PSPOLDIS

Description

PSPOLDIS calculates a number of polarimetric discriminators for a fully polarimetric SAR (POLSAR) data set. Polarimetric discriminators are useful to characterize the features in your image by identifying the different types of scattering mechanism. The discriminators are based on the polarimetric synthesis, and describe the polarimetric response of features in the image. These include:

• Minimum and maximum degree of polarization
• Minimum and maximum completely polarized component
• Minimum and maximum completely unpolarized component
• Minimum and maximum received power
• Minimum and maximum scattered intensity
• Coefficient of variation
• Fractional polarization

The orientation and ellipticity angles for the extrema of the completely polarized component are also written to the output file.

Parameters

pspoldis(fili, filo, steppsi, stepchi)

Name	Type	Caption	Length	Value range
FILI*	str	Input polarimetric SAR image	1 -
FILO*	str	Output polarimetric discrimators	1 -
STEPPSI	List[int]	Orientation angle step size (degrees)	0 - 1	1 - 90 Default: 10
STEPCHI	List[int]	Ellipticity angle step size (degrees)	0 - 1	1 - 45 Default: 10

* Required parameter

Parameter descriptions

FILI

Specifies the name of the input polarimetric SAR data set, which must be either non-symmetrized or symmetrized fully polarimetric (quad-polarization) complex data . The input data set must be in covariance, coherence, or Kennaugh matrix format. Since the depolarization effects cannot be inferred from a single-look matrix, most discriminators provide no useful information for single-look complex data and therefore, it is required that the input data set have an equivalent number of looks (ENL) of more than 1, which could be achieved by applying a polarimetric filter (such as boxcar) when the input data set is single-look complex.

The input data set must be in PCIDSK (.pix) format created by SARINGEST or it may be the key file name of any GDB-supported POLSAR data set in its distribution format. For more information and a complete list of supported polarimetric SAR sensors and data products, see the SARINGEST Help.

FILO

Specifies the name of the output file that will hold the polarimetric discriminators. The output file has the same dimensions as the input SAR image, and 16 channels. The output channels contain the polarimetric discriminators stored in the following order (the intensity values are in linear scale):

1. Maximum degree of polarization
2. Minimum degree of polarization
3. Maximum intensity of the of the completely polarized component
4. Orientation angle (psi) at the maximum of the completely polarized component
5. Ellipticity angle (chi) at the maximum of the completely polarized component
6. Minimum intensity of the completely polarized component
7. Orientation angle (psi) at the minimum of the completely polarized component
8. Ellipticity angle (chi) at the minimum of the completely polarized component
9. Maximum intensity of the completely unpolarized component
10. Minimum intensity of the completely unpolarized component
11. Maximum of the received power
12. Minimum of the received power
13. Maximum of the scattered intensity
14. Minimum of the scattered intensity
15. Coefficient of variation
16. Fractional polarization

The specified file must not already exist.

STEPPSI

Optionally specifies the step, in degrees, for the orientation (psi) angle that is used in the search for the minimum and maximum of the polarization response. The specified value must be between 1 and 90 degrees; the default value is 10.

STEPCHI

Optionally specifies the step, in degrees, for the ellipticity (chi) angle that is used in the search for the minimum and maximum of the polarization response. The specified value must be between 1 and 45 degrees; the default value is 10.

Details

PSPOLDIS calculates a number of polarimetric discriminators for a fully polarimetric SAR data set and the corresponding orientation and ellipticity angles. The discriminators are based on the polarimetric synthesis at every image pixel and step size.

Because PSPOLDIS searches for the extrema of the response at every pixel, the processing can take a long time, depending on the number of lines and pixels in the image, and on the step size values. Reducing values of step size for orientation and ellipticity increases the processing time but makes the results more accurate. For example, changing STEPPSI and STEPCHI from the default values of 10 degrees to 5 degrees almost quadruples the processing time, but the determined extrema are accurate to within plus or minus 2.5 degrees.

Example

In the following example, compute polarimetric discriminators for an SLC RADARSAT-2 image that has already been filtered by PSBOXCAR using a 5x5 window. The image is then used as an input to PSPOLDIS with five-degree steps for each angle.

from pci.pspoldis import *

fili="r2_enl25.pix"
filo="r2_enl25_poldis.pix"
steppsi=[5]
stepchi=[5]

pspoldis( fili, filo, steppsi, stepchi )

            

Algorithm

PSPOLDIS computes a number of polarimetric discriminators based on polarimetric synthesis. It uses data in the the Kennaugh matrix format, and the transmit and receive Stokes vectors. At every pixel, the Stokes vectors for the transmitted Ft and scattered Fs waves are related by:

Fs = k * Ft

The non-symmetrized Kennaugh matrix k is shown. For symmetrized data, the matrix K is used.

