Optimum Index Factor

Functionality / Algorithm

The Optimum Index Factor (OIF) is a statistic value that can be used to select the optimum combination of three bands in a satellite image with which you want to create a color composite. The optimum combination of bands out of all possible 3-band combinations is the one with the highest amount of 'information' (= highest sum of standard deviations), with the least amount of duplication (lowest correlation among band pairs).

Preparation:

• Create a map list which contains the multi-spectral bands of your satellite image.
• Calculate a variance-covariance matrix or a correlation matrix of this map list.
• Open the Properties dialog box of your map list and click the Additional Info button.

The ranked OIF values are shown with the corresponding band combinations. For more information, refer to How to calculate Optimum Index Factor.

Example:

Consider an input map list containing 7 bands, named tmb1, tmb2, ... tmb7. For each combination of three bands in the map list, OIF values are calculated through a simple formula which uses the standard deviations of the bands and correlation coefficients between band pairs (see algorithm below). The OIF values may read:

OIF Index Highest Ranking

The OIF values suggest that from the 7 bands in the map list, the combination of bands tmb4, tmb5 and tmb6 is the best statistical choice to create a color composite.

Notes:

• By using the three bands with the highest OIF value for a color composite, it is not implied that you will create the 'best' color composite since this greatly depends on the purpose of your work.
• 'Noise' (such as dropouts) in one of the input bands is considered as high variance, hence this band will appear in all high ranking combinations.

Input requirements:

To calculate Optimum Index Factors, a map list is required which contains at least 3 raster maps; the raster maps must all use the Image domain or the same value domain, and they must have the same georeference. Furthermore, it is necessary that a correlation matrix or a variance-covariance matrix has been calculated for the map list; this will provide the standard deviations and correlation coefficients which are required for the OIF calculation.

For more information, refer to How to calculate Optimum Index Factor.

Output OIF values:

After a variance-covariance matrix or a correlation matrix has been calculated for the input map list, you can display the ranked OIF values and corresponding band combinations by clicking the Additional Info button in the Properties dialog box of the input map list.

The OIF values are stored in the object definition file of the map list (.MPL).

Note:

It is not possible to calculate OIF values from the command line.

Algorithm:

1. First the number of possible combinations of three bands within the map list is determined as:

 



 

where:

N

is the total number of bands in the map list.

 

For 3 bands, there is only 1 combination;

for 4 bands, there are 4 combinations;

for 5 bands, there are 10 combinations;

for 6 bands there are 20 combinations; and

for 7 bands, there are 35 combinations.

 

2. Then, for each combination of three bands, the OIF is calculated as:

 



 

where:

	Stdi	standard deviation of band i
	Stdj	standard deviation of band j
	Stdk	standard deviation of band k
	Corrij	correlation coefficient of band i and band j
	Corrik	correlation coefficient of band i and band k
	Corrjk	correlation coefficient of band j and band k

 

3. Finally, the OIF values are ranked.

See also:

How to calculate Optimum Index Factor

Variance-Covariance matrix

Correlation matrix