Total power is the energy received by all polarized channels of a polarimetric radar system. The total power is proportional to the sum of the diagonal elements of the covariance, coherence, or Kennaugh matrix and can be used to check that the matrices have been computed correctly.
A total-power image is well suited to portraying spatial features, such as edges and homogenous regions that correlate with the spatial distribution of different ground covers. For the same reason, you can use a total-power image as an input to operations that require image segmentation.
Pedestal height represents the amount of unpolarized power and indicates the number of various scattering mechanisms found in a target.
With a target for which the scattered and the backscattered waves are fully polarized, the pedestal height is zero. When the signature is calculated from an average of several targets, and the targets contain multiple, dissimilar scatterers, the pedestal height is greater than zero. The pedestal height is also greater than zero when the received signal is noisy. Higher values mean a higher amount of depolarization.
Pedestal height is well suited to classifying land cover.
The Pauli decomposition is well suited to analysis of high-resolution SAR data, because it operates coherently on the individual pixels. It further characterizes scatterers based on the following physical concepts:
Pauli components are well suited to classifying land cover. Each intensity can be color coded (alpha to R; beta to G; and gamma to B). An RGB display of the intensity of the first three Pauli components is useful for manual interpretation.
The van Zyl method is a model-based decomposition of the covariance or coherency matrix. The method classifies samples or groups of averaged samples as odd-bounce, even-bounce, or diffuse scatterers. The classification is based on the principle that scatterers of simple geometrical structures 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 degrees for every bounce).
A van Zyl classification decomposes the image into primitive reflector types that correspond to elements of objects of interest. Further classification can consist of proximal combinations of those reflector types to identify objects.
The van Zyl classification does not retain information about the nondominant reflection mechanisms for each pixel.
The model-based Freeman-Durden unsupervised classification computes the reflected power contributions of each pixel of a polarimetric SAR image (they must be symmetrized covariance matrices) into Bragg scatter (surface or single-bounce scattering), double-bounce (dihedral-corner reflectors), and random-canopy scatterers (volume, randomly oriented dipoles).
A Freeman-Durden classification can provide a higher-level classification of the image, including model-based classification. Unlike the results of the van Zyl classification, the Freeman-Durden results retain information about the nondominant reflection mechanisms for each pixel.
The three Freeman-Durden parameters can provide a useful color rendition of the information in a polarimetric radar image. You can use Freeman-Durden classification results as the initial classification with an unsupervised Wishart classification.
The Cloude-Pottier method can extract various scattering mechanisms from the coherency matrix. The entropy, alpha angle, and anisotropy, which are related to the physical scattering mechanisms of the terrain, can be computed from the eigenvalues and eigenvectors. The scattering mechanisms are surface, volume, and multiple scattering. The associated eigenvalue represents the relative strength of that scattering mechanism.
You can use a subsequent classification of the image according to a default partitioning, or one you specify, of the entropy, anisotropy, and alpha-angle feature space to classify land cover. If the image data is single-look, operations must be performed on neighborhoods of pixels rather than individual pixels.
You can use a Cloude-Pottier classification as the initial classification with an unsupervised Wishart classification function.
Polarimetric parameters discriminate among various types of scatterers. The polarimetric discriminators are derived from the Kennaugh matrix.
The principle behind polarimetric discriminators is to synthesize transmitted radiation at fine increments of orientation and ellipticity for the polarimetric SAR image pixels, and to calculate the maximum and minimum value for each discriminator quantity at each increment.
You can use polarimetric discriminators to discriminate among targets. Polarimetric discriminators are most useful for analyzing multilook data.
The Touzi decomposition method performs an incoherent target-scattering decomposition on a fully polarimetric (quad pole) data set. Like the Cloude-Pottier incoherent target scattering decomposition, the Touzi decomposition is based on the characteristic decomposition of the coherency matrix. With reciprocal targets, the characteristic decomposition leads to the representation of the coherency matrix as the incoherent sum of three single scatterers each weighted by its normalized and positive eigen value.
A Touzi decomposition uses the Touzi scattering vector model to represent each coherency eigenvector of unique target characteristics. Each coherency eigenvector is characterized uniquely by five independent parameters. Scattering type is described with a complex entity, whose magnitude (alpha_s) and phase (phi) characterize the magnitude and phase of target scattering. The helicity (tau) characterizes the symmetric-asymmetric nature of target scattering. The orientation angle (psi) is the conventional Huynen tilt angle. Target scattering can be characterized by a deep analysis of the parameters of the three eigenvectors.
The entropy (H), anisotropy (A), alpha angle (a), and beta angle (B) parameters perform a partially coherent scattering at each pixel in a fully polarimetric SAR data set. The symmetrized coherency matrix is decomposed into a three-by-three unitary matrix U and a three-by-three diagonal matrix D. The unitary matrix comprises three eigenvectors. Each eigenvector represents an orthogonal scattering mechanism and is specified as a Pauli component. The diagonal matrix has three real, nonnegative elements that represent the eigenvalues of the three scattering mechanisms. The eigenvalues are sorted in a nonincreasing order along the diagonal.
The four parameters are computed from the real eigenvalues and complex eigenvectors in the D and U matrices. The entropy (H, between 0 and 1) characterizes the amount of mixing among the three scattering mechanisms. The entropy H=0 indicates one dominant scattering mechanism with a single nonzero eigenvalue. The entropy H=1 indicates an equal mixture of the three scattering mechanisms with the three eigenvalues equal.
The anisotropy (A, between 0 and 1) characterizes the amount of mixing between the second and third scattering mechanism. The anisotropy A=0 indicates that the two mechanisms are mixed in equal proportions, and that their eigenvalues are equal. The anisotropy value close to 1 indicates that the second mechanism dominates over the third, and that the second eigenvalue is much larger than the third. The anisotropy is set to 0 when both eigenvalues are 0.
Each eigenvector can be parametrized in terms of four angles: alpha, beta, delta, and gamma. The alpha angle (between 0 and 90 degrees) characterizes the scattering mechanism for a given eigenvector. For example, alpha=0 degrees indicates a trihedral scatterer or a smooth surface; alpha=45 degrees indicates a dipole scatterer; alpha=90 degrees indicates a dihedral scatterer.
The beta angle (between 0 and 90 degrees) is twice the preferred orientation angle of the scatterer. The overall values of the alpha and beta angles at each pixel are derived as weighted averages of the values for the three eigenvectors. The weight of each value is computed from its eigenvalue divided by the sum of all three eigenvalues.
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