The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
R 0 = R O - cos# (3) 
Where Rq\s the relative reflectance intensity achieved under in 
cident angled, and R 0 is the reflectance intensity achieved under 
zero incident angle. 
In this experiment we have chosen seven different vegetation 
types: (1) black-brush; (2) fir tree; (3) maple leaves; (4) pinon 
pine; (5) Russian olive; (6) sage brush and (7) walnut leaf. 
For each vegetation type we randomly simulated about 700 
simulative spectral curves affected by incidence angles (using 
equation 3) between 0 and 55 degrees. Eventually, there were 
5,000 of such hyperspectral signatures taken under various inci 
dent angles divided into seven sets. The next stage was to choose 
some training and testing population. Classification was then 
performed once on the simulative spectral data itself and once on 
the data representing the parametric relations between the wave 
let coefficients and the reflectance data. 
The classification process was based on Linear Discrimi 
nate Analysis (LDA); the maximum-likelihood criterion 
was used to assign an inquired signature to its class. We 
used supervised classification, where it is possible to ex 
amine the quality of assigning a signature to its true class. 
The classifier was first trained using a training set of pix 
els with their known corresponding classes. Then, classi 
fication performance was evaluated using a test set, con 
sisting of pixels that were not used for the training process. 
The success of classification assignments of the test set 
were summarized for assessing the classification success 
rates. 
5. RESULTS 
Applying the supervised classification method described above, 
we used 1% of the total 5,000 simulative hyperspectral signa 
tures as training set. In order to avoid a bias in the training or test 
procedure, we repeated 5 times the classification process, where 
the training sets were chosen randomly. The following results 
represent the average rate of classification success: 
The average success rates based on spectral reflectance signature 
were 76%, 77% and 72% respectively. 
The success rates based on relations between reflectance and 
wavelet coefficients were 100% for consistently. 
Table 1 describes the confusion matrix using the spectral reflec 
tance values. The number of pixels in each class is depicted in 
the second line of the table. The total number of misclassified 
pixels was 1345, which corresponds to a 27% error rate (and 
hence 73% success rates). It can be seen that for three groups the 
success rates are 100%. This is due to well separated signatures 
between the vegetation types. 
The training set size was again 1% of the total sample size. The 
results show a 100% of success rate. Using those relations re 
duced the misclassified pixels from 1,345 signatures in reflec 
tance domain to zero. These results indicate that using the pro 
posed relations enabled us to isolate the effect of incident angle 
out of the total acquisition process effects. The significant im 
provement of the success rate, up to 100%, illustrates the strong 
correlation between geometric and radiometric characteristics of 
the signatures. The former is embodied through wavelet coeffi 
cients, while the later through intensity values. 
Table 1 : confusion matrix 
for classification based on spectral reflectance 
Number of pixels 
in each class 
629 
647 
615 
608 
644 
615 
1192 
Misclassified pixels 
7 
6 
5 
4 
3 
2 
1 
559 
0 
0 
0 
559 
0 
0 
633 
1 
203 
0 
0 
0 
123 
0 
412 
80 
2 
0 
0 
0 
0 
0 
644 
0 
0 
3 
389 
0 
0 
0 
219 
0 
257 
132 
4 
194 
194 
0 
421 
0 
0 
0 
0 
5 
0 
0 
647 
0 
0 
0 
0 
0 
6 
0 
629 
0 
0 
0 
0 
0 
0 
7 
Group success rates 
100 
100 
68 
36 
100 
67 
53.1 
Table 2 : confusion matrix for classification based 
on relation between reflectance and wavelet coefficients 
Number of pixels 
in each class 
629 
647 
615 
608 
644 
615 
1192 
Misclassified pixels 
7 
6 
5 
4 
3 
2 
1 
0 
0 
0 
0 
0 
0 
0 
1192 
1 
0 
0 
0 
0 
0 
0 
615 
0 
2 
0 
0 
0 
0 
0 
644 
0 
0 
3 
0 
0 
0 
0 
608 
0 
0 
0 
4 
0 
0 
0 
615 
0 
0 
0 
0 
5 
0 
0 
647 
0 
0 
0 
0 
0 
6 
0 
629 
0 
0 
0 
0 
0 
0 
7 
Group success rates 
100 
100 
100 
100 
100 
100 
100 
Table 2 describes the confusion matrix using the relations be 
tween reflectance and wavelet coefficients. 
Note that the classified entities are all associated with different 
species of vegetation, which are characterized by similar spectral 
reflectance signature. 
6. CONCLUSION 
Remote sensing based on spectral reflectance intensity is sensi 
tive to acquisition process effects. These effects remain although 
some calibration processes are carried out. This is due to limita 
tions in assessing several of the external parameters that affect 
the intensity value in hyper-cubes while being acquired. How 
ever, the shape of these signatures is much less influenced by 
those conditions. Linking both radiometry and shape parameters, 
which are derived from an acquired hyper-cube, leads to a reduc 
tion in dissimilarities that exist in the same materials' signature. 
We introduced that linkage by using the RG ratio, where we 
shown that it is possible to improve classification success rates, 
and hence a 
better understanding of the acquisition conditions that affect the 
hyperspectral reflectance intensity analysis. 
REFERENCES 
A. Grapes, 1995. "An introduction to wavelet". Computational 
Science and Engineering, IEEE Volume 2, Issue 2, Summer 
1995 Page(s):50 -61. 
Bruce L., Koger C.H., Li j., 2002. Dimensionality Reduction of 
Hyperspectral Data Using Discrete Wavelet Transform Feature 
Extraction. IEEE TRANSACTION ON GEOSCIENCE AND 
REMOTE SENSING, VOL. 40, NO 10, OCTOBER 2002.