PSSSCM

Description

PSSSCM performs a target classification, based on the symmetric scattering characterization method (SSCM), in a fully polarimetric SAR (POLSAR) data set. For coherent symmetric point targets, the method derives a number of characteristics that describe their properties. The scattering matrix is decomposed such that specific scattering mechanisms (trihedral, dihedral, dipole, cylinder, and narrow dihedral) can be recognized in their received signals.

Parameters

pssscm (fili, file, winsize, clutn1, clutn2, dost, doct, scrt, angletyp, filo)

Name	Type	Caption	Length	Value range
FILI*	str	Input polarimetric SAR image	1 -
FILE	str	Input coherent targets bitmap	0 -
WINSIZE	List[int]	Window size (pixels)	0 - 1	3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 33 Default: 5
CLUTN1	List[int]	Clutter window overall width (pixels)	0 - 1	3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 | 33 Default: 11
CLUTN2	List[int]	Clutter window cut-out width (pixels)	0 - 1	3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | 25 | 27 | 29 | 31 Default: 3
DOST	List[float]	Degree of symmetry threshold	0 - 1	0.0 - 1.0 Default: 0.924
DOCT	List[float]	Degree of coherence threshold	0 - 1	0.0 - 1.0 Default: 0.8
SCRT	List[float]	Signal-to-clutter ratio threshold (decibels)	0 - 1	0 - 50 Default: 15.0
ANGLETYP	str	Angle units	0 - 6	Degrees | Radians Default: Degrees
FILO*	str	Output scattering characteristics raster	1 -

* Required parameter

Parameter descriptions

FILI

The name of the input polarimetric SAR data set, which must be non-symmetrized or symmetrized fully polarimetric (quad-polarization) single-look complex data. The input data set must be in the scattering-matrix format.

The input data set must have already been imported into the PCIDSK (.pix) format with SARINGEST. Input can also be the key-file name of any GDB-supported POLSAR data set in its distribution format. For more information, including a complete list of supported SAR sensors and data products, follow the link to SARINGEST at the end of this topic.

FILE

The name of a file containing coherent point targets. The file must have the same dimensions as the input polarimetric SAR image and at least one bitmap. The "on" pixels in the first bitmap represent locations of the coherent pixels. The value of FILE can be the same as that of FILI, provided it contains the expected bitmap segment. If FILE contains several bitmap segments, the first segment will be used. These coherent point targets can be prepared manually (by analysis of the total power image) or automatically by running PSWHITE.

This parameter is optional.

WINSIZE

The window size for pixel averaging. The value you specify must be an odd integer between 3 and 33; the default value is 5. This parameter defines the size of the window to compute the degree of coherence for distributed targets.

This parameter is optional.

CLUTN1

The overall size of the clutter window, in pixels, that determines the target clutter. The value you specify must be an odd integer between 3 and 33; the default value is 11. It defines both the horizontal and vertical size of the clutter window. This parameter is ignored when the coherent targets are provided.

This parameter is optional.

CLUTN2

The size of the center gap in the clutter window. The value you specify must be an odd integer between 1 and 19; the default value is 3. The value must be smaller than the overall width of the clutter window. This parameter is ignored when the coherent targets are provided.

This parameter is optional.

DOST

The threshold for the degree of symmetry. The value you specify must be a floating point between 0.0 and 1.0; the default value is 0.924. This parameter is ignored when the coherent targets are provided. Pixels are considered to represent symmetric scattering when their degree of symmetry is higher than this threshold.

This parameter is optional.

DOCT

The threshold for the degree of coherence. The value you specify must be a floating point between 0.0 and 1.0; the default value is 0.8. Pixels are considered to be coherent when their degree of coherence is higher than 0.8. This parameter is ignored when the coherent targets are provided.

This parameter is optional.

SCRT

The threshold for the signal-to-clutter ratio, in decibels. The value you specify must be a floating point between 0.0 and 50; the default value is 15. Typically, point targets are considered coherent when they are significantly brighter (>15 dB) than the surrounding clutter. You can adjust the cut-out value for when a target is to be considered coherent by adjusting the signal-to-clutter ratio threshold. This parameter is ignored when the coherent targets are provided.

This parameter is optional.

ANGLETYP

The angle units, either degrees or radians, for the output characteristics that are angular measurements. The default value is Degrees.

This parameter is optional.

FILO

The name of the output file to which to write the scattering characteristics.

The file name you specify must not already exist. The output file will have the same dimensions as the input SAR image, but with six floating-point channels and a bitmap. The bitmap shows the locations of coherent targets. The six channels contain SSCM characteristics as described in the Details section, later in this topic.

Details

PSSSCM performs target classification based on the symmetric scattering characterization method (SSCM). The algorithm uses symmetric scattering targets and extracts a number of characteristics about them from the input SAR image. SSCM is an extension of the Cameron decomposition for the coherent symmetric scatters.

