DECORR

Description

Performs a decorrelation stretch (transformation) on 2 to 256 channels of image data. This type of stretch is especially effective on images in which channels are highly correlated (that is, the spectral bands are very similar). Decorrelation is based upon Principal Component Analysis and uses eigenchannels. Decorrelation stretching is a way of modifying, or stretching, the results of a PCA transformation.

Parameters

decorr(file, dbic, dboc, mask, eigensup)

Name	Type	Caption	Length	Value range
FILE*	str	Input file name	1 -
DBIC*	List[int]	Input raster channels	2 - 256	-1024 -
DBOC*	List[int]	Output decorrelated channels	1 - 256	-1024 -
MASK	List[int]	Area Mask (Window or Bitmap)	0 - 4	Xoffset, Yoffset, Xsize, Ysize
EIGENSUP	List[float]	Eigenchannels to suppress	0 - 16	1 -

* Required parameter

Parameter descriptions

FILE

Specifies the name of the PCIDSK image file that contains the image channels to decorrelate.

DBIC

Specifies the image channels to be decorrelated.

At least two channels must be specified, to a maximum of 256 channels. Duplicate channels are NOT allowed.

DBOC

Specifies the image channels to receive the decorrelated results.

The number of output channels must be the same or fewer than the specified input channels.

Each output channel saves the decorrelated results of the corresponding input channel. Duplicate channels are NOT allowed.

MASK

Specifies the window or bitmap that defines the area to be processed within the input raster.

If a single value is specified, that value represents the channel number of the bitmap segment in the input file. Only the pixels under the bitmap are processed; the rest of the image remains unchanged.

If four values are specified, they define the x,y offsets and x,y dimensions of a rectangular window identifying the area to process. Xoffset, Yoffset define the upper-left starting pixel coordinates of the window. Xsize is the number of pixels that define the window width. Ysize is the number of lines that define the window height.

If no value is specified, the entire channel is processed.

Regardless of the mask area defined, the entire image is decorrelated. The decorrelation is optimized over the mask area.

EIGENSUP

Specifies the eigenchannels to suppress. Eigenchannels are numbered from 1 to the number of specified input channels.

Eigenchannels are often suppressed to reduce noise (error). Error is typically concentrated in the last or last few eigenchannels.

Eigenchannels are generated internally for the decorrelation process. The first eigenchannel contains the most variance, the second the next most variance, and the last the least.

At most, 16 eigenchannels can be suppressed.

Details

Decorrelation stretching is a method of enhancing multispectral image data, typically in an attempt to improve it visually. The basic concept is to force the variance between multispectral image channels to be maximized using a principal component transformation. The resulting imagery is (usually) quite similar to the original imagery, maintaining the average gray level and dynamic range, except that details have been improved, especially in areas which were 'uniform' in color (that is, correlated). Not all images, however, look better after decorrelation.

DECORR performs a decorrelation stretch on a set of input image channels (DBIC) in a PCIDSK image file. The results of the stretch are saved on the output channels (DBOC). Each output channel corresponds to the input channel.

More input channels can be specified than output channels. In these cases, the decorrelation transformation is calculated for all input channels, but only the specified output channels are saved. This is useful, because the extra channels usually contribute some information to the output channels, so the overall information content of the output channels is increased.

The decorrelation can be optimized for a specific region of interest (MASK). This region can be described by either a window (MASK=i,j,k,l) or a bitmap (MASK=i). If the MASK parameter is not specified, the entire image is used. Regardless of the interest region specified, the decorrelation is applied to the entire image.

It is possible to suppress the variance contribution of selected eigenchannels (EIGENSUP). This capability serves to improve image quality by suppressing noise (or error). When an eigenchannel is suppressed, its variance is suppressed, but its mean is still used. This ensures that the resulting decorrelated image has the same mean(s) as the original. Eigenchannels are a calculated, intermediate step in the decorrelation process. There is one eigenchannel for each input channel, and each one holds a decreasing amount of variance. Typically, the last few eigenchannels hold little variance, most of which is error, and these are the ones that are suppressed.

