A technique is outlined that tests the hypothesis Airborne Imaging Spectrometer (AIS) image spectra are produced by mixtures of surface materials. This technique allows separation of AIS images into concentration images of spectral endmembers (e.g., surface materials causing spectral variation). Using a spectral reference library it was possible to uniquely identify these spectral endmembers with respect to the reference library and to calibrate the AIS images

Adams, J. B.

Smith, M. O.

English

NASA Technical Reports Server

INTERPRETATION OF AIS IMAGES OF CUPRITE, NEVADA· USING CONSTRAINTS 
OF SPECTRAL MIXTURES 
N86-11626 Milton O. Smith and John B. Adams 
Department of Geological Sciences 
University of Washington, Seattle, WA. 98195 
ABSTRACT 
A technique is outlined that tests the hypothesis that AIS image 
spectra are produced by mixtures of surface materials. This technique 
allows separation of AIS images into concentration images of spectral 
endmembers (e.g., surface materials causing spectral variation). Using 
a spectral reference library it was possible to uniquely identify these 
spectral endmembers with respect to the reference library and to 
calibrate the AIS images. 
INTRODUCTION 
A primary objective for interpretation of multispectral images is 
to identify the direct physical factors causing spectral variation on 
the ground. We demonstrate in this paper that a spectral mixture model 
makes possible the identification of imag~ spectra, assuming that there 
is a linear relationship between image speFtra and a library of refer-
ence spectra. Modeling spectral mixtures reduces the dimensionality of 
the spectral data and leads tD inferences ~egarding the spatial inter-
relation of spectral classes that have beeh delineated using conven-
tional classification techniques. \ 
Two AIS image scenes from Cuprite, Nevada were analyzed against a 
reference library of laboratory spectra. The first image is from August 
1983 (RUN 10101) and the second July 1984 (RUN 10403). All analyses 
were limited to the wavelength range of 2.1 ~m to 2.4 ~m comprising 32 
spectral channels. The reference library spectra were obtained from 
field samples collected from the Cuprite area. They included a variety 
of altered rhyolites containing opaline silica, kaolinite, and alunite, 
and samples of soils, playa, desert varnish, and green and dry 
vegetation. The laboratory spectra were taken using a Beckman DK2-A 
spectrophotometer. 
An initial objective of our analysis was to determine the spectral 
endmembers and their abundances among the laboratory samples, using the 
method described by Smith et al. (1985). The endmembers are defined as 
those spectra from the reference library that when linearly combined 
(linear mixture model) can form all other spectra. Endmembers must have 
an abundance of 1 and the computed endmember abundances for all other 
spectra must be between 0 and 1. Based on the eigenvalues of spectra in 
the 2.1 to 2.4 pm region there are six potential endmembers among the 
Cuprite samples: opaline silica, desert varnish, alunite, kaolinite, and 
playa, and green vegetation. A plot of the transformed spectra by the 
two primary eigenvectors is depicted in Fig. 1. These plots indicate 
the compositional trends for the reference samples. A major objective 
is to determine to what extent the variation observed in the reference 
spectra is present in the image spectra. 
62 
https://ntrs.nasa.gov/search.jsp?R=19860002159 2020-03-20T16:12:26+00:00Z
.. 
. 
0.02. 
c 
J 0 
• kaolinite ... . , ... 
• ... 
I.. 
• > 
... • 
• I.. 
... 
C,I 
.. 
It varnished rock 
... • 
0 
1/1 
... 
.. 
• c 
... 
• alunite • 
• ~ • ... • u 
c 
... 
.\ • & 
~ vegetation-·. ~7S01l 
c ~oPlline silica 0 C,I .. 
Ul 
-0.03 
-0.06 0.04 
Principal Axis of Spectral Variation 
Fig. 1, The linear transformation of laboratory spectra of field samples 
onto the first two principal axes of variation. Prospective endmember 
spectra are those nearest the outside boundaries. 
COMPARISONS OF NORMALIZED SPECTRA 
For the image spectra we also determine how many endmembers are 
required to predict all other image spectra given the previously stated 
constraints. However, unlike the laboratory spectra, the image spectra 
include variation from the surface orientation, atmospheric absorption, 
etc. Thus, some of the endmember spectra resolved from the image may 
represent factors that are not associated with mixing of the spectra of 
the surface materials. Three unknown spectral endmembers were found for 
the 32 wavelength bands of 2.1 to 2.4 ~m using the calibrated energy 
normalized image of August 1983. Here, normalized spectra are computed 
by dividing each reflectance by the sum of the ref1ectances over the 
wavelength interval of analysis. Mixtures of these image-derived 
endmembers model all image spectra to nearly within the instrumental 
error. Further comparisons need only consider these endmember spectra 
and their uniqueness in causing the observed spectral variation. To 
compare the image spectra with the reference spectra it is necessary to 
calibrate the image data. 
To first order, we select a linear model that maps flux density 
measurements of the surface to reflectance measurements from a 
laboratory spectrophotometer, i.e., 
