CHNSEL

Description

Selects the best image channel combination from a defined channel set for classification, based on the divergence of the signature segments (created by CSG or another program) being discriminated. This reduces the number of channels required for classification. Before running CHNSEL, run CSR to ensure that all segments have been created using the same set of input channels.

Parameters

chnsel(file, nchan, dbic, drule, dsig, tflag, opt, best)

Name	Type	Caption	Length	Value range
FILE *	str	Input file name	1 -
NCHAN *	List[int]	Number of best channels	1 - 1
DBIC	List[int]	Input image channel(s)	0 - 16
DRULE *	str	Decision rule	3 - 3
DSIG *	List[int]	Input class signature segment	2 - 256	-256 -
TFLAG	str	Trace term	0 - 3	ON \| OFF Default: OFF
OPT *	List[int]	Optimization level	1 - 1
BEST	List[int]	Best image channels for classification	0 - 15

* Required parameter

Parameter descriptions

FILE

Specifies the name of the PCIDSK image file containing the channels and signature segments used to determine the optimum classification channel (best channel).

NCHAN

Specifies the number of best channels to select for future classification.

The value of this parameter must be smaller than the number of input channels used to create the signature segments in CSG.

DBIC

Optionally specifies the input image channel(s), selected from the set of channels used to create the signature segments, from which to select an optimum subset.

Duplicate channels are not allowed.

DRULE

Specifies the divergence algorithm to use when selecting the best channels.

Available algorithms are:

IDV: average interclass divergence
TDV: average transformed divergence
PDV: minimum pairwise divergence

DSIG

Specifies the input signature segment for which an optimum discriminatory channel subset will be selected.

Duplicate segments are not allowed.

All signatures must have been collected from the same set of input channels.

Note: For Windows platforms, no more than 128 signatures may be specified.

TFLAG

Specifies whether the trace term is included in the calculation.

Acceptable values are:

ON: the trace term is included in the calculation
OFF: the trace term is excluded from the calculation; this is the default value.

For more information, see the "Details" section.

OPT

Specifies the level of optimization required.

Valid values are from 0 to (DBIC-NCHAN-1). If a value greater than (DBIC-NCHAN-1) is specified, OPT is set to (DBIC-NCHAN-1).

For more information, see the "Details" section.

BEST

BEST is an output parameter. Upon completion, CHNSEL writes a list of the optimum image channels to use for classification to this parameter. This value may be used as input for other functions.

Details

CHNSEL reads a defined set of image channels and selects the best image channel combination to use for classification, based on the divergence of the signature segments (created by CSG or another function) being discriminated. This reduces the number of channels required for classification.

Before running CHNSEL, run CSG to create signature segments based on a subset of image channels from the input file (FILE). CHNSEL selects the best set of channels from this subset, based on the divergence of the input class signatures (DSIG). This reduces the amount of time required to classify a data set that consists of a large number of multispectral channels, without reducing the accuracy of the classification results.

The criteria used to determine the optimum channels for discriminating between a set of classes are based on the divergence between the classes. Divergence is a measure of the dissimilarity between two signature classes, which is calculated from the class sample means and the class covariance matrices. It extends to all of the classes by applying a decision rule over all signature segment class pairs.

Three decision rule methods (algorithms) are supported:

the average interclass divergence
the average transformed divergence
the minimum pairwise divergence

The first two decision rules always yield the same result for BEST channels; the second rule (average transformed divergence) is computationally more complex and is, therefore, more time-consuming. As a result, the second decision rule is redundant; using either the first (average interclass divergence) or third (minimum pairwise divergence) decision rules is recommended.

The accuracy and speed of CHNSEL for a specific data set is influenced primarily by the trace term (TFLAG) and optimization level (OPT) parameters.

The trace term (TFLAG) may be included (ON) or excluded (OFF) in the divergence equation. The trace term considers the inverse class covariance matrix relationship. Using this term in the divergence equation may increase the accuracy of the results, but it also increases the computational time required to achieve the results. In many cases, most of the discriminating divergence information is contained in the quadratic term; the trace term is unimportant and may be omitted. By default, the trace term is excluded from the equation.

The optimization level (OPT) parameter specifies the branch and bound algorithm optimization level. Valid values range from 0 to (DBIC-NCHAN-1). An optimization level of (DBIC-NCHAN-1) guarantees that the obtained channel subset is globally optimal. An optimization level between 0 and (DBIC-NCHAN-1) enumerates fewer nodes in the branch and bound algorithm and is, therefore, more efficient; however, there is no guarantee that the obtained subset is globally optimal. If OPT = 0, a backward selection scheme is applied to the data. The larger the value of this parameter, the more execution time is required to achieve results.

CHNSEL can analyze as many as 16 image channels using a maximum of 256 signature segments (128 for Windows). Use the DBIC (Input Layers) parameter to specify a subset of the selected image channels. Upon completion, CHNSEL updates the BEST (Best Layers) output parameter with a list of the optimum channels.

