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2 , £„oi TV/O-DIMENSIONAL TECHNIQUES 
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While maximum spectral information may be gained from the 
ERTS data by utilization of the four MSS bands simultaneously, 
this incurs significant costs, and with diminishing returns, as 
much of the information in the bands is redundant. Use of two 
carefully chosen bands simultaneously will sometimes include 
all of the information relevant to a particular task, and is 
extremely simple in comparison to operations with three or more 
bands. 
If, for example, land use is being mapped, and a good 
separation of vegetational categories is obtained in band 6 or 
band 7 (e.g., several crop categories, forest, and lawn/park 
situations), and a good discrimination of urban uses in band 5, 
a summary map may be made, which has the classes which may con 
fidently be determined from each of the bands separately, as 
well as other categories which can be determined only by knowing 
the response in two or more bands (in this example, suburban 
residential development and meadows or old fields can be dis 
tinguished only by contrasting their responses In two bands, 
such as band 4 and band 7). 
A very direct and powerful way to utilize data from two 
bands simultaneously is to compute their joint frequency dis 
tribution. This is simply the two-dimensional analogue of the 
: IGURE 1 frequency distribution. It may be represented as in Figure 2, 
where the various gray level responses for band 5 appear on the 
vertical axis, and those of band 7 are on the horizontal axis. 
At the intersection of any two responses Is recorded the number 
of cells in the scene being analyzed which has those values. 
It will be noticed that groups oi* clusters of numbers occur, 
with higher values in their centers, and progressively lower 
numbers toward their peripheries, as at A. These are equivalent 
to the peaks and valleys of the frequency distribution histogram, 
but in two dimensions, and may be visualized as hills with inter 
vening flat areas. Each, of course, represents a class of objects 
which respond similarly in both of the bands. Therefore, the 
gray level limits may be taken from the axes, and a picture or 
map produced using the bands simultaneously. 
TRAINING TECHNIQUES 
The most effective technique for land use analysis and 
general natural resource inventory that research has revealed 
is one involving supervised vector analysis of the multispectral 
data in four dimensions. This method describes each cell by 
locating a point corresponding to it in a four-dimensional color- 
space. If the brightness level of the cell In each band can