n 
Gb (DNb + Ab) = i:1 (fn Rnb) (1) 
where Gb is the gain for band ~, Ab the offset for band b, DNb is the image brlghtness value for band b, fn the fraction of endmember n, and Rnb 
the reflectance of endmember n for band b. The Gb's can be different 
for each wavelength band. If the image is correctly calibrated the Gb 
coefficients can be reduced to one by normalizing both image and 
reference spectra by the sum of flux densities or reflectances over the 
63 
32 wavelengths. Using the 32 channels from 2.1 ~m to 2.4 ~m of Cuprite 
(August, 1983 image) an optimal solution of spectral mixtures providing 
correspondence in spectral variation between the image and the 
reference library was determined to include alunite, kaolinite, and 
playa silt. Using normalized spectra we could not differentiate between 
the playa silt, opaline silica, or vegetation in the 2.1 to 2.4 ~m 
range. 
The use of normalized spectra with a simple calibration model does 
support the hypothesis that image spectra are produced by mixtures of 
surface materials. The disadvantages of this approach are that if the 
attenuations are poorly corre'cted due to instrument-cal ibration errors 
and/or atmospheric uncertainties, then solutions based on the spectral 
library may be wrong. Also, much of the spectral variation is lost from 
normalizing the spectra by whatever method, and thus may result in more 
than a single physical explanation (i.e., reduce the uniqueness) of the 
source of spectral variation. Optimally, it is desired to have a 
technique that validates the atmospheric corrections and instrumental 
calibration assumptions as well as providing a unique solution to the 
source of spectral variation. 
ABSOLUTE SPECTRAL COMPARISONS CALIBRATED TO TWO OR MORE REFERENCE AREAS 
Given laboratory measurements of representative samples, the gains 
and offsets expressed in Equation 1 could be calculated directly by 
hypothesizing analogous image and laboratory spectra. This requires 
that pixels exist in the image that encompass spectrally pure and homo-
geneous areas on the ground (training areas) and that such spectra also 
exist in the reference library. To determine the gains in Equation 1, 
we perform a linear search of the reference library solving for the 
attenuations (Gb) for each spectrum. For a given mixture mode~ of n 
spectral endmemoers in an image, the validity of the attenuations is 
determined from the compositional abundances and rms errors and should 
ideally appear as in Table 1. Note that at this point we introduce 
illumination intensity (shade) as a spectral endmember (Adams et al., 
1985). ---
Table 1. The optimal pattern of reference and library endmember 
abundances if the calculated attenuations (Gb) are valid. 
Abundance of 
Reference 
Spectra 
Abundances of Image Endmember: 
111umlnatlon 
Spectrum A Spectrum B Intensity rms error 
-------------------------------------------------------------------------Sampl e A 
Sampl e B 
Sampl e C . . . 
1.0 
0.0 
0-1 
0.0 
1.0 
0-1 
0-1 
0-1 
0-1 
o 
o 
o 
-------------------------------------------------------------------------
For the July, 1984 uncalibrated AIS image two training areas 
were selected representing a fan containing varnished rhyolites 
(varnished spectrum) and "kaolinite hill" (kaolinite spectrum). 
Searching the spectral reference library for the optimum calibration,as 
defined above, resulted in a single solution (Table 2) that matches the 
above matrix pattern. The search through the reference library included 
64 
" 
I .. 
I ... 
I·" ':: 
140 reference spectra of minerals and vegetation in addition to the 
spectra of samples collected from Cuprite. Abundances that are less 
than zero and greater than one indicate spectral variation that is 
greater than that of the sample for which the attenuation coefficients 
were computed. The model could be changed to incorporate the reference 
spectrum endmember having the greatest degree of variance, which would 
result in all posit·ive fractions with values between zero and one, 
similar to the ideal pattern of Table 1. 
Table 2. An Optimal mixture model fit of the Cuprite, Nevada (July, 1984) 
uncalibrated AIS image. This model provided the best fit for the major 
source of spectral variation in the image. 
Abundance of 
Reference 
Spectra 
Abundance ~ Ima~l Spectra: 
lumlnatlon 
Varnished Kaolinite Intensity rms error 
--------------------------------------~-----------------------------------Varnished Rhyolite #1 
Kaol i nite #2 
Ka 0 1 i n it e # 1 
Varnished Rhyolite #3 
V~rnished Rhyolite #2 
1.0 
0.0 
0.0 
1.6 
1.1 
0.0 
0.6 
0.9 
-0.4 
0.2 
0.0 
0.4 
0.1 
-0.2 
-0.3 
0.00 
0.01 
0.02 
0.01 
0.02 
------~-------------------------~-----------------------------------------
Unlike the example using normalized spectra, the above procedure 
provides a means of calibrating an image absolutely with respect to 
illumination intensity, and thus resolves the effects due to both ~ur­
face orientation and self-shading of surface materials. The illumina-
tion intensity is a spectral endmember analogous to the endmembers of 
the surface materials. An image of the illumination intensity provides 
qualitative evidence of the validity of the model by depicting topo-
