into the model, it is most likely that the radio- 
metric calibration data provided by Moniteq are 
too high for all of the bands. Another normaliza 
tion approach should, therefore, be used to 
convert the raw data directly into reflectances 
without using the calibration data. For this 
purpose, different parameters have to be included 
in the correction procedure; namely, the 
reflectance of the water body in the scene plus 
the extinction coefficients derived from the 
atmospheric model. Other options available in the 
ISDA software are relative normalization 
techniques such as flat field normalization, equal 
energy normalization, and the apparent reflectance 
approach (Roberts et al., 1986; Jet Propulsion 
Laboratory, 1985; Iqbal, 1983). For our 
classification purposes for this paper, however, 
it was not necessary to normalize the data. 
Additional problems were encountered applying the 
radiometric calibration values to the data set. 
A substantial increase of the noise level in the 
spectral domain could be detected, especially 
within the first 100 bands (430 - 560 nm). A 
reduction of the noise can be achieved due to the 
utilization of a cubic spline algorithm or the 
averaging of the signal in adjacent bands. The 
second method results in a noise reduction of /2, 
but it allows the possibility that some informa 
tion in the spectral domain is lost, depending 
upon the band characteristics (sampling interval, 
bandwidth) and the data analysis to be performed. 
Averaging of two adjacent bands is not that 
critical for the PMI data because of the narrow 
sampling interval (1.3 nm) and the overlapping of 
the bands (1.3 nm). 
Aircraft Attitude Variations 
Geometric distortions of the PMI data caused by 
aircraft motion (pitch, roll, and yaw) could not 
be compensated for due to the lack of navigation 
data (an inertial platform was not available) and 
the nature of the data acquisition process. As 
mentioned earlier, the PMI sensor works in a rake 
mode providing forty profiles and not a contiguous 
image. Thus, for example, it is not possible to 
shift an image line for a specific number of 
pixels in order to account for the distortion 
caused by the roll parameter. For the purposes of 
this study, a geometrically rectified data set was 
not necessary in order to combine the ground 
information with the PMI data because of the 
obvious location of the agricultural objects in 
the image. 
CLASSIFICATION 
Classification of high-resolution spectral data 
is a challenging task due to the large number of 
bands (up to 288) involved. Analysis methods are 
required that take advantage of the high spectral 
resolution to extract the most information while 
minimizing the computation time. Two possible 
classification methodologies are: (1) full 
spectrum classification; and (2) feature 
selection, followed by classification. An example 
of the first method (Piech and Piech, 1989; Mazer 
et al., 1987) combines techniques for a symbolic 
representation of the spectrum derived for each 
pixel with similarity measures used for 
classification purposes. The second method uses 
techniques and transformations for data reduction 
and extraction of the most useful information 
(Rundquist and Di, 1989). This approach permits 
one to use image classification software already 
implemented in existing image analysis systems. 
A data reduction procedure, band-moment 
(Rundquist and Di, 1989), was applied to 
band PMI data set in order to reduce the 
dimensionality. The formulae for the 
case are: 
Band moments: 
1 N 
M„ = — E [i*> * f(i)] 
i=l 
analysis 
the 268- 
spectral 
discrete 
(1) 
Mean: 
M, 
M„ 
Central band moments: 
1 N 
P* = E [(i-i) p *f(i)] 
i=l 
Skewness : 
Yi = 
P 
3/2 
Kurtosis: 
Y* = 
P* 
Concentrated-band moment : 
1 N 
P~ = -5- E [ (i- I i-i I T*f(i)] 
i=l 
(2) 
(3) 
(4) 
(5) 
(6) 
where p = 0,1,2, ... is the moment order; N is the 
number of bands; i = 1, ... N, is the band number; 
and f(i) is the pixel intensity in DN for band i. 
Since the bands are evenly spaced, one can use 
either band number or the wavelength for this 
calculation. This technique was applied in the 
spectral domain on each pixel resulting in eight 
central band moments as follows: (1) mean, (2) 
ordinary moment (Mo), (3) variance (p 2 ), (4) 3rd 
moment, (5) 4th moment, (6) skewness, (7) 
kurtosis, and (8) band-concentrated moment(p 2ci ). 
The computed real values of these eight moments 
were then transformed linearly into an 8-bit data 
set. In five of the eight bands, the images seem 
to be similar. However, an improvement in the 
information content, especially for the agricul 
tural objects, could be detected when compared 
with original single-band or three-band data 
sets. The images for the moments 4, 6, and 7 are 
different and appear visually to have less infor 
mation content. 
A feature selection procedure, the branch and 
bound algorithm as described by Goodenough et al. 
(1978), was used to determine the globally best 
subset of bands involving the following classes 
(sizes in pixels): wheat (230), barley (155), 
corn (232), potatoes (94), fallow (151), mixed 
grass (239), water (212), and forest (234). The 
results for these training data are shown in Table 
3. The best four-band subset was (1,6,7,8), 
corresponding, respectively, to the following 
moments: mean, skewness, kurtosis, and the band 
concentrated moment. The average pairwise trans 
formed divergence of the selected classes was used 
to select the best subset. For each subset, a 
maximum likelihood classification was carried out, 
resulting in the weighted mean classification 
accuracy and standard error of the mean (s.e.m.) 
given in Table 3. The classification accuracies 
were weighted by the frequencies of occurrence of 
each class. 
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