PSSWIS

Description

PSSWIS performs a supervised Wishart classification of a fully polarimetric SAR (POLSAR) data set. The classification method is similar to the standard supervised maximum likelihood classification, except that the distance measure is customized for polarimetric data. The output image is a single-channel image with pixel values that represent the class number between one and the number of input training classes provided.

Parameters

Name	Type	Length	Value range
Input: Input polarimetric SAR image*	Raster port	1 -
InputSamples: Input training sample data (bitmap or vector)*	Mixed port	1 -
Output: Output Wishart classified raster*	Raster port	1 -

* Required parameter

Parameter descriptions

Input: Input polarimetric SAR image

The name of the input data set that contains the complex polarimetric SAR data to process. the data can be either nonsymmetrized or symmetrized fully polarimetric (quad-polarization) complex. The input data set must be in one of the following matrix formats: covariance, coherence, or Kennaugh. The input data set should have an equivalent number of looks (ENL) of at least 25. If the data set is single-look complex, an ENL of 25 could be achieved by applying a polarimetric filter, such as boxcar.

The input data must be a data set already 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.

InputSamples: Input training sample data (bitmap or vector)

The name of the file that contains vector targets, bitmap targets, or both. The file must be in in PCIDSK (.pix) format. If necessary, you can specify the same file as your input polarimetric SAR data set.

A bitmap target must have the same dimensions as the input data. A vector target must overlap and have the same georeferencing as the input data. The maximum number of input layers is 255.

Pixels encompassed by geocoded vector polygons, or the "on" pixels in each bitmap, represent training areas for one input class. Training areas for a different class must be provided in another vector layer or in a separate bitmap. All vector layers or bitmaps in your input polarimetric SAR data set are used.

If necessary, you can create targets in CATALYST Professional Focus or import targets from another image. You can generate geocoded vector targets in Focus or CATALYST Professional SAR Polarimetry Target Analysis, or you can import the targets from another source.

Output: Output Wishart classified raster

The name of the output file that contains the classification results. The output file has the same dimensions as the input, and one 8-bit channel. Its pixel values specify the class number assigned to each pixel. Pixels that cannot be classified (usually with zero values in all input channels) are represented by a pixel value of 0. The output file can hold up to 255 classes.

The file name you specify must not already exist.

Details

PSSWIS performs a supervised Wishart classification of a polarimetric SAR data set.

The input file must represent a nonsymmetrized or symmetrized fully polarimetric (quad-polarization) data set in one of the following matrix formats: covariance (c4r6c or C3r3c), coherency (t4r6c or T3r3c), or Kennaugh (k16r or K9r). If required, the input matrix is converted internally to the symmetrized covariance matrix C3r3c before processing.

The training sites are used to form the average covariance matrix for a given class. If all training pixels for a class have zero values for all matrix elements, it will cause an error. In such cases, the average covariance matrix cannot be inverted for the class and the classification is not possible.

PSSWIS functions similarly to PSUSWIS. Both use the same algorithm to classify SAR data. However, they differ in that PSSWIS requires training classes you provide, whereas PSUSWIS derives its own training classes based on a polarimetric decomposition algorithm similiar to the Freeman-Durden or Cloude-Pottier decompositions.

Algorithm

The PSSWIS algorithm is based on the article cited in the reference 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 POLSAR data with the covariance (and coherency) matrices following the complex Wishart distribution.

Given a class, m, with a mean covariance matrix (V_hat)m and a pixel (i,j) with the covariance matrix V(i,j), the distance, d, is defined as follows:

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

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

The processing in PSSWIS proceeds as follows.

• If the input data set is not in the covariance matrix format, it is converted. For more information on the conversion process, follow the link to PSCONV, later in this topic.
• For each class, m:
  • Extract the training pixels and calculate the average covariance matrix as follows:

                1    Nm
    (V_hat)m = --- * Sum( V(i,j)n )
               Nm    n=1  
                                

    Nm represents the number of training pixels for class m. V(i,j)n represents the covariance matrix for the training pixel (i,j)n of the class m. The averaging is performed for all elements (channels) of the covariance matrix.

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

    Am = (V_hat)m^-1  
    bm = ln|(V_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:
    • Compute the distance, dm, between the pixel and the current class, as follows:

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

    • If the Trace() is zero, skip the current pixel (leave it unclassified).
    • 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.

When the algorithm is complete, each pixel in the output channel represents the closest class, according to the minimum distance criteria defined above. The pixels for which classification fails have the value of 0 (null class).

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.R. Grunes, and R. Kwok. "Classification of multi-look polarimetric SAR imagery based on complex Wishart distribution", International Journal of Remote Sensing, 15, no. 11, (1994): 2299-2311.