CHNSEL produces a report that contains the following information:

the channels from which the optimum set is selected
the initial value of the criteria found with all channels
the value of the criteria for the optimum channel set
the number of new nodes reached by the branch and bound algorithm
a table that summarizes the number of expanded and rejected nodes at each optimization level
the channels included in the optimum set
the initial divergence matrix (can be printed in sections)
the final divergence matrix (can be printed in sections)

Examples

Determine the three optimum channels for classifying the TM image on irvine.pix, using the eight signature segments from the input file. Use only the simplest optimizations.

from pci.chnsel import chnsel

file	=	"irvine.pix"
nchan	=	[3]
dbic	=	[]
drule	=	"IDV"
dsig	=	list(range(17, 24 + 1))
tflag	=	"OFF"
opt	=	[0]
best	=	[]

chnsel( file, nchan, dbic, drule, dsig, tflag, opt, best )

The following report is produced:

 Initial Channels:   1,  2,  3,  4,  5

 Initial Criteria Value :  0.177623E+03
 Final Criteria Value   :  0.149688E+03

 The Number of New Nodes :     2

 Level           :   1,   2
 Nodes Expanded  :   1,   1
 Nodes Rejected  :   3,   1

 Optimal Channels:   3,  4,  5

 Initial Divergence Table:

            17       18       19       20       21       22       23
    +---------------------------------------------------------------
  18|   70.401
  19|  130.804  781.235
  20|   66.543  162.869   49.106
  21|   81.176  112.440  132.000   28.142
  22|  181.905  500.171   30.352   86.053  181.644
  23|  448.252  400.642   46.085   24.684  109.479  817.404
  24|   41.086  103.017  145.273   14.009   23.270   68.654  136.756


 Final Divergence Table:

            17       18       19       20       21       22       23
    +---------------------------------------------------------------
  18|   24.817
  19|  110.942  563.641
  20|   58.071  139.385   26.972
  21|   75.367   80.974   88.987   27.516
  22|  171.969  442.687   20.108   84.741  179.095
  23|  444.549  379.103   39.412   22.512  103.620  808.730
  24|   12.327   29.969   74.142    5.807   11.567   56.127  108.134

Given a texture analysis that has been performed on a single channel of radar data to produce 12 texture-measure images and class signatures that have been produced for 12 cover types for the 12 texture-measure images, determine which combination of six channels from the 12 produce the optimum classification results for the 12 signatures. All 12 classes must be considered equally important, with the highest accuracy, in the divergence calculations.

For example, if channels 4, 5, 8, 9, 10, and 11 are the six optimal input channels for the classifier, signatures must be recreated by CSG specifying only these input channels. MLC can then run with the newly created signatures.

from pci.chnsel import chnsel

file	=	"radarsat.pix"
nchan	=	[6]	# select six optimum channels
dbic	=	[]	# use all channels
drule	=	"IDV"	# use interclass divergence
dsig	=	list(range(22, 33 + 1))	# 12 classes
tflag	=	"ON"	# trace term for accuracy is on
opt	=	[5]	# highest possible optimization

chnsel( file, nchan, dbic, drule, dsig, tflag, opt, best )

Algorithm

CHNSEL uses a branch and bound algorithm to select the optimum channel combination.

To determine the optimum channel set for class discrimination from a given set of channels, some criteria must be established based on divergence (dissimilarity between two classes). This is calculated from the class sample means and the class covariance matrices:

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:

D(i,j) is the divergence between classes i and j
M(i) is the sample mean vector for class i; this is a vector with Nchannel elements, where Nchannel is the number of channels in the current set
S(i) is the class i covariance matrix. This is an Nchannel by Nchannel matrix
InvS(i) is the inverse of matrix S(i)
Trace[matrix] denotes the trace of the matrix
T[matrix] denotes the transpose of the matrix
I denotes the identity matrix

The divergence is extended to all classes, NCLASS > 2, by applying a decision rule over all NCLASS*(NCLASS-1) pairs.

You may choose one of the following averaging methods:

IDV: The average interclass divergence is the average of all pairs of the divergence for each pair. This measure considers all classes to be equally important.
```
IDV = (1/(NCLASS*(NCLASS-1))*SUM [D(i,j)]
```
where:
- SUM [x] is the sum of all values of i and j, i < j
TDV: The average transformed divergence is based on the exponential of the divergence (Mahalanobis distance) and reduces the dominance of classes that have the highest divergence.
```
TDV = (1/(NCLASS*(NCLASS-1)*SUM [2*(1-EXP(-D(i,j)/8)]
```
PDV: The minimum pairwise divergence is the smallest divergence for all pairs in a set. This criteria maximizes the classification accuracies for the worst case; that is, the resultant subset is optimal for the classification of the two classes with the most confusion between them.
```
PDV = Min (D(i,j))    with i<j.
```

The divergence criteria is all monotonic in M, the number of required optimum channels; that is, the criteria is never improved by removing a channel from a set of optimum channels. This monotonic characteristic allows a branch and bound selection algorithm to determine the optimum set of M channels.

The algorithm works as follows:

The algorithm starts with a complete set of N channels and systematically evaluates channel subsets of a size greater than or equal to the number of optimum channels (NCHAN). The lower bound, B, is the current optimum value of the criteria for an optimal channel subset (NCHAN). If any larger set is worse than B, all channel subsets of this set are eliminated. The algorithm performs all necessary bookkeeping to keep track of the enumeration, and ensures that all channel sets are either implicitly rejected by the branch and bound test or are explicitly evaluated. Finally, an optimum channel set is chosen.

The algorithm used by CHNSEL is based on the FEATUR program, which is part of LDIAS (LANDSAT Digital Image Analysis System), developed by CCRS (Canada Centre for Remote Sensing) in Ottawa, Canada.

References

Narendra, P.M. and K. Fukunaga. "A Branch and Bound Algorithm for Feature Subset Selection", IEEE Transactions in Computers, c.26, no. 9 (1977): 914-922.

Environments	PYTHON :: EASI :: MODELER
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