AUTOMER

Description

Merges signature pairs that have the lowest separability among a set of signatures, until a minimum separability threshold value is reached. AUTOMER uses the SIGSEP, SIGMERG, DAS, and PCIMOD functions.

Parameters

automer(file, sepme, dsig, septhres)

Name	Type	Caption	Length	Value range
FILE *	str	Input file name	1 -
SEPME	str	Separability measures	0 - 2	TD \| BD Default: BD
DSIG *	List[int]	Input class signature segment	2 - 256
SEPTHRES	List[float]	Separability threshold	0 - 1	0 - 2

* Required parameter

Parameter descriptions

FILE

Specifies the name of the PCIDSK file that contains the input imagery and segments to process.

SEPME

Specifies the type of separability measure used. For more information, see the DETAILS section.

DSIG

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

All segments must be created using the same set of input channels. Duplicate segments are not allowed.

SEPTHRES

Optionally specifies a separability threshold value for the report. If this parameter is not specified, 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 defined values are printed (one pair per line).

Details

AUTOMER calculates the separability between each pair of classes among two to 256 classes and merges signature pairs that have the lowest separability among a set of signatures until a minimum separability threshold value is reached.

When the merging is complete, AUTOMER prints a brief report that shows the number of segments merged, the final signature segments, and the minimum separability.

Class signature segments can be created using KCLUS, or ISOCLUS. Pairs of classes with poor separabilities should be merged before performing a classification with MLC.

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

AUTOMER uses two class separability measures:

TD: Transformed Divergence
BD: Bhattacharyya (or Jeffries-Matusita) Distance

The Transformed Divergence (TD) measure is a popular empirical measure that is computationally simpler than the Bhattacharyya Distance (BD) measure; however, 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 (using MCL or MINDIS). The following rules are suggested for the possible ranges of separability of value '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)
the two signatures can be merged using the 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 prefereable, however, to improve separability if possible. Low signature separability is usually caused by improper combinations of image bands or training sites, or both, which have large internal variability within each class.

AUTOMER should be used to examine the quality of training sites (bitmaps) and class signatures before performing classification. To improve class separabilities, consider the following options:

Select a different combination of multispectral image bands that are better suited for separating certain classes when creating signature segments.
Create a new set of classes that are more separable, given the available image data.
Modify existing training sites for classes that have the largest internal variance.
Merge those pairs of classes whose signature separabilities are too low.

Note: The formula used to calculate the Bhattacharyya Distance measure provided in "Remote Sensing Digital Image Analysis" is incorrect. Check the reference in the book to find the right formula (see References).

Example

TBD

from pci.automer import automer

file	=	"irvine.pix"
sepme	=       ""	
dsig	=	[17,18]
septhres	=	[]

automer( file, sepme, dsig, septhres )

Algorithm

To determine the separability between a pair of class signatures, 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)]

where:

TD(i,j) = Transformed Divergence between classes i and j
D(i,j) = divergence between classes i and j
D(i,j) = 0.5*T[M(i)-M(j)]*[InvS(i)+InvS(j)]*[M(i)-M(j)]+ 0.5*Trace[InvS(i)*S(j) +InvS(j)*S(i) -2*I ]

where:

M(i) = mean vector of class i, where the vector has Nchannel elements (Nchannel is the number of channels used)
S(i) = covariance matrix for class i, which has Nchannel by Nchannel elements
InvS(i) = inverse of matrix S(i)
Trace[] = trace of matrix (sum of diagonal elements)
T[] = transpose of matrix
I = identity matrix

        BD Measure
  ____________________________

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

where:

BD(i,j) = Bhattacharyya Distance between class i and j
a(i,j) = 0.125*T[M(i)-M(j)]*Inv[A(i,j)]*[M(i)-M(j)] + 0.5 *ln{det(A(i,j))/SQRT[det(S(i))*det(S(j))]}

where:

T, M, S, and Inv are as defined for TD measure
A(i,j) = 0.5*[S(i)+S(j)]
det() = determinant of a matrix
ln{} = natural logarithm of scalar value
SQRT[] = square root of scalar value

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

References

Richards, J. A., "Remote Sensing Digital Image Analysis". Berlin: Springer-Verlag, 1986.

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AUTOMER

Automatic signature merging

Description

Parameters

Parameter descriptions

Details

Example

Algorithm

References