PSUSWIS

Description

PSUSWIS performs an unsupervised Wishart classification of a polarimetric SAR (POLSAR) data set. The classification method is similar to the standard supervised maximum likelihood classification, except that the distance measured is customized for polarimetric data. The training classes are derived from an existing unsupervised classification result. The output image is a single-channel image with pixel values representing the class number, which can be between one and nine for a PSFREDUR and PSKROG input, between one and 12 for PSG4U2 and PSPHDW and between one and 16 for a PSCLOPOT input. The use of iteration refines the classification, but increases the processing time.

Parameters

Name	Type	Caption	Length	Value range
FILI*	String	Input polarimetric SAR image	1 - 192
FILE*	String	Input classified raster (Decomposition)	1 - 192
ITERATIO	Integer	Number of iterations	0 - 1	0 - 11 Default: 5
FILO*	String	Output Wishart classified raster	1 - 192
MONITOR	String	Monitor mode	0 - 3	ON, OFF Default: ON

* Required parameter

Parameter descriptions

FILI

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 one of the following matrix formats: covariance, coherence, or Kennaugh. It is suggested that the input data set have an equivalent number of looks (ENL) of at least 25. If the data set is single-look complex, an ENL of 25 can be achieved by applying a polarimetric filter, such as boxcar, prior to classification.

The input file must be a data set that has already been imported into the PCIDSK (.pix) format by 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 POLSAR sensors and data products, follow the link to SARINGEST at the end of this topic.

FILE

The name of the initial classification source raster, which must contain either one classified byte channel or multiple floating-point channels, depending on the classification method used. If the classification source contains only one byte-layer channel, it is assumed to be a Cloude-Pottier or van Zyl classification. If the classification source contains multiple floating-point channels, the Freeman-Durden, Krogager, G4U2, or PHDW classification is assumed to be the source. The file must have the same dimensions as the input SAR image. The classification source represents training areas for the output classes in the Wishart classification.

ITERATIO

The number of iterations used to refine the classification. The default number of iterations is 5, and the maximum number is 11. Increasing the number of iterations improves the discrimination, but linearly increases the processing time.

This parameter is optional.

FILO

The name of the output file that will hold the classification results. The output file has the same number of dimensions as the input SAR image, and one channel. Its pixel values specify the class number assigned to each pixel. The output image is a single-channel image with pixel values representing the class number, which can be between one and nine for a PSFREDUR and PSKROG input, between one and 12 for PSG4U2 and PSPHDW and between one and 16 for a PSCLOPOT input. The use of iteration refines the classification, but increases the processing time. Pixels that cannot be classified are represented by the pixel value of 0, usually with a value of 0 in all channels of the input image.

The file name you specify must not already exist.

MONITOR

The program progress can be monitored by printing the percentage of processing completed. A system parameter, MONITOR, controls this activity.

Available options are:

• ON: Turns the monitor ON (default)
• OFF: Turns the monitor OFF (recommended if running in batch or background mode)

Details

PSUSWIS performs an unsupervised Wishart classification of a polarimetric SAR data set. The classification algorithm is similar to the PSSWIS algorithm, except that the training classes are provided by the results of an earlier classification performed on the same data set.

The initial classification source can be obtained by running PSFREDUR, PSKROG, PSG4U2, or PSPHDW. Results classified previously from PSCLOPOT and PSVANZYL can be refined by increasing the number of iterations.

The input data set must contain fully polarimetric (quad-polarization) data in one of the following matrix formats: covariance (c4r6c or C3r3c), coherence (t4r6c or T3r3c), or Kennaugh (k16r or K9r), with a suggested number of looks (ENL) of at least 25.

The training classes in the initial classification source are used to form the average coherence matrix for every class. The class value 0 is assigned to pixels with invalid matrix representations (a 0 value or negative determinant) because the classification is not possible in this case.

When the algorithm is completed, each pixel in the output channel represents the closest class according to the defined minimum distance criteria. The pixels for which classification is not possible have a value of 0 (null class). The classes present in the output depend on the input data. The output raster has metadata summarizing the classes.

Output class descriptions when the input is from Freeman-Durden:

• Class 0 = Unclassified
• Class 1 = Low Surface Scattering
• Class 2 = Medium Surface Scattering
• Class 3 = High Surface Scattering
• Class 4 = Low Double Bounce Scattering
• Class 5 = Medium Double Bounce Scattering
• Class 6 = High Double Bounce Scattering
• Class 7 = Low Volume Scattering
• Class 8 = Medium Volume Scattering
• Class 9 = High Volume Scattering

Output class descriptions when the input is from Krogager:

• Class 0 = Unclassified
• Class 1 = Low Dipole Scattering Power
• Class 2 = Medium Dipole Scattering Power
• Class 3 = High Dipole Scattering Power
• Class 4 = Low Helical Scattering Power
• Class 5 = Medium Helical Scattering Power
• Class 6 = High Helical Scattering Power
• Class 7 = Low Spherical Scattering Power
• Class 8 = Medium Spherical Scattering Power
• Class 9 = High Spherical Scattering Power

