Interpretation Based on Scattering Models

The next higher level of complexity involves an understanding of the scattering mechanisms present. Van Zyl introduced an unsupervised classifier in which image pixels are assigned to classes of "odd bounce", "even bounce" and "diffuse" scattering mechanisms . This is based upon the principle that scatterers of simple geometrical structure have primarily a co-pol response, but the number of bounces or reflections that the radar signal experiences creates a recognizable phase difference between the HH and the VV channels (the relative phase changes by 180° for every bounce). Van Zyl developed a simple mathematical test to separate each pixel into these three classes van Zyl 1989.

Another set of scattering models based on physical principles was introduced by Freeman and Durden Freeman & Durden. Taking a tree on rough ground as a generic scatterer, the radar energy backscattered by the canopy, the trunk and the ground are modelled and used to categorize naturally occurring scatterers. A mathematical procedure was developed that computed the percentage of each type of scatterer in each pixel. The method is similar to that of van Zyl, except that a physical model is used to separate scattering mechanisms in the data, rather than a purely mathematical rule.

When faced with a large number of measured parameters, classifiers work better if the parameter set can be transformed into an orthogonal set, and the dimensionality of the set reduced to those parameters containing meaningful information (i.e. removing noisy parameters). Eigenvalue methods can be used to advantage, and it is helpful to use scattering models that are independent of the scene content. One of the latest methods of parameter selection is based on an eigenvalue decomposition of the coherency matrix developed by Cloude and Pottier Cloude & Pottier 1996 Cloude decomposition), where the parameters of polarimetric entropy, polarimetric anisotropy and alpha angle are calculated from the eigenvalues and eigenvectors of the matrix.

Entropy (H) represents the randomness of the scattering, with H = 0 indicating a single scattering mechanism and H = 1 representing a random mixture of scattering mechanisms, i.e. a depolarizing target. Values in between indicate the degree of dominance of one particular scatterer. The Greek small letter alpha angle is based upon the eigenvectors and is a number indicative of the average or dominant scattering mechanism. The lower limit of Greek small letter alpha = 0° indicates surface scattering, Greek small letter alpha = 45° indicates dipole or volume scattering, while the upper limit of Greek small letter alpha = 90° represents a dihedral reflector or multiple scattering. Another parameter that provides useful scattering information is anisotropy, a parameter based upon the ratio of eigenvalues, which indicates multiple scatterers.