The wave emitted by the SAR antenna is completely polarized. Its unit Stokes vector (Ft) is defined by its orientation (psi) and ellipticity (chi) angles, as follows:

Ft = Transpose( 1, cos(2*psi)*cos(2*chi), sin(2*psi)*cos(2*chi), sin(2*chi) )

The transmitted wave is partially de-polarized when it scatters from many types of targets. The Stokes vector of the scattered wave can be split into a completely polarized component Fpol and a completely unpolarized component Funpol as follows:

Fs = Fpol + Funpol

The Stokes vectors Fs, Fpol and Funpol can be expressed as follows:

Fs = Transpose( Fs1, Fs2, Fs3, Fs4 )
Fpol = Transpose( p*Fs1, Fs2, Fs3, Fs4 )
Funpol = Transpose( (1-p)*Fs1, 0, 0, 0 )
     sqrt(Fs2^2 + Fs3^2 + Fs4^2)
p =  ---------------------------
                 Fs1

The factor p represents the degree of polarization of the scattered wave. It equals one for a completely polarized wave and zero for a completely unpolarized wave.

The scattered wave is received by the antenna with the polarization Fr. The received power, Pr, is given by:

      1                        1 
Pr =  - * Transpose(Fr) * Fs = - * Transpose(Fr) * k * Ft 
      2                        2

For a fixed transmit polarization, the received power is maximized when the receive polarization is matched to the scattered wave and it is minimized when the receive polarization is orthogonal to the scattered wave; therefore:

           1
(Pr)max =  - * Fs1 * (1+p)
           2
           1
(Pr)min =  - * Fs1 * (1-p)
           2

The extrema of the scattered intensity, Fs1, are given analytically as follows:

(Fs1)max =  k11 + sqrt( k12^2 + k13^2 + k14^2 )
(Fs1)min =  k11 - sqrt( k12^2 + k13^2 + k14^2 )

The coefficient of variation, V, and the fractional power, F, are computed as follows:

    (Pr)min
V = -------
    (Pr)max
    
    (Pr)max - (Pr)min   1 - V
F = ----------------- = -----
    (Pr)max + (Pr)min   1 + V

If required, the input is converted to the Kennaugh matrix format. A symmetrized or non-symmetrized matrix matches the symmetry of the input data set.

PSPOLDIS then loops over all lines and pixels of the input data set. The processing at every pixel proceeds as follows:

• Compute the total power, W, at the current pixel as follows:
  • W = 2 * k11 for the non-symmetrized data
  • W = 2 * ( K22 + K33 + K44 ) for the symmetrized data
• Initialize the extrema as follows:
  • Degree of polarization:
    • pmax = 0
    • pmin = 0
  • Completely polarized component:
    • Fpol_max = Transpose( 0, 0, 0, 0 )
    • Fpol_min = Transpose( W, W, 0, 0 )
  • Completely unpolarized component:
    • Fpol_max = Transpose( 0, 0, 0, 0 )
    • Fpol_min = Transpose( W, 0, 0, 0 )
  • Received power:
    • (Pr)max = 0
    • (Pr)min = W
• Search for extrema:
• For psi, from -90 degrees to +90 degrees, in STEPPSI-degree increments
  • For chi, from -45 degrees to +45 degrees, in STEPCHI-degree increments
    • Derive the transmit Stokes vector Ft with the current values of the psi and chi angles, as shown above
    • Derive the scattered Stokes vector: Fs = k * Ft
    • Derive the degree of polarization p from the elements of the scattered Stokes vector, as shown above
    • Verify all computed parameters against their overall minimum and maximum values, and update the extrema when exceeded. If the extrema of the completely polarized component are updated, the current values of the psi and chi angles are also stored.
• Calculate the extrema of the scattered intensity at the current pixel, Fs1_max and Fs1_min, as shown above
• Calculate the coefficient of variation, V, and the fractional power, F, at the current pixel, as shown above
• Write out all computed discriminators at the pixel.

Depolarization effects cannot be inferred from the SLC data. For such data, only the extrema of the scattered intensity provide meaningful information: (Pr)max = (Fs1)max, (Pr)min = 0. Other discriminators are either zero or one within the rounding errors of computations.

Acknowledgements

PCI Geomatics gratefully acknowledges the financial support provided by the Canadian Space Agency through the Earth Observation Application Development Program (EOADP), contract number 9F028-034946.

References

Touzi R., S. Goze, T. Le Toan, A. Lopes, and E. Mougin. "Polarimetric discriminators for SAR images", IEEE Trans. Geosci. Remote Sensing, 30, no. 5 (1992): 973-980.