590 
class description with the associated discrimination scores for ground cover of 0-30% is shown as follows. 
Class-1 (Ground Cover 0-30%): ((((Second-Max (15 135)) t) 1.0) (((Greater-Than (60 315) (45 315)) nil) 
1.0) (((Greater-Than (60 315) (30 315)) nil) 1.0) (((Second-Min (45 315)) t) 0.8) ((First-Min (60 315)) t) 0.8) 
(((Greater-Than (45 315) (30 315)) nil) 0.8) (((Greater-Than (60 315) (15 315)) nil) 0.6) (((Greater-Than (45 
315) (15 315)) nil) 0.6)) 
Class-2 (Ground Cover 31-100%): (((Second-Max (15 135)) nil) 1.0) (((Greater-Than (60 315) (45 315)) 
t) 1.0) (((Greater-Than (60 315) (30 315)) t) 1.0) (((Second-Min (45 315)) nil) 0.8) (((First-Min (60 315)) nil) 
0.8) (((Greater-Than (45 315) (30 315)) t) 0.8) (((Greater-Than (60 315) (15 315)) t) 0.6) (((Greater-Than 
(45 315) (15 315)) t) 0.6)) 
In Class-1 above, the first three instances show that the second maximum reflectance value always occurs 
at (15 135), the (45 315) reflectance value is always greater than the (60 315) value, and the (30 315) 
reflectance value is always grater than the (60 315) value. Since the discrimination scores are all 1.0 for 
these three instances they are never true for class-2 samples. Essentially all sparse canopies show these 
characteristics-peak reflectance in the solar direction that decreases continually in the direction of the 
extreme forward scatter direction as was discussed previously. In contrast the first three instances in Class-2 
are just the opposite of the first three instances for Class-1. This trivial relationship exists because there is 
only two classes. In general for dense canopies the minimum reflectance occurs near nadir and increases 
with increasing off-nadir view angle for all azimuthal directions as was discussed previously. In contrast, 
intermediate canopies can have a wide variety of reflectance trends as a function of sun angle, leaf geometry, 
type of substrate, and wavelength. 
Run #2 had the same inputs as Run #1 except that three classes were defined of ground cover, (0-30%) 
(31-60%) (61-100%), rather than two for Run #1. The classification score was 1.00 for Run #2. 
The classification score of 0.67 for Run #3 was very poor. Apparently there is little structural informa 
tion that is very discriminating for height, however, there were only two cover types, a deciduous forest and 
a pine forest, that were greater than 10 m. 
Run #4 used only three poorly dispersed view angles. The classification score of 0.65 was relatively 
poor, however, it is surprising that the results are this good considering the tighdy clumped view angles used 
as input. The first four instances for class-1 (0-30% ground cover) were: (((First-Min (0 0)) nil) 0.25) ((First- 
Min (15 0)) t) 0.25) (((Greater-Than (0 0) (15 0)) t) 0.25) (((First-Max (0 0)) t) 0.25) ((First-Max (0 0)) ?) 
0.001)). This example shows that relative directional-reflectance relationships can provide a significant 
amount of information even with extremely poorly placed view angles. In contrast the amount of information 
contained in the absolute reflectance data would be minimal. 
These results demonstrate that important features that characterize classes in a similar manner as would 
an expert using relative directional relationships in symbolic form can be achieved. The program picks out 
those important features or combination of features that discriminate between the classes the best. An other 
advantage of this learning approach is that knowledge is explicitly represented and can be used to capture 
generalizations which can be insightful to the researcher. It also allows increased flexibility to try other 
directional relationships and classes. The approach can be applied to any combination of directional view 
angles no matter what the relative placement of the view angles. 
3.3. View Angle Extension 
Most recently, VEG was extended to infer any unknown directional reflectance(s) of a vegetation target 
given any combination of directional reflectance(s) of the target (Kimes et al. 1994). Directional viewing of 
terrestrial scenes using remote-sensing systems from satellite platforms offers the advantage of increasing the 
temporal coverage of any given scene. The obvious problem with using directional view angles to increase 
temporal coverage, however, is that the sensor response changes with changing view angle. Specifically, in 
some remote sensing missions, it would be useful to extend the reflectance value of a single off-nadir view 
angle to a nadir response. In addition, in some scenarios several off-nadir view angles of a target may be col 
lected and need to be extended to the nadir view. There are many scenarios where it would be desirable to 
extend one or a few view angles to the entire directional reflectance distribution, for example, in the case of 
characterizing the scattering properties of the background for atmospheric modeling studies. 
Section 2.2 of this paper presents a description of the processing in VEG needed to make a view angle 
extension. It also describes the array of individual techniques for view angle extension for various conditions.