entropy double or 'even' bounce scattering events, such as provided by isolated dielectric and metallic dihedral scatterers. The upper entropy boundary for this zone is chosen on the basis of tolerance to perturbations of first order scattering theories (which generally yield zero entropy for all scattering processes). By estimating the level of entropy change due to second and higher order events, tolerance can be built into the classifier so that the important first order process can still be correctly identified. Note also that system measurement noise will act to increase the entropy and so the system noise floor should also be used to set the boundary. H = 0.5 is chosen as a typical value accounting for these two effects.
• Zone 3: High Entropy Multiple Scattering (forest)
  In this region region we can still distinguish double bounce mechanisms in a high entropy environment. Such mechanisms can be observed in forestry applications or in scattering from vegetation which has a well developed branch and crown structure.
  
• Zone 4: Medium Entropy Surface Scatter (low vegetation)
  This zone reflects the increase in entropy due to changes in surface roughness. In surface scattering theory the entropy of low frequency theories like Bragg scatter is zero. Likewise, the entropy of high frequency theories like Geometrical Optics is also zero. However, in between these two extremes, there is an increase in entropy due to the physics of secondary wave propagation and scattering mechanisms. Thus as the roughness/correlation length of a surface changes, its entropy will increase. Further, a surface cover comprising oblate spheroidal scatterers (leafs or discs for example) will generate a high entropy. This class contains mainly different types of surfaces or dipole scatterers.

We used a hyper-box classifier for this approach. The location of the boundaries are based on knowledge of the scattering processes which occur on the different objects as well as on the knowledge of Radar calibration, measurement noise floor, variance of parameter estimates etc. Regarding the result of this classification (Fig. 5.2), we can see, that these boundaries, although rather simply chosen, do offer sensible segmentation of experimental SAR data.

Figure 5.2: H - $\alpha$ classification result using hyper-boxes,(L-band) SIR-C data set, Oberpaffenhofen, Germany

The segmentation of the H-$\alpha$ space with hyper-boxes was merely done to illustrate our classification strategy and to emphasize the geometrical segmentation of physical scattering processes. Since no additional information but those contained in the data itself is used, it is suited for an unsupervised, data independent approach to the target classification problem. Nonetheless, it is desirable to have more flexible boundaries than the rather crude hyper-box borders. In order to achieve this a rather simple feed forward neural networks or fuzzy logic methods, can be applied [Hellmann2000].

J.S. Lee Approach

Based on the entropy - $\alpha$ - decomposition, Lee presented an unsupervised approach in 1998 [Lee98].

For this approach an initial segmentation of the entropy - $\alpha$ - feature space is performed as outlined [Cloude97] and is used as an initial classification. The result of this classification is then used as initial training sets for a maximum likelihood classifier based on the Wishart distribution of the polarimetric covariance matrix [Lee94a]. The classified results are then used as training sets in order to compute new distance measures which are used for the next iteration. The iterations are performed until the number of pixels switching between the classes becomes smaller than a defined limit or a maximum number of iterations is reached.

This automated approach, providing information about the inherent scattering characteristics for terrain identification, is very sophisticated, but still the results are not yet sufficient for the creation of large scale topographic maps. A reason for this is, as discussed in the previous section, the problem that different cartographic objects, like water and road like structures, have the same (surface) scattering behavior and can therefore not be separated satisfyingly. This means that we have to use additional information in order to resolve this ambiguity, as shown in the following sections.

Entropy / $\alpha$/ Anisotropy Approach

A pure polarimetric classification, based on the entropy - $\alpha$ approach, was presented by Pottier [Pottier98b]. As described in a previous section the entropy H feature provides information about the amount of scattering mechanisms within a resolution cell. For low or medium entropy ( $\lambda_1 > \lambda_2 , \lambda_3$), however, the entropy yields no information about the relation between the two minor eigenvalues $\lambda_2 , \lambda_3$. In that case the anisotropy A contains additional information, as discussed in previously. For classification purposes Pottier proposed the use of a feature vector I [Pottier98b]

$$\vec{I} = \left[ \begin{array}{c} \bar{\alpha} HA H(1-A) (1-H)A (1-H)(1-A) \end{array} \right]$$ (5.1)

Where the $\bar{\alpha}$ feature contains the information about the scattering mechanism while the features derived from the Anisotropy A and Entropy H {HA, H(1-A), (1-H)A, (1-H)(1-A)}, shown in Fig. 5.3, yield information about the type of scattering process.

Figure 5.3: Features derived from the Anisotropy A and Entropy H, calculated from a L-band E-SAR data set from the test site Oberpfaffenhofen, Germany

Fig. 5.3 is not actually a classification but visualizes the additional information content of the anisotropy. The approach is described in detail in [Pottier98a], [Pottier98b] and shall not be discussed further in this treatment.

