Best band combination should make use of the characteristic of hyerspectral data. Hyper spectral data has many channels. Every channel has a very narrow band width, 10 nanometer for AVIRIS as an example. For any given ground feature, when plotted as intensity versus wavelength a meaningful spectral curve can be drawn through the sufficient number of points. This means when target ground feature determined , its spectral curve is also determined. The best band combination is chosen according to the shape of the spectral curve and the relationship among them. The basis rules we set are:

1. The best band combination should be composed of channels with the greatest divergence degree.
   
   In a chosen channel, the intensity of target ground feature should be separated from each other as even as possible. Suppose N ground feature have been selected as target feature. I_max and I_min are, respectively, the maximum and the minimum intensity of these N feature in a channel. Let K=(I_max -I_min) /2N. If the intensity difference between two features is greater than K, these two ground feature are then considered as divergent to each other in this channel. It is easy to each other in this channel. It is easy to infer that the greatest possible divergent pairs for N ground feature is (N-1)+…….+3+2+1. We define the divergence degree as the ratio of actual divergent pairs to the greatest possible divergent pairs. Calculation according to the above definition, we could get target ground feature divergence degree in every channel. The best band combination should be composed of channels with great divergence degree, for example, channels with divergence degree equal or greater than 0.9.
   
   
2. As far as the target feature are concerned, the correlation degree among 3 selected channels should be smallest.
   
   Hyperspectraldata data has a very high spectral resolution. If the target ground feature divergence degree in channel m is great, the divergence degree in channel in its neighbor channels (channel m-1and channel m+1) will generally also great. Obviously the combination of these 3 channels will produce a nearly black& white image. We should not choose these 3 channels as RGB combination band. They are too much similar. In another word , they are too much correlative. So, in addition to divergence degree condition as stated above, the best band combination between the selected channels.
   
   Suppose the intensity of N target ground features in channel m and channel n area x₁, x₂, ... ... , x_N and y₁, y₂, ... ... , y_N respectively. According to mathematical correlation theory, we have
   
   
   r_xy is correlation coefficient , while
   
   
   The correlation coefficient between every 2 channels could be calculated with the formula. Since the best band combination is composed of 3 channels ( 1, m,n) should be chosen is a minimum. That is to say, r_lm+r_ln+r_nm is a minimum.

Example
Here we use an AVIRIS hyper spectral data to show how the above method works.

Selected channels with greater divergence degree as candidate channels for the next input. In this test we set divergence degree ³0.9. Among all of 224 channels, 79 channels agree with the condition. We then calculate the correlation coefficient between every 2 channels among these 79 channels For every possible 3 channels combination,

The data is line 512 by pixel 664 by 224. Flight number: 940719B. Run 9. Acquired time: July 19,94. Area: Cascade, Washington, USA. Scene center latitude: N48:31:56, longitude: W121:23:54.

First step is to choose target ground features. This could be done as follows. Read the test data into ENVIsystem. Display the image using 3 channels at random, better one in green waveband, one in red waveband and one in infrared waveband. Point the concerned ground features with mouse and record the value associated with it.