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percent ground cover is the dependent variable. The normalized difference is calculated using a near nadir 
red band and near infrared band (NIR - red) / (NIR + red). This technique can give VEG a crude estimate 
of the percent cover of the target (e.g. 0-35% ground cover). 
Next, VEG generates a list of techniques for extending view angles that can be applied to the input data 
set. The various view angle extension techniques in VEG are described as follows. The technique Min- 
Distance is the simplest technique possible that uses no additional knowledge from VEG’s internal 
knowledge bases. The technique simply assigns to each extended view angle the reflectance value of the 
input view direction that is closest to the extended view angle. The error using technique Min-Distance is 
calculated for comparison with the following more sophisticated techniques that use additional knowledge 
contained in VEG’s internal knowledge bases. Technique 1-View-to-l-View uses any single off-nadir view 
angle to infer a single extended view angle. It uses a simple linear correction to calculate the extended 
reflectance value from the reflectance value of the input off-nadir view angle. The coefficients are derived 
from the restricted data set (as discussed below) using a least squares technique. Technique 2-View-to-l- 
View uses two off-nadir view angles to infer a single extended view angle. It uses a linear correction to cal 
culate the extended reflectance value from the reflectance values of the input off-nadir view angles. The 
coefficients are derived from the restricted data set using a least squares technique. Technique Multiple- 
View-to-l-View uses three or more input view angles to infer any single extended off-nadir view angle. A 
form fitting equation (Walthall 1984) containing three unknown coefficients is fitted to the input data using a 
linear least-squares technique. The resulting equation approximates the entire reflectance distribution for the 
target. In addition, a simple linear correction is applied to the single extended view angle. The coefficients 
are derived from the restricted data set using a least squares technique. Technique Multiple-View-to- 
Multiple-View uses three or more input view angles to infer any single extended off-nadir view angle. The 
same form fitting equation as mentioned above is used to approximate the entire reflectance distribution for 
the target. The knowledge base contains data driven rules that can assert what techniques to use based on 
the occurrence of certain characteristics of the input and the desired view angle extension. VEG then ranks 
the various extension techniques according to their expected accuracy. This knowledge is gained from studies 
in the literature. 
Once the input data and target have been characterized, and one to three extension techniques have been 
chosen to try, these techniques are applied on the appropriate spectral input data to calculate the extented 
directional reflectance(s). VEG uses message passing to execute the appropriate technique on the appropriate 
data object. 
VEG uses the historical database of field data to provide a rigorous estimate of the accuracy of the 
extended directional reflectance(s). VEG first generates a restricted data set to test the generated techniques 
on. The restricted data set consists of all of the reflectance distributions in the knowledge base of directional 
reflectance distributions that match the conditions at hand (e.g. ground cover 0-30%, 52° solar zenith angle, 
and 0.68 pm wavelength). A minimum number of data sets must be found to meet some specified statistical 
requirement. If this requirement is not met after the first search then VEG begins to expand the matching 
criteria. A data set of directional reflectance distributions for a wide range of cover types and sun angles is 
stored in the historical cover type database and is discussed in Section 2.3. 
VEG has now defined a restricted data set that matches as closely as one can (considering the limitations 
of the size and contents of the historical database) the target characteristics, wavelength, sun angle, and any 
other relevant knowledge that we may have about the target conditions. VEG uses a hierarchy of methods to 
interpolate/extrapolate each reflectance distribution to create a data set that matches the exact view directions 
of the input spectral data or subset of input spectral data that would be used for each extension technique. 
The restricted data set also contains the true extended directional reflectance(s) for each reflectance distribu 
tion. VEG then applies the chosen extension techniques to the appropriate restricted data set A statistic 
based on errors (true view angle reflectance minus inferred view angle reflectance) for the restricted data set 
is calculated for each technique yielding an error bound for each technique. The statistic that is used for all 
inferences is calculated as 
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