H-$\alpha$-$\lambda _1$ Approach

As discussed above, for the creation and updating of large scale topographic maps, the $H$-$\alpha$ parameters alone do not provide a sufficient interclass resolution [Hellmann97], therefore additional information is needed. In the previous section we showed, that the backscatter intensity information contained in the eigenvalues may provide such additional information. The pure entropy - $\alpha$ approach has a limited interclass resolution and the eigenvalue approach, described in the previous section lacks the information about the type of scattering. Therefore we developed a combination of both. For this approach we used the entropy and $\alpha$ parameters as well as the 1st eigenvalue $\lambda _1$. The images of the 3 parameters are shown in Fig. 5.4 for the E-SAR data set. It turned out, that the first eigenvalue is sufficient to get a good interclass resolution and therefore, the 2 other eigenvalues $\lambda_2$ and $\lambda_3$, which are already contained in the entropy parameter need not to be applied. In spite of the magnitude image of one chanel the image of the 1st eigenvalue has the advantage, that it has the same geometry as the entropy and $\alpha$ image, which is, due to the windowed calculation of the entropy and $\alpha$-angle, not the case for the magnitude images of the 4 channels. The eigenvalues have to be computed for the calculation of the entropy and therefore do not cause any additional computational effort. The additional information about the backscatter intensity is mainly useful for interclass resolution improvement in the areas where surface scattering occurs. Namely to discriminate between the classes of low vegetation, road like structures and water. In this areas we expect a dominant 1st eigenvalue $\lambda _1$ and therefore the remaining 2 other eigenvalues $\lambda_2$ and $\lambda_3$ can be neglected. With the additional information of the 1st eigenvalue $\lambda _1$ a better interclass resolution can be achieved due to the different reflectivity of different groups of scatterers. In the first step the different classes are separated by the analysis of their backscatter intensity.

Figure 5.4: H (left), $\alpha$ (middle) and $\lambda _{1}$ (right) images for the E-SAR data set, L-band, Oberpfaffenhofen airfield

For the airborne E-SAR data (Fig. 5.4) the analysis of $\lambda _1$ enables us to separate 5 groups:

• very high backscatter :
  This class contains buildings and corner reflectors.
• high backscatter :
  In this class we can find forest.
• medium backscatter :
  This class consists of medium vegetation (e.g bushes/ sweet corn) and fresh ploughed fields.
• low backscatter :
  This class contains low vegetation (e.g. grass).
• very low backscatter :
  This class consists of very smooth surfaces (e.g. runway and taxiways of the Oberpfaffenhofen air field, water and harvested fields.

In the second step these areas are identified using their scattering properties which can be interpreted with the $H$-$\alpha$ parameters. This classification leads to 6 classes for the E-SAR data set as shown in Fig. 5.5:

Figure 5.5: Classification result, E-SAR data set, Oberpaffenhofen test site, buildings(white), forest(grey), medium vegetation (dark grey), low vegetation (very dark grey)road like structures and harvested fields (pale grey), ploughed fields (black)

• buildings :
  Very high values for $\lambda _{1}$, low or medium entropy and high values for the $\alpha$-angle
  This is due to the fact that man made structures show a high backscatter intensity and only one (or two) dominant scattering process of double bounce behavior.
• forest :
  High values for $\lambda _{1}$, high entropy and high values for $\alpha$
  The trees have a quite good reflectivity, the entropy is high because all kinds of scattering processes takes place (e.g. volume scattering in the canopy, double bounce scattering at the trunks and surface scattering at the ground).
• medium vegetation :
  Medium values for $\lambda _{1}$, medium entropy and low or medium values for $\alpha$
  In such areas the surface scattering process is dominant but a second one (resulting from the interaction with the vegetation) - even if much lower - is present.
• low vegetation :
  Low values for $\lambda _{1}$ low entropy and low values for $\alpha$
  Over low vegetation mainly surface scattering processes appear but the vegetation layer contributes a small additional scattering mechanism.
• smooth surfaces (roads, runway taxiways, and harvested fields, water):
  Very low values for $\lambda _{1}$, low to medium entropy and $\alpha$ values
  Over smooth surfaces also mainly surface scattering processes appear, but since the signal is reflected away from the sensor, the backscatter intensity is very low and the Signal to Noise Ratio (SNR) is degraded, which results in an increase of the entropy and $\alpha$ values.
• ploughed fields:
  Medium values for $\lambda _{1}$, low entropy and low values for $\alpha$
  This fields show also surface behavior, as expected, but due to the roughness more energy is reflected towards the sensor and the backscatter intensity is higher than for non ploughed fields.

As shown above this method provides a good interclass resolution as well as a good classification accuracy. It could be shown that this algorithm is suitable for an unsupervised classification approach.