On basis of field spectroscopic investigations we selected samples
and subsequently areas that could serve as spectral end-members for
the different lithologies. Their TM spectra as we extracted these
from the TM data cube are shown in Fig. 4. It should be noted
that non of these end-members can be considered "pure" in the
sense that it comprises only one single surface material. On the
contrary, we selected those areas that show a representative mix
of different ground materials (e.g. green vegetation, dry
vegetation, soil lithology) that are characteristic for the
particular lithologic unit.
CROSS CORRELOGRAM SPECTRAL MATCHING
(CCSM)
Background
A cross correlogram is constructed by calculating the cross
correlation coefficient between a test spectrum, usually a pixel
spectrum, and a reference spectrum, usually a laboratory
spectrum at different match positions (or lags). By convention,
we move the reference spectrum and refer to a negative match
position when shifting toward shorter wavelengths and to a
positive match position when shifting toward a longer
wavelength. Thus match position -1 means that we are
calculating the cross correlation between the test spectrum and
the reference spectrum in which all channels have been shifted
by one channel position number to the lower end of the
spectrum. The cross correlation, r,, at each match position, m, is
equivalent to the ordinary linear correlation coefficient and is
defined as the product of the covariance and the sum of the
standard deviations as
COV
tr
ue (1)
ss,
where COV,. is the covariance between the overlapped portions of
the test spectrum, f, and reference spectrum, r, and s, and s, are the
corresponding standard deviations. If we denote the test and
reference spectrum as À, and À,, respectively, and define n as the
number of overlapping positions, the cross correlation for match
position m can be calculated as
RAA RNA
Tm 3 (2)
JA (ZA) [n ZA2-(ZA
The significance of the cross correlation coefficient can be assessed
by the following #-test
(3)
which has (n-2) degrees of freedom and tests the null hypothesis
718
stating that the correlation between the two spectra at a specific
match position is zero.
Kaolinite - um em Gm am um um == rm wn un us zs Gm
seas 309 09 89: 59 Alunite ; ;
Buddingtonite
1 —e bz
0.9 > m > °° es "a,
Pd >
os| > 2° »
‘ » ~
0.7% x x »
0.6 M > »
os X X e.
0.4 Pd i »
os| ,* x e
* Skewness X s
o2 Kaolinite = 0 x ?
Bou ‘a Alunite = -1.489 x
= 9 S Buddingtonite = -1.162 =»
E 01 x x
902 ‘a »
03 Sw 3
0.4 w =
* *
-.$ Sa >
-0.6 Wu "^, >»
. . -
97| * *-"- *Buddingtonite ^. an
-.8| > > ->—->Alunite # t
9| € 9-9- 9Kaolinitc LE
He pe de
ol
-10 -9 -8 -7 -6 -S -4 -3 2 -1 0 1 2 3 4 S 6 7 8 9 10
Match position (in spectral channels)
100
m-
20 me
~
^
^
~ -
^ -
- 4 -
^M - 4
* 60 = nt
8 NM oL. speret
Su lc nee Cr M LI UM are cet
Qa TE AA DEM rrr rene TEE
e hos 3 ga ent
3 Mtr saee rn ceo saa easet nt ma naa
3
dj 40
0
P
ao] omm mm kaolinite
An teer alunite
mtm buddingtonite
0
2.1 2.12 2.14 2.16 2.18 2.2 2.22 2.24
Wavelength (in um)
Fig. 5. Cross Correlograms for kaolinite (reference) vs.
kaolinite, buddingtonite and alunite (test).
Sensitivity of the method
In order to test the sensitivity of the cross correlogram as a tool for
spectral matching, we first applied the method to reflectance spectra
from the NASA-JPL laboratory spectral library. Spectra in this
library were measured on a Beckman UV 5240 spectrophotometer
which has a sampling interval of 1 nm in the wavelength range of
0.4 to 0.8um, and a sampling interval of 4 nm in the wavelength
range of 0.8 to 2.5um. Bandwidth ranges from 1 nm at 0.4pm to 40
nm at 25um with a spectral resolution (defined as
bandwidth/wavelength) better than 2 percent at all wavelengths.
As a reference spectrum we have selected kaolinite and compared
it with two other clay minerals; alunite and buddingtonite. Kaolinite
has a strong absorption feature at 1.4pm and a double absorption
feature centered at 2. 161m and 2.2um. Due to the lack of H,O, the
feature at 1.9um is weakly developed or missing. Alunite is
characterized by absorption features at 2.16pm and 2.20pm. due to
OH frequency stretching and a nearly symmetrical shape in the
2.08-2.28um. region. A second broad absorption feature occurs at
2.32um. An absorption feature at 2.02um. and a vibrational
absorption feature due to NH, at 2.11pm. are the main diagnostic
features distinguishing buddingtonite spectrally from other clay
minerals.
The correlogram (not shown here) of kaolinite vs. kaolinite is
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B7. Vienna 1996
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