PCLT

Description

Generates and saves a linear transformation matrix (and its inverse) that can be used by LINTRN to transform selected channels of the input image into principal component channels.

Parameters

Name	Type	Length	Value range
Input File Name *	String	1 -
Transformation Parameters File Name *	String	1 - 1
Image Channel List	Integer	0 - 1024
Wavelength Interval	Float	0 - 2
Valid Bands Only	String	0 - 1	YES | NO Default: NO
Sampling Interval for X, Y	Integer	0 - 2	1 - Default: 1,1
Report	String	0 - 192	See parameter description

* Required parameter

Parameter descriptions

Input File Name

Specifies the name of the image file containing the channels for which the transformation is to be computed.

Transformation Parameters File Name

Specifies the name of the MATLAB save/load format file that will be created and to which the parameters of the linear transformation will be written.

Image Channel List

Specifies a subset of the input channels to which the channel selection is to be restricted.

Wavelength Interval

Specifies that the selected bands are to be restricted to those whose center wavelength is either inside or outside a closed interval, specified in nanometers. By default, no restriction is applied.

This parameter has no effect if the input file contains no band center wavelength metadata.

Valid Bands Only

Specifies whether the selected bands are to be restricted to those with "plot" or "bmask" (begin mask) quality values. The default is NO.

This parameter has no effect if the input file contains no band-validity metadata.

Sampling Interval for X, Y

Specifies the X and Y sampling interval within the specified input window.

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

PCLT considers an image to be a raster of image-value vectors, with one vector per pixel location. The components of these vectors are drawn from pixel values in selected channels at the same pixel location.

The forward transformation of each image-value vector consists of subtracting the mean vector from the image-value vector, then pre-multiplying the vector by the forward transformation matrix. This can be performed by LINTRN.

The mean vector subtraction and application of the linear transformation is meant to be performed using LINTRN. The application of the inverse of the linear transformation to a modified (for example, for noise removal) forward transformation result, followed by the addition of the mean vector, can also be performed using LINTRN.

Typically, the input image data for the inverse transformation is a modified version of forward-transformed channels. The modification typically consists of filtering the principal component images in which noise is concentrated. The output of the inverse transformation is typically used to replace the original input image channels with their modified (noise removed) counterparts.

Algorithm

The Principal Components transformation is based on computing the eigenvalues and eigenvectors of the band-vector covariance matrix. (Because this matrix is real and symmetric, finding a set of n orthonormal eigenvectors is always possible, where n is the dimension of the band-vectors).

Let us call the transformation matrix T. The first row of T is the covariance matrix eigenvector with the largest eigenvalue, the second row of T is the eigenvector with the second-largest eigenvalue, and so on. Because T is an orthogonal matrix, its inverse is its transpose.

Let x be an original band vector, m be the mean band-vector, and y be the transformation result. Then y = T*(x - m). The inverse transformation is computed according to x = (transpose(T)*y) + m.

PCLT saves the elements of T and m to the file specified by FILLT (Linear Transformation Parameters file).

Acknowledgements

PCI Geomatics received financial support from the Canadian Space Agency/L'Agence Spatiale Canadienne through the Earth Observation Application Development Program (EOADP) for the development of this software, under contract 9F028-0-4902/12.