graphical features. From this calibration, it was possible to determine 
that the albedo of the most likely spectral reference endmember was 
associated with the playa silt. The opaline silica and vegetation 
spectra that were simflar to the playa when normalized are distinct and 
separable when spectral variation due to illumination intensity was 
removed and comparisons made on non-normalized spectra. 
Vertical striping occurred in the endmember abundance images, and 
is a result of assuming that all vertical lines had equal attenuation 
coefficients (Gb). This is true to a first approximation, but for 
extraction of t~e minor absorption features characteristic of minerals 
such as alunite and·kaolinite these differences in gain must be exact. 
The presence of the vertical striping indicates the calibration proposed 
by Equation 1 is not valid in the case of the AIS images, where each 
vertical line can have a different gain and offset as well as each 
wavelength band. 
ABSOLUTE SPECTRAL COMPARISONS CALIBRATED TO MIXTURES OF ENDMEMBERS 
Reference (training) areas of spectrally pure materials do not 
always exist on the pixel scale in an image. More typically all pixels 
contain spectral mixtures. A more generalized approach requires only 
that the mixture space in the spectral library exist in the image. For 
65 
the simple case of two mixture components in an image the following 
equations are applicable: 
Gs Gb DNeib = f 1a Relb + ( I - f 1a ) Re2b 
Gb DNe2 = fib Relb + ( I - fIb) Re2b 
(2) 
(3) 
Gb is the gain for band b, Gs a gain due to differential illumination 
of the image endmembers, DNeib and DNe2b are the 16-bit image brightness 
values for two spectral endmembers el and e2 in the raw data AIS image, 
f 1a and fIb are the fractions of reference spectra that mix to form the image spectra, and Re2 and ReI are the library reflectances of two 
reference spectra at 5and b. Our objective is to identify those combi-
nations of spectra in the reference library that provide a solution to 
the fractions in Equations 2 and 3 and to determine how unique the 
solution is with respect to the reference library. The example is based 
on two spectra for simplicity; however,multiple spectra were actually 
used. By algebraic manipu'lation of Equations 2 and 3, one can solve for 
the mineral abundances (f ia and fIb) independent of the gains Gb. Since the fractions should be constant at each wavelength for a given mixture 
of materials, the 32 wavelength bands from the AIS image allow a least 
squares fit (or coefficient of variation) to be determined for each 
fraction from any combination of two library reference spectra. By 
searching the spectral 1 ibrary using all combinations of two spectra in 
the reference library we can rank solutions by their fit to all 32 
bands. For the Cuprite images this search procedure also led to the 
spectra of kaolinite and varnished rhyolite. 
It is also possible to use Equations 2 and 3 to test the assumption 
that the calibration gains and offsets are spatially equal as well as to 
compute them. In the previous example we found that this assumption was 
not valid. Spatial gains and offsets can be calculated by identifying 
the spectral endmembers in each line independently. For an image with 
two spectral endmembers Equations 2 and 3 can then be applied to solve 
for the gains Gb between each line rather than between the image and the 
reference library. It is not necessary that all endmembers be repre-
sented in the image spectra from line to line, but at least two of the 
endmembers must be present. 
CONCLUSIONS 
We have demonstrated an approach using spectral mixture models and 
a spectral reference library that identifies the origin of spectral 
variation in AIS images. To make use of the spectral library it was 
necessary to separate the effects of spectral variation in the image 
that were not due to surface materials, e.g., illumination intensity, 
atmospheric attenuation, and instrument calibration. The Cuprite image 
was modeled successfully as spectral playa silt, kaolinite, alunite, and 
shade. These materials form spectral endmembers in the 2.1 to 2.4um 
range, whereas other samples are spectral endmembers in other wavelength 
regions (e.g., green vegetation in the 0.4 to 1.1 um range). 
The alignment of image and reference library spectral endmembers 
provides evidence that linear spectral mixtures are applicabl~ to or-
ganizing the high spectral-spatial resolution of AIS images. The 
inverted approach to calibration presented here does not rely on ' 
66 
'. 
statistical a~sum~tions or local parameter uncertainties in removing 
eff'ects due to atmosphe,~ic attenuation and instrumental calibration, and 
so provides an independent test on the applied calibrations. 
REFERENCES 
Adams, J. B., M. D. Smith, and P. E. Johnson, Viking Lander 1: A new map 
of rock and soil types, Abst. Proc. Lunar Planet. Sci. Conf. 16th. 
Smith, M. D., P. E. Johnson, and J. B. Adams, Quantitative determination of 
mineral ty~es and abundances from reflectance spectra using principal 
components' analysis, Prot. Lunar Planet. Sci. Conf. 15th, C797-C8D4, 
1985. 
67 
,e. 


Interpretation of AIS Images of Cuprite, Nevada Using Constraints of Spectral Mixtures

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