SIGSEP

Description

Prints a report of class signature separabilities among 2 to 256 classes. Separabilities can be calculated using either the Transformed Divergence or the Bhattacharyya (Jeffries-Matusita) Distance measure. The separability between two classes can be used to determine if the classes should be merged using SIGMERG.

Parameters

Name	Type	Length	Value range
Separability Measures	String	2 - 1	TD | BD Default: BD
InputSIG: Input class signature segments *	SIG port	2 - 256
Separability Threshold	Float	0 - 1
Average	Real	0 - 1024
Minimum	Real	0 - 1024
Maximum	Real	0 - 1024
Lowest Separability (first from pair)	Real	0 - 1024
Lowest Separability (second from pair)	Real	0 - 1024
Report	String	0 - 192	See parameter description

* Required parameter

Parameter descriptions

Separability Measures

Specifies the type of separability measure to use.

See the Details section for information about these measures.

InputSIG: Input class signature segments

Specifies 2 to 256 signature segments for which separabilities are calculated.

Duplicate segments are NOT allowed. All segments must have been created using the same set of input channels.

Separability Threshold

Optionally specifies a separability threshold value for the report.

If this parameter is not specified (default), a matrix of separabilities for all class signature pairs is printed.

If this parameter is specified, separabilities for only those class signature pairs with separabilities less than the specified threshold are printed, one pair per line.

Average

Upon successful completion of SIGSEP, this parameter contains the average of all separabilities.

Minimum

Upon successful completion of SIGSEP, this parameter contains the minimum separability.

Maximum

Upon successful completion of SIGSEP, this parameter contains the maximum separability.

Lowest Separability (first from pair)

Upon successful completion of SIGSEP, this parameter contains the channel number of the first signature of the pair that has the lowest separability value.

The values of this parameter and the Lowest Separability (second from pair) can be used as input to SIGMERG, to merge the signature pair with the lowest separability values.

Lowest Separability (second from pair)

Upon successful completion of SIGSEP, this parameter contains the channel number of the second signature of the pair that has the lowest separability value.

The values of this parameter and the Lowest Separability (first from pair) can be used as input to SIGMERG, to merge the signature pair with the lowest separability values.

Report

Specifies where to direct the generated report.

Available options are:

• LOG: generates a report on the terminal (default)
• <modulename.RPT>: appends a report to the module's RPT file
• DISK: generates a report on file "IMPRPT.LST"

Details

SIGSEP calculates the separability between each pair of classes among 2 to 256 classes, and prints the results in a separability matrix. Class signature segments can be created using the CSG, KCLUS, or ISOCLUS functions. The purpose of SIGSEP is to determine whether some classes should be merged using SIGMERG. Pairs of classes with poor separability values should be merged before performing classification using MLC.

If a separability threshold (SEPTHRES) is specified, only those class signature pairs with a separability less than the defined threshold are printed. This is useful if a large number of signature segment are specified, and you want to list only those signatures which should be merged.

The Transformed Divergence (TD) measure is a popular empirical measure, which is computationally simpler than the Bhattacharyya Distance (BD) measure. The BD measure is more theoretically sound because it is directly related to the upper bound of the probabilities of classification errors.

Both TD and BD separability measures yield real values between 0 and 2, where 0 indicates complete overlap between the signatures of two classes, and 2 indicates a complete separation between the two classes. TD and BD measures are monotonically related to classification accuracies. The larger the separability values, the better the final classification results will be (using the MCL or MINDIS).

The following rules are suggested for each of the possible ranges of separability values 'x':

0.0 < x < 1.0   (very poor separability)
1.0 < x < 1.9   (poor separability)
1.9 < x < 2.0   (good separability)

Very poor separability (0.0 < x 1.0) indicates that the two signatures are statistically very close to each other. The user has two options. One signature can be arbitrarily discarded (which is suggested when the separability is closer to 0), or the two signatures can be merged using SIGMERG (which is suggested when the separability is closer to 1).

Poor separability (1.0 < x 1.9) indicates that the two signatures are separable, to some extent. It is desirable, however, to improve separability, if possible. Low signature separability is usually caused by improper combinations of image bands, and/or training sites that have large internal variability within each class.

Algorithm

To determine the separability between a pair of class signatures, two criteria, Transformed Divergence (TD) and Bhattacharyya Distance (BD), are used. They are calculated from class means and covariance matrices as follows:

 TD Measure
 __________

  TD(i,j) = 2*[1-exp(-D(i,j)/8)]

 BD Measure
 __________

  BD(i,j) = 2*[1-exp(-a(i,j))]

SIGSEP calculates the separabilities of all the possible pairs among 'n' classes, where 'n' is the number of classes.

References

Richards, J. A. (1986). Remote Sensing Digital Image Analysis. Springer-Verlag. New York. pp. 206-225.