With SSCM analysis, targets must be symmetric and coherent. Coherent targets can either be provided or found automatically. When no targets are provided, PSSSCM will be applied to the input SAR image to find coherent targets. Using a moving window, defined by the overall and cut-out width of the clutter window, pixels are determined to be targets using the thresholds defined by the degree of symmetry, degree of coherence, and signal-to-clutter ratio thresholds. After determining coherent targets, the algorithm computes characteristics for each target.

The six channels that are output represent the following SSCM characteristics:

1. Degree of coherence
2. Scattering-vector direction (eta)
3. Phase difference (phi) between the target and a copolarized signal
4. Target sphere angle (psi)c, which is the maximum polarization orientation relative to the horizontal
5. Target sphere angle (chi)c, which is the maximum ellipticity relative to the linear
6. Rotation angle (psi)

Only the degree of coherence values is computed for all pixels in the image. The other five characteristics are computed only at the coherent and symmetric target locations, because only at those locations is it appropriate to apply this method.

The output target sphere angles can provide insight about the objects in the original SAR image. Different objects scatter the radar pulse differently, and some conclusions about the objects can be drawn by examining the angles in the output file. The target sphere angles relate a scatterer to the elemental symmetric scatterers as follows:

        +========================+===========+===========+
        |   Elemental symmetric  |  (psi)c   |  (chi)c   |
        |        scatterer       | [degrees] | [degrees] |
        +========================+===========+===========+
        |  Trihedral             |      0    |      0    |
        |  Dihedral              |     90    |      0    |
        |  Dipole                |     45    |      0    |
        |  Cylinder              |  18.43    |      0    |
        |  Narrow dihedral       |  71.57    |      0    |
        |  Quarter wave          |    N/A    |  +/-45    |
        +========================+===========+===========+
      

Examples

Perform the SSCM analysis of a SIR_C data set. The input SIR-C SLC-Q data set is already imported into the PCIDSK format. The coherent targets bitmap is prepared in advance by thresholding the total power image and manually editing the resulting bitmap. All other parameters have default values.

from pci.pssscm import *

fili	=	"sir_slc.pix"
file	=	"sir_slc.pix"
winsize	= []
clutn1	=	[]
clutn2	=	[]
dost	=	[]
doct	=	[]
scrt	=	[]
angletyp	=	""
filo	=	"sc_sscm.pix"

pssscm( fili, file, winsize, clutn1, clutn2, dost, doct, scrt, angletyp, filo )
      

In the following example, perform the SSCM analysis of an SLC RADARSAT-2 image in the distribution format. For more robust results, use the coherent targets detected automatically, larger window sizes, and increased thresholds.

from pci.pssscm import *

fili	=	"product.xml"
file	=	""
winsize	= []
clutn1	=	[13]
clutn2	=	[5]
dost	=	[0.999]
doct	=	[0.85]
scrt	=	[40]
angletyp	=	""
filo	=	"r2_sscm.pix"

pssscm( fili, file, winsize, clutn1, clutn2, dost, doct, scrt, angletyp, filo )

      

Algorithm

SSCM is an extension of the Cameron decomposition for symmetric coherent targets. It maps symmetric scatterers onto one half of the unit Poincare sphere, which provides a more complete representation of scatterers. PSSSCM also verifies the symmetry and coherence of the targets.

SSCM is a complex processing algorithm and requires the following initial definitions.

Pauli components

The four elements of the non-symmetrized scattering matrix, sij, can be transformed to form a 1 x 4 complex vector (for example, the Stokes vector). In the SSCM algorithm, the Pauli vectorization is used. The four Pauli components are defined as follows:

        a0 = (shh + svv) / sqrt(2)
        b0 = (shh - svv) / sqrt(2)
        g0 = (shv + svh) / sqrt(2)
        d0 = (shv - svh) / sqrt(2)
      

The fourth Pauli component is 0 for a symmetrized scattering matrix. In the following expressions, the non-symmetrized matrix s4c is used. For brevity, the symbols a0, b0, g0, and d0 are used in place of the angles alpha0, beta0, gamma0, and delta0, respectively.

Rotation angle

The Cameron decomposition and SSCM algorithm rotate the scattering matrix about the line of sight. A rotation by an angle, psi, transforms the Pauli components as follows:

        ap = a0
        bp = b0 * cos(2*psi) - g0 * sin(2*psi)
        gp = b0 * sin(2*psi) + g0 * cos(2*psi)
        dp = d0
      

The psi that maximizes the symmetric scattering is derived from the requirement that the third Pauli has a minimum value. The minimum or maximum of g0 is given by:

        1         2 * Re(b0 * (g0)*)
psi = - - * atan( ------------------ )
        4           |b0|^2 - |g0|^2
      

Re() represents the real part of a complex number. The asterisk (*) represents the complex conjugate of a number.

If |b0|=|g0|, there are three possible cases. When Arg(b0)-Arg(g0)=90 degrees, then the target is a right-handed helix. When Arg(b0)-Arg(g0)=-90 degrees, then the target is a left-handed helix. In either case, the SSCM algorithm cannot be applied and the target is ignored; otherwise, psi=-22.5 degrees. Arg() represents the argument (phase) of a complex number.