Output class descriptions when the input is from G4U2:

• Class 0 = Unclassified
• Class 1 = Low Double Bounce Scattering Power
• Class 2 = Medium Double Bounce Scattering Power
• Class 3 = High Double Bounce Scattering Power
• Class 4 = Low Volume Scattering Power
• Class 5 = Medium Volume Scattering Power
• Class 6 = High Volume Scattering Power
• Class 7 = Low Surface Scattering Power
• Class 8 = Medium Surface Scattering Power
• Class 9 = High Surface Scattering Power
• Class 10 = Low Helical Scattering Power
• Class 11 = Medium Helical Scattering Power
• Class 12 = High Helical Scattering Power

Output class descriptions when the input is from PHDW:

• Class 0 = Unclassified
• Class 1 = Low Diplane Scattering Power
• Class 2 = Medium Diplane Scattering Power
• Class 3 = High Diplane Scattering Power
• Class 4 = Low Helix Scattering Power
• Class 5 = Medium Helix Scattering Power
• Class 6 = High Helix Scattering Power
• Class 7 = Low Plate Scattering Power
• Class 8 = Medium Plate Scattering Power
• Class 9 = High Plate Scattering Power
• Class 10 = Low Wire Scattering Power
• Class 11 = Medium Wire Scattering Power
• Class 12 = High Wire Scattering Power

Output class descriptions when the input is Cloude-Pottier:

• Class 0 = Undefined (neutral)
• Class 1 = High Entropy, Anisotropic, Multiple Scattering
• Class 2 = High Entropy, Anisotropic, Volume Scattering
• Class 3 = Medium Entropy, Anisotropic, Multiple Scattering
• Class 4 = Medium Entropy, Anisotropic, Volume Scattering
• Class 5 = Medium Entropy, Anisotropic, Surface Scattering
• Class 6 = Low Entropy, Anisotropic, Multiple Scattering
• Class 7 = Low Entropy, Anisotropic, Dipole Scattering
• Class 8 = Low Entropy, Anisotropic, Surface Scattering
• Class 9 = High Entropy, Isotropic, Multiple Scattering
• Class 10 = High Entropy, Isotropic, Volume Scattering
• Class 11 = Medium Entropy, Isotropic, Multiple Scattering
• Class 12 = Medium Entropy, Isotropic, Volume Scattering
• Class 13 = Medium Entropy, Isotropic, Surface Scattering
• Class 14 = Low Entropy, Isotropic, Multiple Scattering
• Class 15 = Low Entropy, Isotropic, Dipole Scattering
• Class 16 = Low Entropy, Isotropic, Surface Scattering

Output class descriptions when input is van Zyl:

• Class 0 = Undefined (neutral)
• Class 1 = Odd Number of Reflections
• Class 2 = Even Number of Reflections
• Class 3 = Diffuse Scattering

Example

Perform an unsupervised Wishart classification of a RADARSAT-2 data set. The input RADARSAT-2 SLC-Q data set has been ingested with SARINGEST and is first averaged with PSBOXCAR to increase its ENL to 25. PSCLOPOT is used with the default class boundaries to derive the starting classes. PSUSWIS is then used to refine the initial Cloude-Pottier classification. Because of the nature of the classification, the output has the same number of classes as the input Cloude-Pottier classification, but the output numbers do not match the Cloude-Pottier feature space.

EASI>FILI="rsat2_slc.pix" 
EASI>FILO="R2_enl25.pix"
EASI>FLSZ=5
EASI>run PSBOXCAR

EASI>FILI="R2_enl25.pix" 
EASI>CBDT=""
EASI>FILO="Clopot.pix"
EASI>run PSCLOPOT

EASI>FILI="R2_enl25.pix" 
EASI>FILE="Clopot.pix" 
EASI>ITERATIO=5
EASI>FILO="R2_Uswis.pix"
EASI>run PSUSWIS
      

Algorithm

The unsupervised Wishart classification algorithm is defined in the article cited in the References section. The maximum likelihood classification of each pixel is provided by the class that minimizes the distance between the pixel and the class. The distance measure is optimized for polarimetric SAR data with the coherence (and covariance) matrices following the complex Wishart distribution.

Depending on the input classification used for training data, the PSUSWIS algorithm follows two different processing flows. In the following description, the number of classes for the Cloude-Pottier classifier is 16. If the customized class boundaries are used, the actual number used in computation will be same as the number of classes in the input classified source raster. With the Freeman-Durden classification, pixels are allowed to change class only if the old and new classes both represent the same dominant scattering mechanism.

With both classification flows, the distance is similarly defined. Given a class, m, with a mean coherence matrix (T_hat)m, and a pixel (i,j) with the coherence matrix T(i,j), the distance, d, is defined as follows:

        d = ln|(T_hat)m| + Trace( ((T_hat)m)^-1 * (T(i,j) )
      

The vertical bars (||) represent the determinant of the matrix. Trace() represents the trace of the matrix, which is defined as the sum of its diagonal elements.

The processing in PSUSWIS with a Cloude-Pottier classification in FILE proceeds as follows.

