USGS MIPS Stats Documentation

USGS MIPS Stats Documentation

This program computes multivariate statistics using two to seven images . The images should be from a multispectral data set or in some way geometrically registered. The statistics generated include:

Averages
Standard deviations
Variances
Correlation coefficients
Covariances
Optimum Index Factor (OIF)

Also, it produces the equations required for principal component analysis.

Files

This program requires as input two to seven unsigned 8-bit image files. The statistical information about the images will be output to the print file . In addition, if an output file is given, the eigenvectors required for principal component analysis will be stored in that file.

Parameters

LINC and SINC: These parameters are used to sub-sample the images when collecting the statistics. Sub-sampling can be used to reduce the amount of time required for this program to execute without seriously affecting the statistics. The default is 1 for both the parameters.
MIN and MAX: These parameters are used to eliminate DNs in the images that could adversely effect the outcome of the statistics. For example, an image containing a large border of zeroes would reduce the average of the image. By setting MIN to one the zereos would not be included when computing the statistics. The default values are 1 and 254 respectively.
OIF: This parameter is used to select the size of the subset when computing the Optimum Index Factor (OIF) table. The default value for OIF is 0 which will not produce an OIF table. More information about the OIF can be found under Uses or Special Issue of Applied Photographic Engineering, 1982, 8(1): pp. 23-30 by Chavez, P.S., Jr., Berlin, G.L., and Sowers, L.B.

Uses

This program has several uses. First, the multivariate statistics (covariance and correlation coefficients) can be used to evalute the similarity and/or disimilarity between the images. This program is also a precursor to principal component analysis. That is, this program must be executed and produce the output eigenvector file prior to executing the program Pca. If only one of the principal component images is desired, then the coefficients from the corresponding principal component equation in the print file can be used as input to the program WTCMBO.

Finally, the OIF can be used to determine which combination of a given subset of images will contain the most information with the least amount of duplication. This can be useful when selecting the images for a color composite. For example, given six input images and a value of three for the OIF parameter, this program will produce an OIF table using combinations of three images from the six images. Thus, the OIF will be calculated for 20 subsets, each subset containing a combination of three images. The subsets with the largest OIF values should contain the most information with the least amount of duplication.

Examples

From left to right, Landsat TM bands 1 and 2.

[Example Image]

From left to right, Landsat TM bands 3 and 4.

[Example Image]

From left to right, Landsat TM bands 5 and 7.

[Example Image]

Below is the statistical information produced by STATS using the above images.

                               Standard               Percent
File Specification   Average   Deviation   Variance   Variance
------------------   -------   ---------   --------   --------
sfpeaks_tm1           92.693     15.080      227.42     10.82
sfpeaks_tm2           42.672      8.958       80.24      3.82
sfpeaks_tm3           51.104     14.555      211.85     10.08
sfpeaks_tm4           64.192     15.850      251.23     11.95
sfpeaks_tm5           95.294     31.851     1014.48     48.25
sfpeaks_tm7           49.247     17.816      317.40     15.10


Correlation Coefficient Matrix:

            File 1   File 2   File 3   File 4   File 5   File 6   
            ------   ------   ------   ------   ------   ------   
  File 1:   1.0000  
  File 2:   0.9757   1.0000  
  File 3:   0.9616   0.9904   1.0000  
  File 4:   0.2159   0.3883   0.3804   1.0000  
  File 5:   0.6635   0.7792   0.8046   0.7181   1.0000  
  File 6:   0.7943   0.8744   0.9047   0.5473   0.9510   1.0000  


Covariance Matrix:

               File 1       File 2       File 3       File 4       File 5       File 6     
               ------       ------       ------       ------       ------       ------     
  File 1:     227.415   
  File 2:     131.800       80.239   
  File 3:     211.064      129.122      211.851   
  File 4:      51.603       55.127       87.761      251.228   
  File 5:     318.682      222.308      373.015      362.548     1014.479   
  File 6:     213.394      139.547      234.598      154.543      539.633      317.404   


Principal Component Equations:

  PC1 =  0.2786*FILE1 +  0.1863*FILE2 +  0.3090*FILE3 +  0.2547*FILE4 +  0.7457*FILE5 +  0.4138*FILE6
  PC2 =  0.5507*FILE1 +  0.2388*FILE2 +  0.3790*FILE3 + -0.6355*FILE4 + -0.2758*FILE5 +  0.1271*FILE6
  PC3 =  0.3923*FILE1 +  0.2424*FILE2 +  0.2508*FILE3 +  0.7008*FILE4 + -0.4010*FILE5 + -0.2693*FILE6
  PC4 = -0.2980*FILE1 + -0.0398*FILE2 +  0.1556*FILE3 +  0.1767*FILE4 + -0.4511*FILE5 +  0.8066*FILE6
  PC5 = -0.5559*FILE1 +  0.0946*FILE2 +  0.7640*FILE3 + -0.0758*FILE4 +  0.0590*FILE5 + -0.2985*FILE6
  PC6 = -0.2595*FILE1 +  0.9160*FILE2 + -0.3002*FILE3 + -0.0561*FILE4 +  0.0007*FILE5 +  0.0198*FILE6

                             Standard               Percent
Component Number   Average   Deviation   Variance   Variance   Offset
----------------   -------   ---------   --------   --------   ------
pc1                129.355     42.034     1766.84     84.03      -28
pc2                146.782     16.122      259.91     12.36      127
pc3                180.039      7.985       63.76      3.03      127
pc4                113.711      3.001        9.00      0.43      127
pc5                104.607      1.646        2.71      0.13      127
pc6                124.131      0.624        0.39      0.02      127


  OIF         File         OIF     Sum of    Sum of
Ranking    Combination    Value    Sd Dev     |CC| 
-------    -----------    -----    ------    ------
   1           145        39.30    62.781     1.598
   2           345        32.71    62.256     1.903
   3           146        31.30    48.746     1.557
   4           245        30.05    56.659     1.886
   5           456        29.56    65.517     2.216
   6           134        29.20    45.486     1.558
   7           156        26.88    64.747     2.409
   8           346        26.32    48.221     1.832
   9           135        25.31    61.486     2.430
  10           124        25.25    39.888     1.580
  11           356        24.14    64.222     2.660
  12           246        23.55    42.624     1.810
  13           125        23.11    55.889     2.418
  14           256        22.51    58.624     2.605
  15           234        22.38    39.363     1.759
  16           235        21.51    55.364     2.574
  17           136        17.84    47.451     2.661
  18           126        15.83    41.854     2.644
  19           236        14.92    41.329     2.769
  20           123        13.18    38.593     2.928