The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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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.