The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008
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RMS =
-i 1/2
X ( fa ) 2 ln
(5)
where, LiX : reflectance or radiance for pixel Z in
band A.;
f ki : abundance of endmember k for pixel
Z ;
RkX : reflectance or radiance value of endmember
k in band A, ;
Si A, . residual of pixel Z in band A.;
VI : the number of Endmembers in the image,
which is less than the number of bands plus
one;
RMS: root mean square error for pixel Z.
Linear Spectral Mixture Model includes two sequential
processing steps: Endmembers selection and linear spectral
unmixing . The first step is very important and pivotal. Before
solving a spectral mixture model, endmembers with unique
spectral signatures need to be identified(Xin Miao et al,2006).
Image endmembers have an advantage over library endmembers
because they are collected under nearly the same conditions and
it is the most common method to collect endmember
spectra(Plaza et al, 2004). In addition ,the existence of possible
vertical scaling anomalies in ASTER data and SWIR crosstalk
from band 5 and band 9 makes the data difficult to use for
spectral analysis based on direct comparisons with library or
field spectra (Fang Qiu et al,2006;NASA ASTER,2004).
Therefore, image endmembers were used in this research.
Previous literatures(Li,2004; Van der Meer & De Jong,2000)
demonstrated that the spectral correlations between
endmembers could negatively affect the abundance estimates
and to enlarge the separabilities between endmember spectra
was essential for unmixing successfully. Wu (2004) discussed
in his research that significant brightness variation witch could
blur the separation of object spectra existed in the spectra of
endmember, and simultaneously, proposed a normalization
method to remove or reduced the spectra variance while
maintaining the useful information to separate the
endmembers .To magnify the separabilities between the
endmember spectra, normalization approach was applied to
pre-C corrected and post-C corrected ASTER data as follows:
Lb =
(6)
Where, Lb is the original reflectance or radiance for band b in
a pixel; Lb is the normalized reflectance or radiance for band b
in a pixel; n is the total number of bands (9 for ASTER imagery
in this study).
To effectively extract endmembers from relative high
dimensional ASTER data and to reduce subsequent
computational requirement, a minimum noise fraction (MNF)
transform was introduced into to reduce the dimensionality and
to segregate the noise in the original and terrain corrected
ASTER data. The MNF transform is composed of two
consecutive standard principle component transforms(PC)
producing the result data that were not correlated and were
arranged in terms of decreasing information content with
increasing MNF band number (Green et al, 1988; Research
Systems, Inc., 2002). Because the information content in the
higher-order MNF eigenimages from 1 to 7 in both original and
C corrected ASTER imagery was over 95%, consequently,
seven ASTER MNF eigenimages was retained for subsequent
data processing .
Unlike training site during classification of multispectral data,
which takes the mean spectral value of the site as the spectrum
of corresponding class, identifying endmember pixels whose
spectra are extreme is a complex procedure which usually is
equipped with rigorous mathematical algorithms. Especially it is
much more difficulty in relative coarse resolution imagery due
to the existence of a number of mixture pixels. To determine
automatically the pure endmembers, the algorithm namely Pixel
Purity Index(PPI) was applied to the MNF
eigenimages(generated from pre-C corrected and post-C
corrected ASTER) respectively chosen from above procedure.
By repeatedly projecting n-dimensional scatter plots of the
MNF images onto a random unit vector, two PPI images were
formed in which the digital number of each pixel corresponded
to the total number of times that the pixel was judged as
spectrally pure in all projections. Typically, the brighter the
pixel in the PPI image the higher the relative purity because it
was more frequently recorded as being a spectrally extreme
pixel(Boardman, 1993; Boardman et al., 1995). To reduce the
number of pixels to be analyzed for endmember determination
and to facilitate the separation of purer materials from mixed
pixels(Fang Qiu et al,2006), a iteration number of 10000 and a
threshold factor of 2.5 is adopted to the MNF images to select
the most pure PPI pixels.
To further refine the selection of the most spectrally pure
endmembers from the derived two-dimensional PPI image and
more importantly, to label them with specific endmember types,
it is essential to reexamine visually the selected pixels in the
n-dimensional feature space and to assign them manually to
appropriate types(Boardman, 1993; Boardman and Kruse, 1994).
So two or more MNF eigenimages were selected to form a
n-dimensional scatter plot. All the pixels that were previously
selected using the PPI threshold procedure are displayed as
pixel clouds in the n-dimensional spectral space. With
interactive rotation and visualization in the spectral space, the
convex comers of the pixel clouds can be located and
designated as the purest spectral endmembers. In our study any
combination of bands were selected and the mean spectra of
endmember which was represented one type were extracted.
Finally, five major types of endmembers were determined from
pre-C corrected ASTER imagery and labeled with different
types including vegetation, water, impervious area, bare soil and
shadow, similarly four endmembers from post-C corrected
ASTER imagery and named vegetation, water, impervious area,
and bare soil , the spectra of the endmembers extracted from
two ASTER data sets were displayed in Fig.4.
With the endmembers collected previously full constrained least
square LSMM was applied to pre-C corrected and post-C
corrected ASTER data and the vegetation abundance images
labeling F1 and F2 were derived.