• If necessary, convert the input data set to the symmetrized coherence matrix format. For more information on the conversion process, follow the link to PSCONV at the end of this topic.
• For each iteration, (k = 1 to NITERS), calculate the following:
  • For each class, (m = 1 to 16):
    • Calculate the average coherence matrix as follows:

                          1    Nm
                          (T_hat)m = --- * Sum( T(i,j)n )
                          Nm    n=1
                        

      Nm represents the number of pixels currently assigned to class m. T(i,j)n represents the coherence matrix for the pixel (i,j)n of the class m. The averaging is performed for all elements (channels) of the coherence matrix.

    • Derive the inverse of the average coherence matrix, Am, and the natural log of its determinant, bm:

                          Am = (T_hat)m^-1
                          bm = ln|(T_hat)m|
                        

  • Loop over all lines and pixels (i,j) of the input data set. The processing at every pixel proceeds as follows:
    • Initialize the minimum distance for the pixel, dmin, and the best-matching class, mmin, as follows:

                          dmin = MAX_FLOAT
                          mmin = 0
                        

    • Loop over all classes. For each class, (m = 1 to N):
      • Compute the distance, dm, between the pixel and the current class, as follows:

                                dm = bm + Trace( Am * T(i,j) )
                              

        If the Trace() is 0, skip the current pixel (assign it to class 0).

      • If dm is less than dmin, update the best-matching class, as follows:

                                dmin = dm
                                mmin = m
                              

• Store the best-matching class number, mmin, in the current pixel of the output channel.

The processing in PSUSWIS, with a Freeman-Durden classification as FILE, proceeds as follows.

• If necessary, convert the input data set to the symmetrized coherence matrix format. For more information on the conversion process, follow the link to PSCONV at the end of this topic.
• Generate the initial classification.
  • For each pixel (i,j) determine its scattering class based on the highest Freeman-Durden scattering power at the pixel.
  • For each scattering class m, calculate its mean, (mu)m, and standard deviation, (sigma)m, from all pixels assigned to this class, as follows:

                    1    Nm
                    (mu)m = --- * Sum( Pm(i,j)n )
                    Nm    n=1
                    1     Nm                       Nm
                    (sigma)m = sqrt( ---  * Sum( (Pm(i,j)n)^2 ) - ( ---- * ((mu)m)^2 ) )
                    Nm-1   n=1                     Nm-1
                  

    Nm represents the number of pixels in class m. Pm(i,j)n represents the power contribution from the scattering mechanism for a given class at the pixel (i,j)n of this class. The averaging is performed for all elements (channels) of the coherence matrix.

  • Split each class into three subclasses. This is done by using thresholds (mu)m - 0.43*(sigma)m and (mu)m + 0.43*(sigma)m within the three existing classes. At every class, the corresponding power contribution is used for the subdivision.
• For each iteration, (k = 1 to NITERS) calculate the following:
  • For each class, (m = 1 to 3* number of layers):
    • Calculate the average coherence matrix as follows:

                          1    Nm
                          (T_hat)m = --- * Sum( T(i,j)n )
                          Nm    n=1
                        

      Nm represents the number of pixels currently assigned to class m. T(i,j)n represents the coherence matrix for the pixel (i,j)n of the class m. The averaging is performed for all elements (channels) of the coherence matrix.

    • Derive the inverse of the average coherence matrix, Am, and the natural log of its determinant, bm:

                          Am = (T_hat)m^-1
                          bm = ln|(T_hat)m|
                        

  • Loop over all lines and pixels (i,j) of the input data set. The processing at every pixel proceeds as follows:
    • Initialize the minimum distance for the pixel, dmin, and the best-matching class, mmin, as follows:

                          dmin = MAX_FLOAT
                          mmin = 0
                        

    • Determine the class range (m1-m2) examined for this pixel based on its scattering mechanism. If the pixel maximum is on the first layer, classes (1-3) are examined; if the pixel maximum is on the second layer, classes (4-6) are examined; if the pixel maximum is on the third layer, classes (7-9) are examined, and so on.
    • Loop over all classes. For each class, (m = m1 to m2):
      • Compute the distance, dm, between the pixel and the current class, as follows:

                                dm = bm + Trace( Am * T(i,j) )
                              

        If the Trace() is 0, skip the current pixel (assign it to class 0).

      • If dm is less than dmin, update the best-matching class within the current scattering class (s, d or v), as follows:

                                dmin = dm
                                mmin = m
                              

• Store the best-matching class number, mmin, in the current pixel of the output channel.

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

Lee, J. S., M. Grunes, E. Pottier, and L. Ferro-Famil. "Segmentation of Polarimetric Images that Preserves Scattering". Proceedings of the European Conference on Synthetic Aperture Radar (EUSAR), Cologne, June 4-6, 2002.

Lee, J. S., M. R. Grunes, T. L. Ainsworth, L.J. Du, D. L. Schuler, and S. R. Cloude. "Unsupervised classification using polarimetric decomposition and the complex Wishart classifier", IEEE Trans Geoscience and Remote Sensing, 37, no. 5, (1999): 2249-2258.