Examples

Channels 1, 2, and 3 of the file irvine.pix represent Landsat TM true color; however, these channels (in this particular scene) are highly correlated. The user wishes to perform a decorrelation stretch on these channels to enhance the visual appearance when shown on the display. Channels 1 through 5 are used as input, though only decorrelated channels 1, 2, and 3 are saved on output to channels 7, 8, and 9.

from pci.decorr import *

file	=	'irvine.pix'
dbic	=	[3,2,1,4,5]
dboc	=	[7,8,9]	# save results for 3,2,1 only
mask	=	[]	# default, quick sampling of entire image
eigensup	=	[]	# no eigenchannels suppressed

decorr( file, dbic, dboc, mask, eigensup )
        

The output generated is shown in "Output report" in the Algorithm section. Transferring channels 7, 8, 9 to the display (using IVI) and using a linear enhancement, the user notices very poor image quality and a large amount of noise. Examining the report produced, the user notices that most of the variance ( > 99%) is concentrated in the first three eigenchannels. The last two eigenchannels are mostly error, and are scaled so much that they ruin the visual appearance of the image. The user decides to rerun the decorrelation with these last two eigenchannels suppressed.

from pci.decorr import *

file	=	'irvine.pix'
dbic	=	[3,2,1,4,5]
dboc	=	[7,8,9]	# save result for 3,2,1 only
mask	=	[]	# default, quick sampling of entire image
eigensup	=	[4,5]	# suprres eigenchannels 4 and 5

decorr( file, dbic, dboc, mask, eigensup )

Algorithm

A decorrelation stretch attempts to maximize the variance between output channels. The basis for this is Principal Component Analysis, which is discussed in detail in the PCA documentation.

Suppression of eigenchannels (components) is done in step 2. Instead of scaling to match the variance of the first component, DECORR sets the scale factor to 0.

A visual interpretation of the effects of the decorrelation stretch using two channels is demonstrated in their scatterplots before and after decorrelation:

 C |                               C |                        
 h |                               h |             *          
 a |           *                   a |           *            
 n |          **                   n |        *  * *          
 n |        ***                    n |     ** *** *           
 e |        **                     e |      * * *  *           
 l |       ***                     l |     * * **              
   |      **                         |      **                 
 A |     *                         A |     *                    
   +------------------------         +------------------------
             channel B                         channel B

   Fig.1: Before decorrelation       Fig.2: After decorrelation

For further information on decorrelation stretching consult the following paper:

Gillespie, A.R., A.B. Kahle, R.E. Walker, 1986. "Color Enhancement of Highly Correlated Images. I. Decorrelation and HSI Contrast Stretches". Remote Sensing of Environment, Vol.20, p.209-235.

Using many channels

Although DECORR can handle up to 256 channels of data, using more than 32 is not recommended. The internal calculations are done in single precision (32-bit) floating point mathematics. Using a large number of channels tends to result in numerical instability and eventually poor results or program failure.

Output Report

The report below is an example of the report generated by DECORR.

irvine.pix                      [S  14PIC  512P   512L] 14-Aug-90

Input  Channels:   3   2   1   4   5
Output Channels:   7   8   9
Sampling Window:      0      0    512    512
Sampling Bitmap: none used
Sample size    :  32768


Input Channel       Mean       Deviation

     3            29.1240          9.5824
     2            25.4875          5.9492
     1            64.4771         10.0178
     4            39.7752         11.2962
     5            25.9260         11.1319

Covariance matrix for input channels:

              3           2           1           4           5
   +-----------------------------------------------------------
  3|     91.822
  2|     55.315      35.392
  1|     91.265      57.234     100.356
  4|     53.626      35.933      51.623     127.605
  5|     86.124      49.949      76.609      61.284     123.920

Eigenchan Eigenvalue  Deviation  %Variance  Scale Factor (Used)

     1      353.9080    18.8124     73.87%         1.00 ( 1.00)
     2       81.4424     9.0245     17.00%         2.08 ( 2.08)
     3       39.5849     6.2917      8.26%         2.99 ( 2.99)
     4        3.0105     1.7351      0.63%        10.84 (10.84)
     5        1.1499     1.0723      0.24%        17.54 (17.54)

Eigenvectors of covariance matrix (arranged by rows):

  0.48655427  0.29934525  0.48355350  0.41353855  0.51847798
  0.24679996  0.11529773  0.28296703 -0.90557152  0.16020662
  0.18398458  0.19743498  0.49801043  0.08589405 -0.81962007
  0.72211707  0.19005740 -0.63968229 -0.01107403 -0.18195906
 -0.38347274  0.90664017 -0.16999383 -0.03775945  0.02506943

Inverse eigenvector matrix (channels arranged by rows):

  0.48655421  0.24679999  0.18398456  0.72211707 -0.38347280
  0.29934525  0.11529772  0.19743498  0.19005737  0.90664023
  0.48355344  0.28296697  0.49801043 -0.63968223 -0.16999382

References

Gillespie, A.R., A.B. Kahle, R.E. Walker, 1986. "Color Enhancement of Highly Correlated Images. I. Decorrelation and HSI Contrast Stretches". Remote Sensing of Environment, Vol.20, p.209-235.