The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
444 
Signal 
oAWV 
Wavelet 
iV 
a 
- 
b 
Figure 1. Correlation between mother wavelet to a specific 
signal segment (Matlab© documentation). 
The wavelet mathematical description is given by: 
CUr,s) 
X x 0)-v( 
t=o 
t - T 
s 
) 
(1) 
The results show that the relative dissimilarities occurred in the 
spectral reflectance signatures was reduced by a factor of 10 
when using the wavelet first coefficients. In previous work [XX] 
we showed that by using wavelet first coefficients, the total dis 
similarity is approximately five times lower than the one among 
the reflectance intensity signature. We assume that this differ 
ence occurred due to additional factors affecting the spectral re 
flectance signature such as atmospheric behavior, backscattering 
and more. 
Different illumination conditions affect spectral reflectance in 
tensity, but yet maintain the signature's geometric shape. Using 
wavelet transform, this shape is analyzed with relatively low in 
fluence by the intensity component, thus potentially reducing the 
illumination reflectance intensity effects. 
Where: C\|/,x(x,s) the correlation coefficient; x is the translation 
location; s is the scaling factor for the specific iteration; x(t) is a 
signal in time domain with discretized length t and y is the 
wavelet mother function. 
3. METHODOLOGY 
3.1 Incident angle effects reduction 
In this work we first assessed the reduction of the effects from 
differences in illumination angles by using wavelet first level de 
tailed coefficients, extracted from the above described hyper- 
spectral cubes data. In order to evaluate the efficiency of such 
reduction we calculated a normalized difference value between 
two curves representing two differential hyperspectral signatures 
of the same material acquired under different sun incident angles. 
For each band we calculated the differences between the inten 
sity values divided by the difference between maximum and 
minimum values among both curves. The result of this calcula 
tion for each band was named Normalized Band Difference In 
dex (NBDI) and is described as: 
hr. — lr 
NBDI. = —(2) 
hr -lr 
where hr, is the highest signals value in the i th band, /r, is the 
lowest signals value in i th band, hr is the absolute highest value 
among the signal, and lr is the absolute lowest value among the 
signal. 
After calculating NBDI index for each band, we calculated the 
area below the NBDI graph to normalize the total amount of 
difference between two spectral signatures. This process was 
repeated for both spectral reflectance signatures and wavelet first 
coefficients. For the comparison of the dissimilarities we 
examined the area below each NBDI graph: the lower the area is, 
the higher the similarity. Fig. 2 illustrates vegetation spectral 
reflectance signature of one pixel, acquired under two different 
incident angles; a) spectral reflectance intensity; b) wavelet first 
detailed coefficients; c) normalized ratio at each band. The 
simulative incident angles were 0 and 45 degrees. We can 
observe that the dissimilarity in reflectance intensity values is 
greater in comparison to the dissimilarity in wavelet 
coefficients. 
'wave length 
Figure 2. Two types of vegetation curves; a) spectral signature; 
b) wavelet first detailed coefficients; c) the NBDI curves. 
3.2 Relations between wavelet coefficients and reflectance 
Empirical assessment of material classification based on full 
wavelet coefficients had yielded moderate and low accuracies 
very similar to those obtained by classifying based on the spec 
tral reflectance data itself. Thus we propose a new approach of 
using features that are based on ratios between reflectance inten 
sity values and wavelet coefficients. 
4. EXPERIMENTAL SETUP 
The experimental setup included simulative and field data. The 
simulative data represented only illumination angle effects. 
Some vegetation hyperspectral signatures were taken from 
known spectral libraries such as: USGS / JPL libraries. For simu 
lating change in illumination angles we assumed that the library 
signatures were taken with a spectro-radiometer in ideal condi 
tions in order to ensure analogue zero degrees incident angle. 
Radiation beam flux density, which hit an object, is depended 
mainly on incident angle; the lower the incident angle is, the 
higher the flux density. In order to simulate the incident angle ef 
fect we calculated reflectance intensity for each incident angle 0, 
thus simulating the intensity decrease via the cosine angle, which 
can be written as: 
The areas under the NBDI curves shown in Fig. 2 which repre 
sent the relative dissimilarities in both spectral reflectance signa 
tures and wavelet first coefficients, are 310 and 30 respectively.