Degree of symmetry

The degree of symmetry, dsym, for the optimum angle psi is given by:

        |ap|^2 + |bp|^2
dsym = ------------------------
        |a0|^2 + |b0|^2 + |g0|^2
      

With the SSCM analysis, the target must be symmetric and coherent. A target is considered symmetric if it has a high degree of symmetry (dsym). With PSSSCM, it must exceed the threshold specified for the DOST parameter.

Degree of coherence

The tests for coherence are different for the distributed and point targets. A distributed target is considered coherent when it has a high degree of coherence, psym, defined as follows:

        sqrt( (<|ap|^2> - <|bp|^2>)^2 + 4 * |<ap * (bp)*>|^2 )
psym = -------------------------------------------------------
                   <|ap|^2> + <|bp|^2>
      

The angle brackets (<>) represent the spatial averaging over all pixels of the distributed target. With PSSSCM, psym must exceed the threshold specified for the DOCT parameter.

A point target is considered coherent when it is significantly brighter (for example, more than 15 dB) than the surrounding clutter. This is determined from the signal-to-clutter ratio for the transmit and receive polarizations that provide the maximum returned power (Huynen decomposition). With PSSSCM, the ratio must exceed the threshold specified for the SCRT parameter.

Representations of the maximum symmetric component

The SSCM algorithm provides two representations of the maximum symmetric component. The first, the scattering matrix, (Ssym)max, is expressed in terms of the direction, eta, of the scattering vector and the phase difference, phi, on the dihedral-trihedral basis, as follows:

(Ssym)max = exp(i*Arg(ap)) * sqrt(|ap|^2 + |bp|^2) * M
        m11 = cos(eta) + exp(i*phi) * sin(eta)
        m12 = 0
        m21 = 0
        m22 = cos(eta) - exp(i*phi) * sin(eta) )
      

Here, i represents the imaginary unit (i = sqrt(-1)).

In the second representation, the maximum scattering component is represented as a point on the unit Poincare target sphere. The latitude and the longitude of the point, 2*(psi)c and 2*(chi)c, are given as follows:

        2*(psi)c = atan2( |ap|^2 - |bp|^2, 2*Re(ap * (bp)*) )

                        2*Im(ap * (bp)*)
        2*(chi)c = asin( ---------------- )
                         |ap|^2 + |bp|^2
      

The target sphere angles relate a scatterer to the elemental symmetric scatterers as follows:

        +========================+===========+===========+
        |   Elemental symmetric  |  (psi)c   |  (chi)c   |
        |        scatterer       | [degrees] | [degrees] |
        +========================+===========+===========+
        |  Trihedral             |      0    |      0    |
        |  Dihedral              |     90    |      0    |
        |  Dipole                |     45    |      0    |
        |  Cylinder              |  18.43    |      0    |
        |  Narrow dihedral       |  71.57    |      0    |
        |  Quarter wave          |    N/A    |  +/-45    |
        +========================+===========+===========+
      

Processing flow

The preceding definitions and expressions are used in the PSSSCM processing, which proceeds as follows:

• Use the Cameron decomposition to compute the following parameters for each pixel:
  • The rotation angle, psi, for the maximum symmetric scattering component
  • The Pauli coefficients, ap and bp, of the maximum symmetric scattering component
  • The degree of symmetry, dsym
• Compute the distributed target degree of coherence, psym, for each pixel. The averaging is of all pixels of the square window with the pixels and lines specified for WINSIZE, centered on the current pixel.
• Create the bitmap of coherent point targets, bcpt, using the Huynen decomposition and the SCRT threshold
• If the bitmap of targets is not provided (TARGBM=N), derive the bitmap of symmetric coherent targets, bsct. It combines distributed targets with a high degree of coherence and a high average degree of symmetry, and coherent point targets with a high degree of symmetry. Each bit (i,j) of the bitmap is set as follows:

              IF (dsym(i,j) >= DOST) AND (psym(i,j) >= DOCT OR bcpt(i,j) = TRUE) THEN
              bsct(i,j) = TRUE
              ELSE
              bsct(i,j) = FALSE
              ENDIF
            

• If the pixel is coherent, compute the following SSCM parameters:
  • The scattering-vector direction on the dihedral-trihedral basis:

                    eta = atan(|bp / ap|)
                  

  • The phase difference, based on the dihedral-trihedral:

                    phi = Arg(bp / ap)
                  

  • The target sphere angles:

    (psi)c = atan2( |ap|^2 - |bp|^2, 2*Re(ap * (bp)*) ) / 2
    
                    2*Im(ap * (bp)*)
    (chi)c = asin( ---------------- ) / 2
                    |ap|^2 + |bp|^2
    
         IF (pi/2 < (psi)c <= pi) THEN
                (psi)c = pi - (psi)c
                (chi)c = -(chi)c
         ENDIF
                  

    For non-coherent pixels, all parameters are set to 0.

• Store the computed parameters to the six output channels.

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. and F. Charbonneau. "Characterization of target symmetric scattering using polarimetric SARs", IEEE Trans. Geosci. Remote Sensing, 40, no. 11 (2002): 2507-2516.