REVISED RANGE OF PHOTOGRAPHIC DENSITY VALUES 
TONE LATE TONE LATE 
SPRING (1000 SUMMER (1000 
DEGREE-DAYS) DEGREE-DAYS 
CROP TYPE 
MIN. 
MAX. 
MIN. 
MAX, 
Spring Wheat 
.38 
.46 
.12 
.22 
Oats 
.27 
.37 
.23 
.25 
Barley 
.47 
.56 
.26 
.36 
Sod 
.59 
.75 
.37 
.47 
Summer Fallow 
.76 
.86 
.77 
.95 
FIGURE 4. Results of a subjective assignment to tone 
values for 5 crop types in a manner to provide unique 
tone ranges (compare with Figure 3). 
Construction of an Elementary Probabilistic Key : The problem of 
constructing a useful, accurate identification key under the qualification 
that no clear-cut tone distinctions between crops exists as shown by 
Figure 2, logically resolves to the question: what is the probability 
that an unknown field with given tone values is a particular crop? By 
application of probability theory, the raw descriptive data in Figure 1 
can be used as the basis for a probabilistic key to the five crop types. 
The previous hypothetical example is continued in order to demonstrate such 
a key and to illustrate that probabilistic keys retain and use the informa 
tion inherent in photo-derived diagnostic information. 
Basically, the techniques described below convert the densitometric 
values obtained from photographic imagery and pertinent collateral data 
(published crop statistics) into Bayesian probabilities. From these 
probabilities, a probabilistic key is generated. 
In order to use probabilistic techniques, conditional probabilities 
for photo-density values given the crop type must be estimated from sample 
data. In order to do this efficiently, some assumptions about the form of 
the tone distribution for each crop type must be made. Based upon the sample 
of each distribution as shown in Figure 1, it is assumed that photo-density 
values (t) are normally distributed. 
Figure 1 data was used to calculate the sample mean and variance for 
each crop. A plot of the probability density function (PDF) for each crop 
according to the sample values of X and s— was constructed (Figure 5).