MINDIS -- Minimum Distance Classifier

Performs multispectral classification of image data for up to 256 classes based on Euclidean distance. The output is a theme map directed to a database image channel.

The MINDIS classifier differs from MLC, since it is based on the shortest Euclidean distance to class means rather than the likelihood measure employed by the program MLC.

Progress of this program can be monitored. See MONITOR section.

See Also: MLC, MLR, AGGREG

PARAMETERS

MINDIS is controlled by the following global parameters: 

Name     Prompt                                  Count     Type
FILE     Database File Name                      1-64      Char
DBS1     Class Signature Subset 1                1-256     Int
DBOC     Database Output Channel List            1         Int
MASK     Area Mask (Window or Bitmap)            0-4       Int
REPORT   Report Mode: TERM/OFF/filename          0-64      Char

FILE

Specifies the name of the PCIDSK image file to be classified. 

 EASI>FILE="filespec"

DBS1

Specifies the class signature segments (type 121) to use in the classification. 

 EASI>DBS1=i,j,...,p

DBOC

Specifies the channel to which the output theme map is to be written. 

 EASI>DBOC=i

MASK

Specifies the area in the input channel which should be processed. This can be one of the following: 

 EASI>MASK=xoff,yoff,xsize,ysize        | process window
 EASI>MASK=b                            | process only under bitmap
                                        | stored in segment b
 EASI>MASK=                             | process entire channel

REPORT

Specifies the file to which the generated report should be appended. 

 EASI>REPORT="filename"
 EASI>REPORT=            | defaults to terminal output
Note: The following names have special meaning: 

 EASI>REPORT="TERM"      | generates reports on your terminal
 EASI>REPORT="DISK"      | generates reports on file "IMPRPT.LST"
 EASI>REPORT="OFF"       | usually cancels report generation, but
                         | MINDIS forces REPORT to terminal output

MONITOR

Program progress can be monitored by printing the percentage of completed processing in odometer fashion. A system parameter, MONITOR, controls this activity: 

 EASI>MONITOR="ON"       | turn monitor ON  (default)
 EASI>MONITOR="OFF"      | turn monitor OFF (recommended if
                         | running in batch/background mode)

DETAILS

MINDIS classifies image data on a database file (FILE) using a set of 256 possible class signature segments as specified by DBS1 parameter. Each segment specified in DBS1, for example, stores signature data pertaining to a particular class. Only the mean vector in each class signature segment is used. Other data, such as standard deviations and covariance matrices, are ignored (though this is used by the maximum likelihood classifier, MLC).

The result of the classification is a theme map directed to a specified database image channel (DBOC). A theme map encodes each class with a unique grey level. The grey-level value used to encode a class is specified when the class signature is created (using the parameter VALU for CSG). If the theme map is later transferred to the display, then a pseudo-colour table should be loaded so that each class is represented by a different colour.

The MASK parameter specifies the area which will be processed. Pixels outside this area on the output channel will not be modified. Only the area under mask will be classified and the rest of the image will not be processed. If a single value is specified, then this value refers to a bitmap segment, which defines the area to be classified. When four values are specified, these values define the x,y offsets and x,y dimensions of rectangular window within the image to be classified.

If a report device is selected, MINDIS generates a classification report. Sub-area totalizations can be obtained by running the program MLR.

MINDIS assigns each pixel to the class which has the minimum distance between the pixel value and the class mean. Compared to the MLC program, which takes class covariance matrices into account, MINDIS generally produces poorer classification results, but it executes much more quickly.

It is suggested that MINDIS be used when a quick examination of the classification result is required. MINDIS can also be used in applications in which simple classification is sufficient.

In situations where MLC's multivariate normal distribution assumption does not hold (for example, signature classes generated from texture images which may not have a single-mode normal distribution), MINDIS may perform even better than MLC, because MINDIS does not require make assumptions.

SIGNATURES

Signatures are created by the CSG (supervised classification) program. The signature for each class includes the mean vector, standard deviations, and covariance matrix. MINDIS requires only the class mean vector. The rest of the data is ignored.

Under some circumstances, the user may want to create a class with an explicit user-specified mean vector. In this case, the best approach is to create a dummy signature segment (using CSG and an arbitrary bitmap), then run the CSE program to modify the resulting signature segment means. The modified signature segment can then be used by MINDIS (although it would be useless for MLC).

ALGORITHM

The equation used by MINDIS is the minimum Euclidian distance classifier defined by the following equation: 

                 T
   Gi(X) = (X-Ui) * (X-Ui)

         = SUM[(xj-uj)**2]  for j = 1 to d.

 Gi(X)          is the result for class i on pixel X
 T              indicates transposition of the elements in brackets
 d              is the number of channels in the classification
 X=(x1,...,xd)  is the (d by 1) pixel vector of grey-levels
 Ui=(u1,...,ud) is the (d by 1) mean vector for class i
 j              is the subscript of jth element of a vector
 SUM[]          is the total of elements inside brackets
The distances between the pixel to be classified and each class centre are compared. The pixel is assigned to the class whose centre is the closest to the pixel.

If for all i not equal j, Gj(X) < Gi(X), then X is classified as j.

The diagram below illustrates the classification of 4 pixels into 3 classes, pixels are classified to the nearest class centre. 

 |             Class A                    *   class centre
 |  .    a                      .        ...  class boundary  
 |     .           *          .
 |        .  b             .               Pixel      Class
 |          .          .                  
 |              .    .                       a           A
 |          c     .                          b           A
 |                .                          c           B
 |          *      .     *  Class C          d           C
 |                 .  d                                          
 |       Class B   .                        
 |                .                             
 |                              
 +----------------------------------
Reference: 

 Hodgson, M.E., 1988. "Reducing the computational requirements
 of the minimum-distance classifier."  Remote Sensing of 
 Environment, Vol. 24.

REPORT

An example output listing produced by MINDIS is shown below. This listing can be directed to any report device (REPORT). 

 Seg            segment number of class signature
 Name           Name of class signature segment
 Code           segment value (code) of class signature
                (pixel value used to encode theme map)
 Pixels         Number of pixels in class
 %Image         Percentage of image covered by class

 MINDIS  Minimum Distance Classifier  V5.3 EASI/PACE  18-Nov-93
 
 irvine.pix            [S   11PIC     512P     512L]  14-Aug-90

 Seg Name     Code      Pixels    %Image

  17 Water1     10        6955      2.65
  18 Water2     20        1098      0.42
  19 Urban      30       29031     11.07
  20 Range      40      115954     44.23
  21 Crop1      50       40697     15.52
  22 Crop2      60       27341     10.43
  23 Crop3      70        4615      1.76
  24 Forest     80       36453     13.91

     Total              262144    100.00

EXAMPLE

On the file IRVINE.PIX, the analyst has created 8 class signature segments (numbered 17,18, ..., 24) and wishes to use the minimum distance classifier, MINDIS, to produce an 8-class thematic output image on channel 8. This can be accomplished with the following steps: 

 EASI>FILE="IRVINE.PIX"
 EASI>DBS1=17,-24       | 8 class segments input (17,18,19,20,
                                                  21,22,24,24)
 EASI>DBOC=8                    | output theme map channel 8
 EASI>REPORT="JUNK1.REP"        | create a report in a file
 EASI>RUN MINDIS                | perform the classification
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